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1
Sandmann, Gleb. "Stochastic volatility : estimation and empirical validity." Thesis, London School of Economics and Political Science (University of London), 1997. http://etheses.lse.ac.uk/1456/.
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Estimation of stochastic volatility (SV) models is a formidable task because the presence of the latent variable makes the likelihood function difficult to construct. The model can be transformed to a linear state space with non-Gaussian disturbances. Durbin and Koopman (1997) have shown that the likelihood function of the general non-Gaussian state space model can be approximated arbitrarily accurately by decomposing it into a Gaussian part (constructed by the Kalman filter) and a remainder function (whose expectation is evaluated by simulation). This general methodology is specialised to the estimation of SV models. A finite sample simulation experiment illustrates that the resulting Monte Carlo likelihood estimator achieves full efficiency with minimal computational effort. Accurate values of the likelihood function allow inference within the model to be performed by means of likelihood ratio tests. This enables tests for the presence of a unit root in the volatility process to be constructed which are shown to be more powerful than the conventional unit root tests. The second part of the thesis consists of two empirical applications of the SV model. First, the informational content of implied volatility is examined. It is shown that the in- sample evolution of DEM/USD exchange rate volatility can be accurately captured by implied volatility of options. However, better forecasts of ex post volatility can be constructed from the basic SV model. This suggests that options implied volatility may not be market's best forecast of the future asset volatility, as is often assumed. Second, the regulatory claim of a destabilising effect of futures market trading on stock market volatility is critically assessed. It is shown how volume-volatility relationships can be accurately modelled in the SV framework. The variables which approximate the activity in the FT100 index futures market are found to have no influence on the volatility of the underlying stock market index.
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Gu, Ying. "Essays on volatility models using EMM estimation /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/7426.
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Lu, Shan. "Essays on volatility forecasting and density estimation." Thesis, University of Aberdeen, 2019. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=240161.
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This thesis studies two subareas within the forecasting literature: volatility forecasting and risk-neutral density estimation and asks the question of how accurate volatility forecasts and risk-neutral density estimates can be made based on the given information. Two sources of information are employed to make those forecasts: historical information contained in time series of asset prices, and forward-looking information embedded in prices of traded options. Chapter 2 tests the comparative performance of two volatility scaling laws - the square-root-of-time (√T) and an empirical law, TH, characterized by the Hurst exponent (H) - where volatility is measured by sample standard deviation of returns, for forecasting the volatility term structure of crude oil price changes and ten foreign currency changes. We find that the empirical law is overall superior for crude oil, whereas the selection of a superior model is currency-specific and relative performance substantially differs across currencies. Our results are particularly important for regulatory risk management using Value-at-Risk and suggest the use of empirical law for volatility and quantile scaling. Chapter 3 studies the predictive ability of corridor implied volatility (CIV) measure. By adding CIV measures to the modified GARCH specifications, we show that narrow and mid-range CIVs outperform the wide CIVs, market volatility index and the BlackScholes implied volatility for horizons up to 21 days under various market conditions. Results of simulated trading reinforce our statistical findings. Chapter 4 compares six estimation methods for extracting risk-neutral densities (RND) from option prices. By using a pseudo-price based simulation, we find that the positive convolution approximation method provides the best performance, while mixture of two lognormals is the worst; In addition, we show that both price and volatility jumps are important components for option pricing. Our results have practical applications for policymakers as RNDs are important indicators to gauge market sentiment and expectations.
4
Marchese, Malvina. "Whittle estimation of multivariate exponential volatility models." Thesis, London School of Economics and Political Science (University of London), 2015. http://etheses.lse.ac.uk/3173/.
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The aim of this thesis is to offer some insights into two topics of some interest for time-series econometric research. The first chapter derives the rates of convergence and the asymptotic normality of the pooled OLS estimators for linear regression panel models with mixed stationary and non-stationary regressors. This work is prompted by the consideration that many economic models of interest present a mixture of I(1) and I(0) regressors, for example models for analysis of demand system or for assessment of the relationship between growth and inequality. We present results for a model where the regressors and the regressand are cointegrated. We find that the OLS estimator is asymptotically normal with convergence rates T p n and p nT for respectively the non-stationary and the stationary regressors. Phillips and Moon (1990) show that in a cointegrated regression model with non-stationary regressors, the OLS estimator converges at a rate of T p n. We find that the presence of one stationary regressor in the model does not increases the rate of convergence. All the results are derived for sequential limits, with T going to infinity followed by n; and under quite restrictive regularity conditions. Chapters 3-5 focus on parametric multivariate exponential volatility models. It has long been recognized that the volatility of stock returns responds differently to good news and bad news. In particular, while negative shocks tend to increase future volatility, positive ones of the same size will increase it by less or even decrease it. This was in fact one of the chief motivations that led Nelson (1991) to introduce the univariate EGARCH model. More recently empirical studies have found that the asymmetry is a robust feature of multivariate stock returns series as well, and several multivariate volatility models have been developed to capture it. Another important property that characterizes the dynamic evolution of volatilities is that squared returns have significant autocorrelations that decay to zero at a slow rate, consistent with the notion of long memory, where the auto-covariances are not absolutely summable. Univariate long-memory volatility models have received a great deal of attention. However, the generalization to a multivariate long-memory volatility model has not been attempted in the literature. Chapter 3 offers a detailed literature review on multivariate volatility models. Chapter 4 and 5 introduce a new multivariate exponential volatility (MEV) model which captures long-range dependence in the volatilities, while retaining the martingale difference assumption and short-memory dependence in mean. Moreover the model captures cross-assets spillover effects, leverage and asymmetry. The strong consistency and the asymptotic normality of the Whittle estimator of the parameters in the Multivariate Exponential Volatility model is established under a variety of parameterization. The results cover both the case of exponentially and hyperbolically decaying coefficients, allowing for different degrees of persistence of shocks to the conditional variances. It is shown that the rate of convergence and the asymptotic normality of the Whittle estimates do not depend on the degree of persistence implied by the parameterization as the Whittle function automatically compensates for the possible lack of square integrability of the model spectral density.
5
Zhang, Yuzhao. "Essays on return predictability and volatility estimation." Diss., Restricted to subscribing institutions, 2008. http://proquest.umi.com/pqdweb?did=1666139151&sid=3&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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Luo, Ling. "High Quantile Estimation for some Stochastic Volatility Models." Thèse, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/20295.
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In this thesis we consider estimation of the tail index for heavy tailed stochastic volatility models with long memory. We prove a central limit theorem for a Hill estimator. In particular, it is shown that neither the rate of convergence nor the asymptotic variance is affected by long memory. The theoretical findings are verified by simulation studies.
7
Hawkes, Richard Nathanael. "Linear state models for volatility estimation and prediction." Thesis, Brunel University, 2007. http://bura.brunel.ac.uk/handle/2438/7138.
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This thesis concerns the calibration and estimation of linear state models for forecasting stock return volatility. In the first two chapters I present aspects of financial modelling theory and practice that are of particular relevance to the theme of this present work. In addition to this I review the literature concerning these aspects with a particular emphasis on the area of dynamic volatility models. These chapters set the scene and lay the foundations for subsequent empirical work and are a contribution in themselves. The structure of the models employed in the application chapters 4,5 and 6 is the state-space structure, or alternatively the models are known as unobserved components models. In the literature these models have been applied in the estimation of volatility, both for high frequency and low frequency data. As opposed to what has been carried out in the literature I propose the use of these models with Gaussian components. I suggest the implementation of these for high frequency data for short and medium term forecasting. I then demonstrate the calibration of these models and compare medium term forecasting performance for different forecasting methods and model variations as well as that of GARCH and constant volatility models. I then introduce implied volatility measurements leading to two-state models and verify whether this derivative-based information improves forecasting performance. In chapter 6I compare different unobserved components models' specification and forecasting performance. The appendices contain the extensive workings of the parameter estimates' standard error calculations.
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Wang, Jian. "Real time estimation of multivariate stochastic volatility models." Thesis, University of Sheffield, 2017. http://etheses.whiterose.ac.uk/16786/.
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This thesis firstly considers a modelling framework for multivariate volatility in financial time series. As most financial returns exhibit heavy tails and skewness, we are considering a model for the returns based on the skew-t distribution, while the volatility is assumed to follow a Wishart autoregressive process. We define a new type of Wishart autoregressive process and highlight some of its properties and some of its advantages. Particle filter based inference for this model is discussed and a novel approach of estimating static parameters is provided. Furthermore, an alternative methodology for estimating higher dimension data is developed. Secondly, inspired from the idea of Ulig's Wishart process, a new Wishart-Newton model is developed. The approach combines conjugate Bayesian inference while the hyper parameters are estimated by a Newton-Raphson method and here an online volatility estimate algorithm is proposed. The two proposed models are compared with the benchmarking GO-GARCH model in both function execution time and cumulative returns of different dimensional datasets.
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Eratalay, Mustafa Hakan. "Three essays on multivariate volatility modelling and estimation." Doctoral thesis, Universidad de Alicante, 2012. http://hdl.handle.net/10045/26482.
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White, Scott Ian. "Stochastic volatility: Maximum likelihood estimation and specification testing." Thesis, Queensland University of Technology, 2006. https://eprints.qut.edu.au/16220/1/Scott_White_Thesis.pdf.
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Stochastic volatility (SV) models provide a means of tracking and forecasting the variance of financial asset returns. While SV models have a number of theoretical advantages over competing variance modelling procedures they are notoriously difficult to estimate. The distinguishing feature of the SV estimation literature is that those algorithms that provide accurate parameter estimates are conceptually demanding and require a significant amount of computational resources to implement. Furthermore, although a significant number of distinct SV specifications exist, little attention has been paid to how one would choose the appropriate specification for a given data series. Motivated by these facts, a likelihood based joint estimation and specification testing procedure for SV models is introduced that significantly overcomes the operational issues surrounding existing estimators.
The estimation and specification testing procedures in this thesis are made possible by the introduction of a discrete nonlinear filtering (DNF) algorithm. This procedure uses the nonlinear filtering set of equations to provide maximum likelihood estimates for the general class of nonlinear latent variable problems which includes the SV model class. The DNF algorithm provides a fast and accurate implementation of the nonlinear filtering equations by treating the continuously valued state-variable as if it were a discrete Markov variable with a large number of states. When the DNF procedure is applied to the standard SV model, very accurate parameter estimates are obtained. Since the accuracy of the DNF is comparable to other procedures, its advantages are seen as ease and speed of implementation and the provision of online filtering (prediction) of variance. Additionally, the DNF procedure is very flexible and can be used for any dynamic latent variable problem with closed form likelihood and transition functions. Likelihood based specification testing for non-nested SV specifications is undertaken by formulating and estimating an encompassing model that nests two competing SV models. Likelihood ratio statistics are then used to make judgements regarding the optimal SV specification. The proposed framework is applied to SV models that incorporate either extreme returns or asymmetries.
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White, Scott Ian. "Stochastic volatility : maximum likelihood estimation and specification testing." Queensland University of Technology, 2006. http://eprints.qut.edu.au/16220/.
Full textAbstract:
Stochastic volatility (SV) models provide a means of tracking and forecasting the variance of financial asset returns. While SV models have a number of theoretical advantages over competing variance modelling procedures they are notoriously difficult to estimate. The distinguishing feature of the SV estimation literature is that those algorithms that provide accurate parameter estimates are conceptually demanding and require a significant amount of computational resources to implement. Furthermore, although a significant number of distinct SV specifications exist, little attention has been paid to how one would choose the appropriate specification for a given data series. Motivated by these facts, a likelihood based joint estimation and specification testing procedure for SV models is introduced that significantly overcomes the operational issues surrounding existing estimators. The estimation and specification testing procedures in this thesis are made possible by the introduction of a discrete nonlinear filtering (DNF) algorithm. This procedure uses the nonlinear filtering set of equations to provide maximum likelihood estimates for the general class of nonlinear latent variable problems which includes the SV model class. The DNF algorithm provides a fast and accurate implementation of the nonlinear filtering equations by treating the continuously valued state-variable as if it were a discrete Markov variable with a large number of states. When the DNF procedure is applied to the standard SV model, very accurate parameter estimates are obtained. Since the accuracy of the DNF is comparable to other procedures, its advantages are seen as ease and speed of implementation and the provision of online filtering (prediction) of variance. Additionally, the DNF procedure is very flexible and can be used for any dynamic latent variable problem with closed form likelihood and transition functions. Likelihood based specification testing for non-nested SV specifications is undertaken by formulating and estimating an encompassing model that nests two competing SV models. Likelihood ratio statistics are then used to make judgements regarding the optimal SV specification. The proposed framework is applied to SV models that incorporate either extreme returns or asymmetries.
12
Podolskij, Mark. "New theory on estimation of integrated volatility with applications /." Bochum, 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980588391.
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Sun, Yucheng. "Essays in volatility estimation based on high frequency data." Doctoral thesis, Universitat Pompeu Fabra, 2017. http://hdl.handle.net/10803/402831.
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Based on high-frequency price data, this thesis focuses on estimating the realized covariance and the integrated volatility of asset prices, and applying volatility estimation to price jump detection. The first chapter uses the LASSO procedure to regularize some estimators of high dimensional realized covariance matrices. We establish theoretical properties of the regularized estimators that show its estimation precision and the probability that they correctly reveal the network structure of the assets. The second chapter proposes a novel estimator of the integrated volatility which is the quadratic variation of the continuous part in the price process. This estimator is obtained by truncating the two-scales realized variance estimator. We show its consistency in the presence of market microstructure noise and finite or infinite activity jumps in the price process. The third chapter employs this estimator to design a test to explore the existence of price jumps with noisy price data.Basándonos en datos de precios de alta frecuencia, esta tesis se centra en la estimación de la covarianza realizada y la volatilidad integrada de precios de activos, y la aplicación de la estimación de la volatilidad para la detección de saltos en los precios. El primer capítulo utiliza el procedimiento LASSO para regularizar algunos estimadores de matrices de covarianza realizada de alta dimensión. Establecemos propiedades teóricas de los estimadores regularizados que muestran su precisión de estimación y la probabilidad de que revelen correctamente la estructura de red de los activos. En el segundo capítulo se propone un nuevo estimador de la volatilidad integrada que es la variación cuadrática de la parte continua en el proceso de precios. Este estimador se obtiene truncando el estimador de varianza realizado en dos escalas. Demostramos su consistencia en presencia de ruido de microestructura del mercado y saltos de actividad finitos o infinitos en el proceso de precios. El tercer capítulo emplea este estimador para diseñar un test para explorar la existencia de saltos en los precios con ruido.
14
Burnos, Sergey, and ChaSing Ngow. "SVI estimation of the implied volatility by Kalman filter." Thesis, Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-13949.
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To understand and model the dynamics of the implied volatility smile is essential for trading, pricing and risk management portfolio. We suggest a linear Kalman filter for updating of the Stochastic Volatility Inspired (SVI) model of the volatility. From a risk management perspective we generate the 1-day ahead forecast of profit and loss (P\&L) of option portfolios. We compare the estimation of the implied volatility using the SVI model with the cubic polynomial model. We find that the SVI Kalman filter has outperformed the others.
15
Veraart, Almut Elisabeth Dorothea. "Volatility estimation and inference in the presence of jumps." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.670107.
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Barkhagen, Mathias. "Risk-Neutral and Physical Estimation of Equity Market Volatility." Licentiate thesis, Linköpings universitet, Produktionsekonomi, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-94360.
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The overall purpose of the PhD project is to develop a framework for making optimal decisions on the equity derivatives markets. Making optimal decisions refers e.g. to how to optimally hedge an options portfolio or how to make optimal investments on the equity derivatives markets. The framework for making optimal decisions will be based on stochastic programming (SP) models, which means that it is necessary to generate high-quality scenarios of market prices at some future date as input to the models. This leads to a situation where the traditional methods, described in the literature, for modeling market prices do not provide scenarios of sufficiently high quality as input to the SP model. Thus, the main focus of this thesis is to develop methods that improve the estimation of option implied surfaces from a cross-section of observed option prices compared to the traditional methods described in the literature. The estimation is complicated by the fact that observed option prices contain a lot of noise and possibly also arbitrage. This means that in order to be able to estimate option implied surfaces which are free of arbitrage and of high quality, the noise in the input data has to be adequately handled by the estimation method. The first two papers of this thesis develop a non-parametric optimization based framework for the estimation of high-quality arbitrage-free option implied surfaces. The first paper covers the estimation of the risk-neutral density (RND) surface and the second paper the local volatility surface. Both methods provide smooth and realistic surfaces for market data. Estimation of the RND is a convex optimization problem, but the result is sensitive to the parameter choice. When the local volatility is estimated the parameter choice is much easier but the optimization problem is non-convex, even though the algorithm does not seem to get stuck in local optima. The SP models used to make optimal decisions on the equity derivatives markets also need generated scenarios for the underlying stock prices or index levels as input. The third paper of this thesis deals with the estimation and evaluation of existing equity market models. The third paper gives preliminary results which show that, out of the compared models, a GARCH(1,1) model with Poisson jumps provides a better fit compared to more complex models with stochastic volatility for the Swedish OMXS30 index.Det övergripande syftet med doktorandprojektet är att utveckla ett ramverk för att fatta optimala beslut på aktiederivatmarknaderna. Att fatta optimala beslut syftar till exempel på hur man optimalt ska hedga en optionsportfölj, eller hur man ska göra optimala investeringar på aktiederivatmarknaderna. Ramverket för att fatta optimala beslut kommer att baseras på stokastisk programmerings-modeller (SP-modeller), vilket betyder att det är nödvändigt att generera högkvalitativa scenarier för marknadspriser för en framtida tidpunkt som indata till SP-modellen. Detta leder till en situation där de traditionella metoderna, som finns beskrivna i litteraturen, för att modellera marknadspriser inte ger scenarier av tillräckligt hög kvalitet för att fungera som indata till SP-modellen. Följaktligen är huvudfokus för denna avhandling att utveckla metoder som, jämfört med de traditionella metoderna som finns beskrivna i litteraturen, förbättrar estimeringen av ytor som impliceras av en given mängd observerade optionspriser. Estimeringen kompliceras av att observerade optionspriser innehåller mycket brus och möjligen också arbitrage. Det betyder att för att kunna estimera optionsimplicerade ytor som är arbitragefria och av hög kvalitet, så behöver estimeringsmetoden hantera bruset i indata på ett adekvat sätt. De första två artiklarna i avhandlingen utvecklar ett icke-parametriskt optimeringsbaserat ramverk för estimering av högkvalitativa och arbitragefria options-implicerade ytor. Den första artikeln behandlar estimeringen av den risk-neutrala täthetsytan (RND-ytan) och den andra artikeln estimeringen av den lokala volatilitetsytan. Båda metoderna ger upphov till jämna och realistiska ytor för marknadsdata. Estimeringen av RND-ytan är ett konvext optimeringsproblem men resultatet är känsligt för valet av parametrar. När den lokala volatilitetsytan estimeras är parametervalet mycket enklare men optimeringsproblemet är icke-konvext, även om algoritmen inte verkar fastna i lokala optima. SP-modellerna som används för att fatta optimala beslut på aktiederivatmarknaderna behöver också indata i form av genererade scenarier för de underliggande aktiepriserna eller indexnivåerna. Den tredje artikeln i avhandlingen behandlar estimering och evaluering av existerande modeller för aktiemarknaden. Den tredje artikeln tillhandahåller preliminära resultat som visar att, av de jämförda modellerna, ger en GARCH(1,1)-modell med Poissonhopp en bättre beskrivning av dynamiken för det svenska aktieindexet OMXS30 jämfört med mer komplicerade modeller som innehåller stokastisk volatilitet.
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Zeytun, Serkan. "Stochastic Volatility, A New Approach For Vasicek Model With Stochastic Volatility." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/3/12606561/index.pdf.
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In the original Vasicek model interest rates are calculated
assuming that volatility remains constant over the period of
analysis. In this study, we constructed a stochastic volatility
model for interest rates. In our model we assumed not only that interest rate process but also the volatility process for interest rates follows the mean-reverting Vasicek model. We derived the density function for the stochastic element of the interest rate process and reduced this density function to a series form. The parameters of our model were estimated by using the method of moments. Finally, we tested the performance of our model using the data of interest rates in Turkey.
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Yang, Xiaoran. "Essays on volatility estimation and forecasting of crude oil futures." Thesis, University of Essex, 2017. http://repository.essex.ac.uk/19692/.
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Avramidis, Panagiotis. "Estimation of the volatility function : non-parametric and semiparametric approaches." Thesis, London School of Economics and Political Science (University of London), 2004. http://etheses.lse.ac.uk/1793/.
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We investigate two problems in modelling time series data that exhibit conditional heteroscedasticity. The first part deals with the local maximum likelihood estimation of volatility functions which are in the form of conditional variance functions. The existing estimation procedures yield plausible results. Yet, they often fail to take into account special features of the data at the cost of reduced accuracy of prediction. More precisely, many of the parametric and nonparametric conditional variance models ignore the fact that the error distribution departs significantly from gaussian distribution. We propose a novel nonparametric estimation procedure that replaces popular local least squares method with local maximum likelihood estimation. Intuitively, using information from the error distribution improves the estimators and therefore increases the accuracy in prediction. This conclusion is proved theoretically and illustrated by numerical examples. In addition, we show that the proposed estimator adapts asymptotically to the error distribution as well as to the mean regression function. Applications with real data examples demonstrate the potential use of the adaptive maximum likelihood estimator in financial risk management. The second part deals with the variable selection for a particular class of semipara-metric models known as the partial linear models. The existing selection methods are computationally demanding. The proposed selection procedure is computationally more efficient. In particular, if P and Q are the number of linear and nonparametric candidate regressors, respectively, then the proposed procedure reduces the order of the number of variable subsets to be investigated from 2 Q+P to 2Q + 2 P. At the same time, it maintains all the good properties of existing methods, such as consistency. The latter is proven theoretically and confirmed numerically by simulated examples. The results are presented for the mean regression function while the generalization to the conditional variance function is discussed separately.
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Mattiussi, Vanessa. "Non parametric estimation of high-frequency volatility and correlation dynamics." Thesis, City University London, 2010. http://openaccess.city.ac.uk/12095/.
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This thesis addresses the problem of quantitatively evaluating the temporal dynamics that characterized financial time series. In particular, we perform an accurate analysis of the Fourier estimator, a newly proposed nonparametric methodology to measure ex-post volatility and cross-volatilities as functions of time, when financial assets are observed at different highfrequency levels over the day. The estimator has the peculiar feature to employ the observed data in their original form, therefore exploiting all the available information in the sample. We first show how to considerably improve the numerical performance of the Fourier method making possible the analysis of large sets of data, as it is usually the case with high-frequency series. Secondly, we use Monte Carlo simulation methods to study the behavior of three driving parameters in the estimation procedure, when the effects of both irregular sampling and microstructure noise are taken into account. The estimator is showed to be particularly sensitive to one of these quantities, which is in turn used to control the contribution of the above effects. Integrated financial correlation is also analyzed within two distinct comparative studies that involve other multivariate measures. The analysis is then extended to consider the entire evolution of the underlying correlation process. Finally, we propose a new class of nonparametric spot volatility estimators, which is showed to include the Fourier method as a particular case. The full limit theory under infill asymptotics in the pure diffusive settings of the class is derived. Empirical evidence in support of our conclusions is also provided.
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Manikas, Theodoros. "Robust volatility estimation for multiscale diffusions with zero quadratic variation." Thesis, University of Warwick, 2018. http://wrap.warwick.ac.uk/111074/.
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This thesis is concerned with the problem of volatility estimation in the context of multiscale diffusions. In particular, we consider data that exhibit two widely separated time scales. Fast/slow systems of SDEs that adopt a homogenized SDE are employed to model such data. The problem that one is confronted with, is the mismatch between the multiscale data and the homogenized SDE. In this context, we examine whether if by using the multiscale data, the diffusion coefficient of the homogenized SDE can be estimated. Our proposed estimator consists on subsampling the initial data by considering only the local extremals to overcome the issue associated with the underlying model. We provide both theoretical and numerical heuristics, suggesting that our proposed estimator when it is applied to multiscale data of bounded variation is asymptotically unbiased for the volatility coefficient of the homogenized SDE. Furthermore, for the particular example of a multiscale Ornstein-Uhlenbeck process, the numerical results indicate that the L2-error of our estimator is very small. Moreover, we illustrate situations where the proposed estimator can also be used for multiscale data with bounded non-zero quadratic variation.
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Li, Yifan. "Point process based high frequency volatility estimation : theory and applications." Thesis, Lancaster University, 2018. http://eprints.lancs.ac.uk/127786/.
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This thesis is a compilation of three main studies with the common theme: point process based high-frequency volatility estimation. The first chapter introduces a new class of high-frequency volatility estimators and examines its asymptotic properties. The second chapter studies the relative importance of market microstructure (MMS) variables on high-frequency volatility estimation. The third chapter proposes a Markov-switching model for high-frequency volatility estimation and provides intraday measures of information contents in the trading process using the proposed model. In the first chapter, we propose a novel class of volatility estimators named the Renewal Based Volatility (RBV) estimator, and derive its asymptotic properties. This class of estimators is motivated by the work of Engle and Russell (1998), Gerhard and Hautsch (2002), Andersen, Dobrev, and Schaumburg (2008), Tse and Yang (2012), Nolte, Taylor, and Zhao (2018), which use price durations to construct highfrequency volatility estimators. We show that our RBV estimator nests the volatility estimator using price duration, thus providing a theoretical framework to analyse its asymptotic properties. Our theoretical results support the simulation and empirical findings in Tse and Yang (2012) and Nolte, Taylor, and Zhao (2018) that: (1) both the non-parametric duration (NPD) based and the parametric duration (PD) based volatility estimators are more efficient than the Realized Volatility (RV) estimator; (2) a parametric design can greatly improve the efficiency of volatility estimation; (3) the PD estimator can provide accurate intraday volatility estimates. We provide simulation evidence for the performance of the NPD estimator and propose an exponentially smoothed version that can outperform noise-robust RV-type estimators under general market microstructure noise and jumps. In the second chapter, we augment the PD estimator by including MMS variables in the parametric model. Specifically, we use a lognormal version of the Autoregressive Conditional Duration (ACD) model by Engle and Russell (1998), and include trading volume, bid-ask spread, total quote depth, quote depth difference, number of trades, order imbalance and order flow in the ACD model. Moreover, we use a best subset regression (BSR) approach to rank and select the included MMS variables. Our empirical study based on high-frequency trade and quote data from 29 highly liquid securities and a market index ETF shows that, by benchmarking on a Realized Kernel measure, the inclusion of MMS covariates significantly improves the performance of volatility estimates on both daily and intraday levels. The BSR approach is very effective in selecting the most relevant MMS covariates for volatility estimation, and it suggests that contemporaneous number of trades and order flow are the most important variables for intraday volatility estimation. More importantly, intraday volatility estimates can be constructed from the ACD model even in the case when the RV-type estimators cannot be reliably constructed due to a lack of data. In the third chapter, we extend the Autoregressive Conditional Intensity (ACI) model (Russell, 1999) with a Markov-switching (MS) structure. We propose to use the Stochastic Approximation Expectation Maximization (SAEM) (Celeux and Diebolt, 1992) to estimate the MS-ACI model, and provide simulation evidence supporting the validity of the estimation procedure. We apply our MS-ACI model to high-frequency trade and quote data from 9 highly liquid securities and a market index ETF. Our empirical findings suggest that the MS-ACI model captures two distinct volume-volatility regimes in the high-frequency data: a dominant regime that spreads evenly throughout the trading day with strong correlation between cumulative trading volume and price duration, and a minor regime that concentrates at the beginning and end of a trading day with much weaker correlation between cumulative trading volume and price duration. We link this phenomenon to the firm-specific information arrival process into the market, and provide a measure of intraday information content of the transaction process.
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Ruivo, Sandra Cristina Rosa. "Volatility forecasts and value-at-risk estimation using TGARCH model." Master's thesis, Instituto Superior de Economia e Gestão, 2007. http://hdl.handle.net/10400.5/675.
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Mestrado em FinançasValue-at-Risk (VaR) has emerged in recent years as a standard tool to measure and control the risk, mainly the market risk, of financial portfolios. It measures the worst loss to be expected of a portfolio over a given time horizon at a given level of confidence. The calculation of Value-at-Risk commonly, involves estimation of the volatility return price and quantile of standardized returns. In this paper, two parametric techniques were used to estimate the volatility of the returns (market prices) of a Portuguese Financial Institution portfolio. Although to achieve the quantiles of standardized returns, both parametric technique and one nonparametric technique were considered. The quality of the measuring result was analysed through the backtesting technique for the forecasting multiperiod. In this study it is revealed that AR(1)-TGARCH methodology produces the most accurate VaR forecast, for one day holding period. The volatility forecasts for the two other holding periods, considering the three methodologies, revealed to be biased.
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Awasthi, Achal. "Parameter Estimation in Stochastic Volatility Models Via Approximate Bayesian Computing." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1534335592622713.
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Broll, Udo, Soumyatanu Mukherjee, and Rudra Sensarma. "Exchange Rate Volatility and Exports: Estimation of Firms Risk Preferences." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-223571.
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In this companion paper to Broll and Mukherjee (2017), we empirically analyse how exchange rate volatilities affect firms optimal production and exporting decisions. The firms elasticity of risk aversion determines the direction of the impact of exchange rate risk on exports. Based on a flexible utility function that incorporates all possible risk preferences, a unique structurally estimable equation is used to estimate the risk aversion elasticities for a panel of Indian service sector (non-financial) firms over 2004-2015, using the quantile regression method.
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Fang, Yue. "Volatility modeling and estimation of high-frequency data with Gaussian noise." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/11041.
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Kalnina, Ilze. "Essays on estimation and inference for volatility with high frequency data." Thesis, London School of Economics and Political Science (University of London), 2009. http://etheses.lse.ac.uk/3005/.
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Volatility is a measure of risk, and as such it is crucial for finance. But volatility is not observable, which is why estimation and inference for it are important. Large high frequency data sets have the potential to increase the precision of volatility estimates. However, this data is also known to be contaminated by market microstructure frictions, such as bid-ask spread, which pose a challenge to estimation of volatility. The first chapter, joint with Oliver Linton, proposes an econometric model that captures the effects of market microstructure on a latent price process. In particular, this model allows for correlation between the measurement error and the return process and allows the measurement error process to have diurnal heteroskedasticity. A modification of the TSRV estimator of quadratic variation is proposed and asymptotic distribution derived. Financial econometrics continues to make progress in developing more robust and efficient estimators of volatility. But for some estimators, the asymptotic variance is hard to derive or may take a complicated form and be difficult to estimate. To tackle these problems, the second chapter develops an automated method of inference that does not rely on the exact form of the asymptotic variance. The need for a new approach is motivated by the failure of traditional bootstrap and subsampling variance estimators with high frequency data, which is explained in the paper. The main contribution is to propose a novel way of conducting inference for an important general class of estimators that includes many estimators of integrated volatility. A subsampling scheme is introduced that consistently estimates the asymptotic variance for an estimator, thereby facilitating inference and the construction of valid confidence intervals. The third chapter shows how the multivariate version of the subsampling method of Chapter 2 can be used to study the question of time variability in equity betas.
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De, Marco Stefano. "On probability distributions of diffusions and financial models with non-globally smooth coefficients." Phd thesis, Université Paris-Est, 2010. http://tel.archives-ouvertes.fr/tel-00588686.
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Some recent works in the field of mathematical finance have brought new light on the importance of studying the regularity and the tail asymptotics of distributions for certain classes of diffusions with non-globally smooth coefficients. In this Ph.D. dissertation we deal with some issues in this framework. In a first part, we study the existence, smoothness and space asymptotics of densities for the solutions of stochastic differential equations assuming only local conditions on the coefficients of the equation. Our analysis is based on Malliavin calculus tools and on " tube estimates " for Ito processes, namely estimates for the probability that the trajectory of an Ito process remains close to a deterministic curve. We obtain significant estimates of densities and distribution functions in general classes of option pricing models, including generalisations of CIR and CEV processes and Local-Stochastic Volatility models. In the latter case, the estimates we derive have an impact on the moment explosion of the underlying price and, consequently, on the large-strike behaviour of the implied volatility. Parametric implied volatility modeling, in its turn, makes the object of the second part. In particular, we focus on J. Gatheral's SVI model, first proposing an effective quasi-explicit calibration procedure and displaying its performances on market data. Then, we analyse the capability of SVI to generate efficient approximations of symmetric smiles, building an explicit time-dependent parameterization. We provide and test the numerical application to the Heston model (without and with displacement), for which we generate semi-closed expressions of the smile
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Antonakakis, Nikolaos, and Julia Darby. "Forecasting volatility in developing countries' nominal exchange returns." Routledge, 2013. http://dx.doi.org/10.1080/09603107.2013.844323.
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This article identifies the best models for forecasting the volatility of daily exchange returns of developing countries. An emerging consensus in the recent literature focusing on industrialized countries has noted the superior performance of the Fractionally Integrated Generalized Autoregressive Conditionally Heteroscedastic (FIGARCH) model in the case of industrialized countries, a result that is reaffirmed here. However, we show that when dealing with developing countries' data the IGARCH model results in substantial gains in terms of the in-sample results and out-of-sample forecasting performance. (authors' abstract)
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Reno', Roberto. "Volatility estimate via Fourier analysis." Doctoral thesis, Scuola Normale Superiore, 2005. http://hdl.handle.net/11384/85694.
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From the preface: The aim of this Thesis is to study some selected topics on volatility estimation and modeling. Recently, these topics received great attention in the financial literature, since volatility modeling is crucial in practically all financial applications, including derivatives pricing, portfolio selection and risk management. Specifically, we focus on the concept of realized volatility, which became important in the last decade mainly thanks to the increased availability of high-frequency data on practically every financial asset traded in the main marketplaces. The concept of realized volatility traces back to an early idea of Merton (1980), and basically consists in the estimation of the daily variance via the sum of squared intraday returns, see Andersen et al. (2003). The work presented here is linked to this strand of literature but an alternative estimator is adopted. This is based on Fourier analysis of the time series, hence the term Fourier estimator, which has been recently proposed by Malliavin and Mancino (2002). Moreover, we start from this result to introduce a nonparametric estimator of the diffusion coefficient.
The Thesis has two main objectives. After introducing the concept of quadratic variation and the Fourier estimator, we compare the properties of this estimator with realized volatility in a univariate and multivariate setting. This leads us to some applications in which we exploit the fact that we can regard volatility as an observable instead of a latent variable. We pursue this objective in Chapters 3 and 4. The second objective is to prove two Theorems on the estimation of the diffusion coefficient of a stochastic diffusion in a univariate setting, and this is pursued in Chapter 5. [...]
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Kastner, Gregor, and Sylvia Frühwirth-Schnatter. "Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic Volatility Models." WU Vienna University of Economics and Business, 2013. http://epub.wu.ac.at/3771/1/paper.pdf.
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Bayesian inference for stochastic volatility models using MCMC methods highly depends
on actual parameter values in terms of sampling efficiency. While draws from the posterior
utilizing the standard centered parameterization break down when the volatility of volatility parameter
in the latent state equation is small, non-centered versions of the model show deficiencies
for highly persistent latent variable series. The novel approach of ancillarity-sufficiency
interweaving has recently been shown to aid in overcoming these issues for a broad class of
multilevel models. In this paper, we demonstrate how such an interweaving strategy can be
applied to stochastic volatility models in order to greatly improve sampling efficiency for all
parameters and throughout the entire parameter range. Moreover, this method of "combining
best of different worlds" allows for inference for parameter constellations that have previously
been infeasible to estimate without the need to select a particular parameterization beforehand.Series: Research Report Series / Department of Statistics and Mathematics
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Yin, Pei. "Volatility estimation and price prediction using a hidden Markov model with empirical study." Diss., Columbia, Mo. : University of Missouri-Columbia, 2007. http://hdl.handle.net/10355/4795.
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Thesis (Ph. D.)--University of Missouri-Columbia, 2007.The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on December 18, 2007) Vita. Includes bibliographical references.
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Telfah, Ahmad. "Analytical Estimation of Value at Risk Under Thick Tails and Fast Volatility Updating." ScholarWorks@UNO, 2003. http://scholarworks.uno.edu/td/26.
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Despite its recent advent, value at risk (VaR) became the most widely used technique for measuring future expected risk for both financial and non-financial institutions. VaR, the measure of the worst expected loss over a given horizon at a given confidence level, depends crucially on the distributional aspects of trading revenues. Existing VaR models do not capture adequately some empirical aspects of financial data such as the tail thickness, which is vital in VaR calculations. Tail thickness in financial variables results basically from stochastic volatility and event risk (jumps). Those two sources are not totally separated; under event risk, volatility updates faster than under normal market conditions. Generally, tail thickness is associated with hyper volatility updating. Existing VaR literature accounts partially for tail thickness either by including stochastic volatility or by including jump diffusion, but not both. Additionally, this literature does not account for fast updating of volatility associated with tail thickness. This dissertation fills the gap by developing analytical VaR models account for the total (maximum) tail thickness and the associated fast volatility updating. Those aspects are achieved by assuming that trading revenues are evolving according to a mixed non-affine stochastic volatility-jump diffusion process. The mixture of stochastic volatility and jumps diffusion accounts for the maximum tail thickness, whereas the nonaffine structure of stochastic volatility captures the fast volatility updating. The non-affine structure assumes that volatility dynamics are non-linearly related to the square root of current volatility rather than the traditional linear (affine) relationship. VaR estimates are obtained by deriving the conditional characteristic function, and then inverting it numerically via the Fourier Inversion technique to infer the cumulative distribution function. The application of the developed VaR models on a sample that contains six U.S banks during the period 1995-2002 shows that VaR models based on the non-affine stochastic volatility and jump diffusion process produce more reliable VaR estimates compared with the banks' own VaR models. The developed VaR models could significantly predict the losses that those banks incurred during the Russian crisis and the near collapse of the LTCM in 1998 when the banks' VaR models fail.
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Soane, Andrew. "Latent State and Parameter Estimation of Stochastic Volatility/Jump Models via Particle Filtering." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29223.
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Particle filtering in stochastic volatility/jump models has gained significant attention in the last decade, with many distinguished researchers adding their contributions to this new field. Golightly (2009), Carvalho et al. (2010), Johannes et al. (2009) and Aihara et al. (2008) all attempt to extend the work of Pitt and Shephard (1999) and Liu and Chen (1998) to adapt particle filtering to latent state and parameter estimation in stochastic volatility/jump models. This dissertation will review their extensions and compare their accuracy at filtering the Bates stochastic volatility model. Additionally, this dissertation will provide an overview of particle filtering and the various contributions over the last three decades. Finally, recommendations will be made as to how to improve the results of this paper and explore further research opportunities.
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Tunyavetchakit, Sophon [Verfasser], and Rainer [Akademischer Betreuer] Dahlhaus. "Volatility Decomposition and Nonparametric Estimation of Spot Volatility of Models with Poisson Sampling under Market Microstructure Noise / Sophon Tunyavetchakit ; Betreuer: Rainer Dahlhaus." Heidelberg : Universitätsbibliothek Heidelberg, 2016. http://d-nb.info/1180615786/34.
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[Verfasser], Sophon Tunyavetchakit, and Rainer [Akademischer Betreuer] Dahlhaus. "Volatility Decomposition and Nonparametric Estimation of Spot Volatility of Models with Poisson Sampling under Market Microstructure Noise / Sophon Tunyavetchakit ; Betreuer: Rainer Dahlhaus." Heidelberg : Universitätsbibliothek Heidelberg, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:16-heidok-214504.
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Amorino, Chiara. "Bias correction for drift and volatility estimation of jump diffusion processes and non - parametric adaptive estimation of the invariant measure." Thesis, université Paris-Saclay, 2020. https://www.biblio.univ-evry.fr/theses/2020/2020UPASE006.pdf.
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Le sujet de la thèse est l’estimation paramétrique et non-paramétriquedans des modèles de processus à sauts. La thèse est constituée de 3 parties qui regroupent 4 travaux.La première partie, qui est composée de deux chapitres, traite del'estimation des paramètres de dérive et volatilité par des méthodes de contraste depuis des observations discrètes, avec pour objectif principal de minimiser les conditions sur le pas d'observation, afin que celui ci puisse par exemple aller arbitrairement lentement vers 0.La seconde partie de la thèse concerne des développements asymptotiques, et correction de biais, pour l'estimation de la volatilité intégrée.La troisième partie de la thèse, concerne l'estimation adaptative de la mesure stationnaire pour des processus à sautThe thesis deal with the parametric and non-parametric inference in jump process models.It consists of 3 parts which gather 4 chapters.The first part, which contains 2 chapters, focuses on the estimation of the drift and volatility parameters via some contrast function methods starting from a discretely observed process.The main goal is to minimise the conditions on the discretization step so that it can go to $0$ arbitrarily slowly.The second part of the thesis regards some asymptotic developments, and bias correction, for the estimation of the integrated volatility.The third part of the thesis is about the adaptive estimation of the invariant measure for jump processes
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Vives, David Mendez. "Applied financial econometric analysis : the dynamics of swap spreads and the estimation of volatility." Thesis, London School of Economics and Political Science (University of London), 2003. http://etheses.lse.ac.uk/2655/.
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This Thesis contains an examination of the time-series properties of swap spreads, their relation with credit spreads and an estimation of the risk premium embedded in the swap spread curve. Chapter 2 introduces the main institutional aspects of swap markets, and studies the time-series properties of swap spreads. These are shown to be non-stationary and display a time-varying conditional volatility. Chapter 3 provides evidence of cointegration between corporate bond spreads and swap spreads. We estimate an error-correction model, including additional variables such as the level and slope of the yield curve, taking into account the exogenous structural break due to the crisis of August 1998. We find evidence that the relation between swap and credit spreads arises from the swap cash flows being indexed to Libor rates. Chapter 4 studies the risk premium in the term structure of the swap spreads, obtaining evidence that it is time-varying. The slope of the swap spread curve is shown to predict the changes in swap spreads. These results are relevant for the study of the risk premium in credit markets, and extend the existing literature on riskless Treasury securities. Chapter 6 develops the asymptotic properties of the quadratic variation estimator of the volatility of a continuous time diffusion process. We explore the case in which the number of observations tends to infinity, while the time between them remains fixed. For the case of a geometric Brownian motion, we show that the estimator is asymptotically biased, but the bias is a random variable that converges. We study the behaviour of this random variable via a simulation study, that shows that it typically has a "small" effect. We conclude by exploring some practical applications related the specification of the volatility for financial time series.
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Cheng, Xixin, and 程細辛. "Mixture time series models and their applications in volatility estimation and statistical arbitrage trading." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40988053.
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Yevstihnyeyev, Roman. "Estimation of Asset Volatility and Correlation Over Market Microstructure Noise in High-Frequency Data." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:14398547.
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Accurate measurement of asset return volatility and correlation is an important problem in financial econometrics. The presence of market microstructure noise in high-frequency data complicates such estimations. This study extends a prior application of a model-based volatility estimator with autocorrelated market microstructure noise to estimation of correlation. The model is applied to a high-frequency dataset including a stock and an index, and the results are compared to some existing models. This study supports previous findings that including an autocorrelation factor produces an estimator potentially less vulnerable to market microstructure noise, and finds that the same is true about the extended correlation estimator that is introduced here.
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Cheng, Xixin. "Mixture time series models and their applications in volatility estimation and statistical arbitrage trading." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B40988053.
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Kau, Jonas. "Stochastic Volatility Models with Jumps and High Frequency Data : Theory, Estimation, and Option Pricing /." Aarhus : Institut for Økonomi, Aarhus Universitet, 2009. http://mit.econ.au.dk/Library/Specialer/2009/20033896.pdf.
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Popovic, Ray. "Parameter estimation error: a cautionary tale in computational finance." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34731.
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We quantify the effects on contingent claim valuation of using an estimator for the volatility of a geometric Brownian motion (GBM) process. That is, we show what difficulties can arise when failing to account for estimation risk. Our working problem uses a direct estimator of volatility based on the sample standard deviation of increments from the underlying Brownian motion. After substituting into the GBM the direct volatility estimator for the true, but unknown, value of the parameter sigma, we derive the resulting marginal distribution of the approximated GBM. This allows us to derive post-estimation distributions and valuation formulae for an assortment of European contingent claims that are in accord with the basic properties of the underlying risk-neutral process.
Next we extend our work to the contingent claim sensitivities associated with an assortment of European option portfolios that are based on the direct estimator of the volatility of the GBM process. Our approach to the option sensitivities - the Greeks - uses the likelihood function technique. This allows us to obtain computable results for the technically more-complicated formulae associated with our post-estimation process. We discuss an assortment of difficulties that can ensue when failing to account for estimation risk in valuation and hedging formulae.
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Husodo, Za??fri Ananto Banking & Finance Australian School of Business UNSW. "Speed of adjustment, volatility and noise in the Indonesia Stock Exchange." Awarded by:University of New South Wales. Banking & Finance, 2008. http://handle.unsw.edu.au/1959.4/41860.
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This research contains three essays that explore the speed of adjustment, volatility and noise in the Indonesia Stock Exchange. The first essay explores the speed of adjustment in the Indonesia Stock Exchange at daily interval from 2000 to 2004. The model employed is the speed of adjustment with noise. Firstly, I work on the estimation of the speed of adjustment. The estimated speed of adjustment coefficient concludes that the large size leads the smaller size group to adjust to new information. Secondly, I analyse the component in the noise that contributes significantly to the speed of adjustment level. It is confirmed that the factor determining the noise is bid-ask fluctuations. Therefore, it is reasonable to infer the component in the noise from bid-ask component. The decomposition of bid-ask spread into transaction cost and asymmetric information reveals that the latter is found to be a significant component determining the speed of adjustment level. The second essay analyses the fine grain dynamics of the speed of price adjustment to new information from 2000 to 2007. The exact time of adjustment is estimated at intraday frequency instead of at daily frequency. In this work, as an alternative of first moment estimation, second moment model-free estimation using volatility signature plot to estimate of the speed of adjustment is proposed. Both first and second moment estimation of the speed of adjustment provide consistent result of 30 minute adjustment period. Negative relation after 5-minute return interval between speed of adjustment estimate and realized variance is found implying lower noise leads to smaller deviation between observed and equilibrium price. In the third essay, I concentrate the work on the second moment of continuously compounded returns from 2000 to 2007 in the Indonesia Stock Exchange. The main purpose of the last essay is to estimate the noise and efficient variance in the Indonesia Stock Exchange. The realized variance based estimator is employed in the third essay. During the period of the study, noise variance decreases indicating smaller deviation between the observed and equilibrium price, hence improving market quality in the Indonesia Stock Exchange. The optimal frequency to estimate the efficient variance, on average, is nine minutes. The variance ratio of daily efficient variance to daily open-to-close reveals significant private information underlying price process in the Indonesia Stock Exchange.
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Zhou, Dongya. "VALUE-AT-RISK ESTIMATION USING GARCH MODELS FOR THE CHINESE MAINLAND STOCK MARKET." Thesis, Uppsala universitet, Statistiska institutionen, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-412997.
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With the acceleration of economic globalization, the immature Chinese mainland stock market is gradually associated with the stock markets of other countries. This paper predict the return rate of Chinese mainland stock market using several models from GARCH family, test the predictability by calculating Value-at-Risk, also capture the dynamic correlation between other fifive countries or region and mainland China by DCC-GARCH model. The results indicate that E-ARMA-GARCH model fifits the best due to the signifificant heteroscedasticity and leverage effect of Chinese mainland stock market. It has the strongest positive correlation with HongKong while the weakest correlation with the United States.
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Dombeck, Brian. "The Effects of News Shocks and Bounded Rationality on Macroeconomic Volatility." Thesis, University of Oregon, 2017. http://hdl.handle.net/1794/22636.
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This dissertation studies the impact embedding boundedly rational agents in real business cycle-type news-shock models may have on a variety of model predictions, from simulated moments to structural parameter estimates. In particular, I analyze the qualitative and quantitative effects of assuming agents are boundedly rational in a class of DSGE models which attempt to explain the observed volatility and comovements in key aggregate measures of U.S. economic performance as the result of endogenous responses to information in the form of ``news shocks''. The first chapter explores the theoretical feasibility of relaxing the rational expectations hypothesis in a three-sector real business cycle (RBC) model which generates boom-bust cycles as a result of periods of optimism and pessimism on the part of households. The second chapter determines whether agents forming linear forecasts of shadow prices in a nonlinear framework can lead to behavior approximately consistent with fully informed individuals in a one-sector real business cycle model. The third chapter analyzes whether empirical estimates of the relative importance of anticipated shocks may be biased by assuming rational expectations.
By merging the two hitherto separate but complementary strands of literature related to bounded rationality and news shocks I am able to conduct in-depth analysis of the importance of both the information agents have and what they choose to do with it. At its core, the study of news in macroeconomics is a study of the specific role alternative information sets play in generating macroeconomic volatility. Adaptive learning on the other hand is concerned with the behavior of agents given an information set. Taken together, these fields jointly describe the input and the ``black box'' which produce model predictions from DSGE models. While previous research has been conducted on the effects of bounded rationality or news shocks in isolation, this dissertation marks the first set of research explicitly focused on the interaction of these two model features.
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Ishakova, Gulmira. "On the use of Quasi-Maximum Likelihood Estimation and Indirect Method for Stochastic Volatility models." Thesis, Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-1641.
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Stochastic volatility models have been focus for research in recent years.
One interesting and important topic has been the estimation procedure.
For a given stochastic volatility model this project aims to compare two
methods of parameter estimation.
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Gorynin, Ivan. "Bayesian state estimation in partially observable Markov processes." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLL009/document.
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Cette thèse porte sur l'estimation bayésienne d'état dans les séries temporelles modélisées à l'aide des variables latentes hybrides, c'est-à-dire dont la densité admet une composante discrète-finie et une composante continue. Des algorithmes généraux d'estimation des variables d'états dans les modèles de Markov partiellement observés à états hybrides sont proposés et comparés avec les méthodes de Monte-Carlo séquentielles sur un plan théorique et appliqué. Le résultat principal est que ces algorithmes permettent de réduire significativement le coût de calcul par rapport aux méthodes de Monte-Carlo séquentielles classiquesThis thesis addresses the Bayesian estimation of hybrid-valued state variables in time series. The probability density function of a hybrid-valued random variable has a finite-discrete component and a continuous component. Diverse general algorithms for state estimation in partially observable Markov processesare introduced. These algorithms are compared with the sequential Monte-Carlo methods from a theoretical and a practical viewpoint. The main result is that the proposed methods require less processing time compared to the classic Monte-Carlo methods
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TOSCANO, Giacomo. "Non-parametric estimation of stochastic volatility models: spot volatility, leverage and vol-of-vol. Four essays on asymptotic error distributions, finite-sample properties and empirical applications." Doctoral thesis, Scuola Normale Superiore, 2021. http://hdl.handle.net/11384/106264.
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This thesis contains four essays on non-parametric estimators of the spot volatility,
the leverage and the volatility-of-volatility. In particular, the focus of this thesis
is on the study of the asymptotic properties of the estimators, the optimization of
their finite-sample performance and the use of the resulting estimates in empirical
applications.
Specifically, in Chapter 2 we prove a central limit theorem for the estimator
of the integrated leverage based on the Fourier method of Malliavin and Mancino
(2009), showing that it reaches the optimal rate of convergence and a smaller
variance with respect to different estimators based on a pre-estimation of the instantaneous
volatility. Then, we exploit the availability of efficient Fourier-based
estimates of the integrated leverage to show, using S&P500 prices over the period
2006-2018, that adding an extra term which accounts for the leverage effect to the
Heterogeneous Auto-Regressive (HAR) volatility model by Corsi (2009) increases
the explanatory power of the latter.
In Chapter 3 we study the sensitivity of the leverage process to changes of the
price and the volatility. In particular, under the Constant Elasticity of Variance
(CEV) model by Beckers (1980), which is explicitly designed to capture leverage
effects, we find that the derivatives of the leverage with respect to the log-price and
the volatility can be expressed as the ratio of quantities that can be consistently
estimated from sample prices, that is, as the ratio of the price-leverage covariation
and, respectively, the volatility and the leverage. From the financial standpoint,
this suggests that the price-leverage covariation may be interpreted as a gauge of
the responsiveness of the leverage to the arrival of new information that causes
changes in the price or the volatility. Additionally, we also find that the priceleverage
covariation is equal to twice the vol-of-vol under the CEV model, thereby
suggesting that the responsiveness of the leverage (i.e., the price-leverage covariation)
is proportional to the amount of uncertainty about risk (i.e., the vol-of-vol).
After reconstructing the trajectories of the volatility, the leverage, the vol-of-vol
and the price-leverage covariation through the Fourier methodology by Malliavin
and Mancino (2009), we provide empirical evidence supporting this financial interpretation
of the price-leverage covariation in a model-free setting, using 1-second
S&P500 prices over the period March, 2018-April, 2018. In Chapter 4, we perform an analytical study to identify the sources of the
finite-sample bias that typically plagues the simplest and most natural vol-of-vol
estimator, the Pre-estimated Spot-variance based Realized Variance (PSRV) by
Barndorff-Nielsen and Veraart (2009). Based on the full knowledge of its analytical
expression, we show that the finite-sample bias of the PSRV may be substantially
reduced by allowing for the overlap of consecutive local windows to pre-estimate
the spot variance. In particular, we provide a feasible analytical rule for the biasoptimal
selection of the length of local windows when the volatility is a process in
the Chan, Karolyi, Longstaff and Sanders (CKLS) class (see Chan et al. (1992))
and show that selections based on this analytical rule match some selections prescribed
in the literature, based on simulations.
In Chapter 5, we exploit efficient Fourier estimates of the path of the volatility
to empirically investigate the functional link between the latter and the variance
swap rate. Specifically, using S&P500 data over the period 2006-2018, we find
overwhelming empirical evidence supporting the affine link analytically found by
Kallsen et al. (2011) in the context of exponentially affine stochastic volatility models.
Additionally, based on tests performed on yearly subsamples, we find that exponentially
mean-reverting variance models provide a good fit during periods of
extreme volatility, while polynomial models, introduced in Cuchiero (2011), are
suited for years characterized by more frequent price jumps. These empirical results are confirmed when replacing Fourier estimates of the spot volatility with realized local estimates.
Chapter 6 concludes, summarizing the main findings of the thesis.
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CAMPOS, EDUARDO LIMA. "LOCAL SCALE MODEL: AN MULTIPLICATIVE ALTERNATIVE SPECIFICATION TO VOLATILITY ESTIMATION AND FORECASTING FOR FINANCIAL RETIVEN SERIES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1998. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=7771@1.
Full textAbstract:
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOEste trabalho apresenta um modelo de volatilidade estocástica com especificação multiplicativa, chamado modelo de escala local. O modelo trabalha com a precisão (recíproca da variância) de uma série temporal. A precisão é tratada como componente não observável, caracterizando o modelo como estrutural, e é suposta evoluir segundo um filtro Gama, com um ruído multiplicativo que segue distribuição Beta. A função de previsão para a variância é uma média móvel com amortecimento exponencial (EWMA) no quadrado das observações passadas, a mesma função de previsão do modelo IGARCH(1,1). O fator de amortecimento é estimado por máxima verossimilhança. A densidade de medida é Gaussiana, condicional à precisão não observável, e a densidade preditiva resulta t de Student, cujos graus de liberdade são monitorados pelo fator de amortecimento estimado. A densidade de medida Gaussiaan, embora induza excesso de curtose nas distribuições incondicional e preditiva, pode ser inadequada para modelar dados com um grande excesso de curtose, como é o caso de séries financeiras. Por isso, é testada uma densidade de medida mais genérica, a densidade de potência exponencial, que possui a normal como caso particular. O modelo é chamado modelo de escala local generalizado. A introdução de variáveis explicativas é efetuada de maneira trivial. Intervalos de confiança para os parâmetros do modelo são obtidos via Bootstrap paramétrico. Os resultados obtidos são semelhantes àqueles fornecidos pelos modelos GARCH (1,1) e AR(1)-SV, sendo que o modelo de escala local, além da maior facilidade de implementação, fornece soluções exatas, o que não ocorre no AR(1)-SV, e é mais parcimonioso do que o GARCH(1,1).
In this thesis, we investigate, and develop further, a stochastic volatility modelo named local scale model. This model deals the precision, which is the inverse of the variance unobserved component, and so fits within the framework of structural time series models, the precision is assumed to be a Gamma variable, which evolves through a multiplicative equation, scaled by a Beta variable. The measurement density is Gaussian, conditional on the unobserved precision, and the resulting forecast is a Student`s t density, with a scale which is approximately an exponencially weighted moving average (EWMA) of the sqares of the past observations. The degrees of freedom of the Student`s t distribution are controlled by the size of the discount parameter of the EWMA scheme. The Gaussiannity of the measurement density is potentially inadequate when the model is applied to heavy tailed finance data. Instead, this assumption can be replaced by an exponential power density, which allows the modeling of the observed excess kurtosis. The extension of the model to account for explanatory variables is straightforward. Confidence intervals for the parameters are obtained by Bootstrap. The model fits like the GARCH(1,1)mand AR(1)- SV, but the local scale model, besides being easier to fit, provides a more parcimonious alternative to the GARCH (1,1) model, and has an exact filter, rather than a best linear one, like in the AR(1)-SV.