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1
Pitsillis, Zachry Steven. "Estimating dynamic affine term structure models." Master's thesis, University of Cape Town, 2015. http://hdl.handle.net/11427/15731.
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Duffee and Stanton (2012) demonstrated some pointed problems in estimating affine term structure models when the price of risk is dynamic, that is, risk factor dependent. The risk neutral parameters are estimated with precision, while the price of risk parameters are not. For the Gaussian models they investigated, these problems are replicated and are shown to stem from a lack of curvature in the log-likelihood function. This geometric issue for identifying the maximum of an essentially horizontal log-likelihood has statistical meaning. The Fisher information for the price of risk parameters is multiple orders of magnitude smaller than that of the risk neutral parameters. Prompted by the recent results of Christoffersen et al. (2014) a remedy to the lack of curvature is attempted. An unscented Kalman filter is used to estimate models where the observations are portfolios of FRAs, Swaps and Zero Coupon Bond Options. While the unscented Kalman filter performs admirably in identifying the unobserved risk factor processes, there is little improvement in the Fisher information.
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Ziervogel, Graham. "Hedging performance of interest-rate models." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/20482.
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This dissertation is a hedging back-study which assesses the effectiveness of interest- rate modelling and the hedging of interest-rate derivatives. Caps that trade in the Johannesburg swap market are hedged using two short-rate models, namely the Hull and White (1990) one-factor model and the subsequent Hull and White (1994) two-factor extension. This is achieved by using the equivalent Gaussian additive-factor models (G1++ and G2++) outlined by Brigo and Mercurio (2007). The hedges are constructed using different combinations of theoretical zero-coupon bonds. A flexible factor hedging method is proposed by the author and the bucket hedging technique detailed by Driessen, Klaasen and Melenberg (2003) is tested. The results obtained support the claims made by Gupta and Subrahmanyam (2005), Fan, Gupta and Ritchken (2007) and others in the literature that multi-factor models outperform one-factor models in hedging interest-rate derivatives. It is also shown that the choice of hedge instruments can significantly influence hedge performance. Notably, a larger set of hedge instruments and the use of hedge instruments with the same maturity as the derivative improve hedging accuracy. However, no evidence to support the finding of Driessen et al. (2003) that a larger set of hedge instruments can remove the need for a multi-factor model is found.
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Putyatin, Vladislav Evgenievich. "Mathematical models for derivative securities markets." Thesis, University of Southampton, 1998. https://eprints.soton.ac.uk/50648/.
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The classical Black-Scholes analysis determines a unique, continuous, trading strategy which allows one to hedge a financial option perfectly and leads to a unique price for the option. It assumes, however, that there are no transaction costs involved in implementing this strategy, and the stock market is absolutely liquid. In this work some new results are obtained to accommodate costs of hedging, which occur in practice, and market imperfections into the option pricing framework. In Part One transaction charges are dealt with by means of the mean-variance technique, originally developed by Markowitz. This approach is based on the minimisation of the variance of the outcome at expiry subject to spending at most a given initial endowment. Since "perfect" replication is no longer possible in this case, there will always be an unavoidable element of risk associated with writing an option. Therefore, the option price is now not unique. A mean-variance approach makes option pricing relatively easy and meaningful to an investor, who is supposed to choose a point on the mean-deviation locus. In the limit of zero transaction costs, the problem naturally reduces to the Black-Scholes valuation method, unlike alternative approaches based on the utility-maximisation. The stochastic optimisation problem obtained is dealt with by means of the stochastic version of Pontryagin's maximum principle. This technique is believed to be applied to this kind of problem for the first time. In general the resulting free-boundary problem has to be solved numerically, but for a small level of proportional transaction costs an asymptotic solution is possible. Regions of short term and long term dynamics are identified and the intermediate behaviour is obtained by matching these regions. The perturbation analysis of the utility-maximisation approach is also revised in this work, and amendments are obtained. In addition, the maximum principle is applied to the Portfolio Selection problem of Markowitz. The dynamical rebalancing technique developed in this work proves more efficient than the classical static approach, and allows investors to obtain portfolios with lower levels of risk. The model presented in Part Two is an attempt to quantify the concept of liquidity and establish relations between various measures of market performance. Informational inefficiency is argued to be the main reason for the unavailability of an asset at its equilibrium price. A mathematical model to describe the asset price behaviour together with arbitrage considerations enable us to estimate the component of the bid-ask spread arising from the outstanding information. The impact of the market liquidity on hedging an option with another option as well as the underlying asset itself is also examined. Although in the last case uncertainty cannot be completely eliminated from the hedged portfolio, a unique risk-minimising strategy is found.
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蕭德權 and Tak-kuen Siu. "Risk measures in finance and insurance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31242297.
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Cullinan, Cian. "Implementation of Bivariate Unspanned Stochastic Volatility Models." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29266.
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Unspanned stochastic volatility term structure models have gained popularity in the literature. This dissertation focuses on the challenges of implementing the simplest case – bivariate unspanned stochastic volatility models, where there is one state variable controlling the term structure, and one scaling the volatility. Specifically, we consider the Log-Affine Double Quadratic (1,1) model of Backwell (2017). In the class of affine term structure models, state variables are virtually always spanned and can therefore be inferred from bond yields. When fitting unspanned models, it is necessary to include option data, which adds further challenges. Because there are no analytical solutions in the LADQ (1,1) model, we show how options can be priced using an Alternating Direction Implicit finite difference scheme. We then implement an Unscented Kalman filter — a non-linear extension of the Kalman filter, which is a popular method for inferring state variable values — to recover the latent state variables from market observable data
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Wort, Joshua. "Pricing with Bivariate Unspanned Stochastic Volatility Models." Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/31323.
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Unspanned stochastic volatility (USV) models have gained popularity in the literature. USV models contain at least one source of volatility-related risk that cannot be hedged with bonds, referred to as the unspanned volatility factor(s). Bivariate USV models are the simplest case, comprising of one state variable controlling the term structure and the other controlling unspanned volatility. This dissertation focuses on pricing with two particular bivariate USV models: the Log-Affine Double Quadratic (1,1) – or LADQ(1,1) – model of Backwell (2017) and the LinearRational Square Root (1,1) – or LRSQ(1,1) – model of Filipovic´ et al. (2017). For the LADQ(1,1) model, we fully outline how an Alternating Directional Implicit finite difference scheme can be used to price options and implement the scheme to price caplets. For the LRSQ(1,1) model, we illustrate a semi-analytical Fourierbased method originally designed by Filipovic´ et al. (2017) for pricing swaptions, but adjust it to price caplets. Using the above numerical methods, we calibrate each (1,1) model to both the British-pound yield curve and caps market. Although we cannot achieve a close fit to the implied volatility surface, we find that the parameters in the LADQ(1,1) model have direct control over the qualitative features of the volatility skew, unlike the parameters within the LRSQ(1,1) model.
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Endekovski, Jessica. "Pricing multi-asset options in exponential levy models." Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/31437.
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This dissertation looks at implementing exponential Levy models whereby the un- ´ derlyings are driven by Levy processes, which are able to account for stylised facts ´ that traditional models do not, in order to price basket options more efficiently. In particular, two exponential Levy models are implemented and tested: the multi- ´ variate Variance Gamma (VG) model and the multivariate normal inverse Gaussian (NIG) model. Both models are calibrated to real market data and then used to price basket options, where the underlyings are the constituents of the KBW Bank Index. Two pricing methods are also compared: a closed-form (analytical) approximation of the price, derived by Linders and Stassen (2016) and the standard Monte Carlo method. The convergence of the analytical approximation to Monte Carlo prices was found to improve as the time to maturity of the option increased. In comparison to real market data, the multivariate NIG model was able to fit the data more accurately for shorter maturities and the multivariate VG model for longer maturities. However, when looking at Monte Carlo prices, the multivariate VG model was found to outperform the results of the multivariate NIG model, as it was able to converge to Monte Carlo prices to a greater degree.
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Oagile, Joel. "Sequential Calibration of Asset Pricing Models to Option Prices." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29840.
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This paper implements four calibration methods on stochastic volatility models. We estimate the latent state and parameters of the models using three non-linear filtering methods, namely the extended Kalman filter (EKF), iterated extended Kalman filter (IEKF) and the unscented Kalman filter (UKF). A simulation study is performed and the non-linear filtering methods are compared to the standard least square method (LSQ). The results show that both methods are capable of tracking the hidden state and time varying parameters with varying success. The non-linear filtering methods are faster and generally perform better on validation. To test the stability of the parameters, we carry out a delta hedging study. This exercise is not only of interest to academics, but also to traders who have to hedge their positions. Our results do not show any significant benefits resulting from performing delta hedging using parameter estimates obtained from non-linear filtering methods as compared to least square parameter estimates.
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Sylvester, Matthew. "Calibrating Term Structure Models to an Initial Yield Curve." Master's thesis, Faculty of Commerce, 2021. http://hdl.handle.net/11427/33027.
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The modelling of the short rate offers many advantages, with the models explored in this dissertation all offering closed-form, analytic formulae for bond prices and for options on bonds. Often, a vital primary condition is for a model to be calibrated to the initial term structure and to recover the bond prices observed in the market – that is, to be calibrated to the initial yield curve. Under the two exogenous models explored in this dissertation, the Hull-White and the CIR++, the effect of increasing the volatility parameter of the SDE increases the mean of the short rate. Increasing volatility of an SDE is a common approach to stress testing a model, as such, the consequences of bumping volatility in a calibrated model is a vital concern. The Hull-White model and CIR++ model were calibrated to market data, with the former being able to match the observed cap prices, while the latter failed, displaying an upper bound on cap prices. Investigating this, under CIR++ model, bond option prices are shown to not be straightforward increasing functions of the volatility parameter. In fact, for high volatility, bond option prices display an upper limit before decreasing, thus providing a limit to the level of cap prices too. This dissertation points to the reason residing in the underlying CIR model from which the CIR++ is based on, and the manner in which the model is extended
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Guedes, Maria do Carmo Vaz de Miranda. "Mathematical models in capital investment appraisal." Thesis, University of Warwick, 1988. http://wrap.warwick.ac.uk/107492/.
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Neiss, Katharine Stefanie. "Essays on discretionary inflation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ27212.pdf.
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Lapere, Michael. "A comprehensive view of Markov-Functional models and their application." Master's thesis, University of Cape Town, 2006. http://hdl.handle.net/11427/19132.
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Includes bibliographical references.Markov-Functional models are a very powerful class of market models which calibrate and compute prices and Greeks quickly. This dissertation explains, in detail, how Markov-Functional models work as well as discussing all of the specific models developed in the literature. It contains the key points that can be found in the present literature. We explain, in detail, all of the concepts, from the theoretical framework down to the numerical implementation of the specific models. This involves explaining the framework for Markov-Functional models, describing specific models, obtaining a deeper understanding of how the model parameters affect the results, discussing the issues involved in the implementation, implementing various models and investigating the effect of numerical and market parameters on the outcome. Various concepts, not discussed in the present literature, such as considerations for selecting a discretization grid for the numerical implementation, are developed. The practical application of Markov-Functional models is considered as well as alternative fields, such as Actuarial science, where the model can be applied. In summary, this dissertation embodies a complete discussion of the current class of Markov-Functional models.
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Schwellnus, Adrian. "Linear-Rational Term Structure Models With Flexible Level-Dependent Volatility." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29215.
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The Linear-Rational Framework for the modelling of interest rates is a framework which allows for the addition of spanned and unspanned factors, while maintaining a lower bound on rates and tractable valuation of interest rate derivatives, particularly swaptions. The advantages of having all these properties are significant. This dissertation presents the Linear-Rational Framework, and specializes the factor process to a class of diffusion models which allows for the degree of state dependence of volatility to be estimated. This dissertation then finds that the estimated state dependent volatility structure is significantly different to that of typical models, where it is set it a priori. The effect the added degree of freedom has on the model implied swaption skew is then analysed.
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Ramnarayan, Kalind. "Level Dependence in Volatility in Linear-Rational Term Structure Models." Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/31207.
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The degree of level dependence in interest rate volatility is analysed in the linearrational term structure model. The linear-rational square-root (LRSQ) model, where level dependence is set a priori, is compared to a specification where the factor process follows CEV-type dynamics which allows a more flexible degree of level dependence. Parameters are estimated using an unscented Kalman filter in conjunction with quasi-maximum likelihood. An extended specification for the state price density process is required to ensure reliable parameter estimates. The empirical analysis indicates that the LRSQ model generally overestimates level dependence. Although the CEV specification captures the degree of level dependence in volatility more accurately, it has a trade-off with analytical tractability. The optimal specification, therefore, depends on the type of model implementation and general economic conditions.
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Ngwenza, Dumisani. "Quantifying Model Risk in Option Pricing and Value-at-Risk Models." Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/31059.
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Financial practitioners use models in order to price, hedge and measure risk. These models are reliant on assumptions and are prone to ”model risk”. Increased innovation in complex financial products has lead to increased risk exposure and has spurred research into understanding model risk and its underlying factors. This dissertation quantifies model risk inherent in Value-at-Risk (VaR) on a variety of portfolios comprised of European options written on the ALSI futures index across various maturities. The European options under consideration will be modelled using the Black-Scholes, Heston and Variance-Gamma models.
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Mkhwanazi, MA (Mpendulo Armstrong). "Efficient Monte Carlo simulations of pricing captions using Libor market models." Master's thesis, University of Cape Town, 2013. http://hdl.handle.net/11427/9114.
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Includes bibliographical references.The cap option (caption) is one of common European exotic options discussed in literature. This (interest rates) exotic option has no closed form solution and its accurate pricing and hedging in a volatile market is a challenge for traders. The reason for this is that, comparatively, the behaviour on an individual interest rate is more complex than that of a stock price. To price any interest rate product, it is essential to develop an interest rates model describing the behaviour of the entire zero coupon yield curve. The equity and yield curve, respectively, relate to the difference in the dynamics of a scalar variable and vector variable. Moreover, captions are second order with respect to the discount bonds in that they are options on caps (which are also options on bonds). These reasons make it of particular interest to study efficient numerical solutions to price captions. Monte Carlo simulation provides a simple method for pricing this option, and a suitable interest rate model to use is the Libor market model. The approach of describing the behaviour of the entire zero coupon yield curve, in the era post the 2007 credit crunch crisis, is what is called a standard single-curve market practice, and Part l of this work is based on it. . After introducing the framework for option pricing in the interest rate market, the theory and implementation procedure for Monte Carlo simulation using Libor market models is described. A detailed analysis of the results is presented together with a sensitivity analysis, and finally suggestions for efficient pricing of captions are given. In Part II we review the recent financial market evolution, triggered by the credit crunch crisis towards double-curve approach. Unfortunately, such a methodology is not easy to build. In practice an empirical approach to price and hedge interest rate derivatives has prevailed in the market. Future cash flows are generated through multiple forwarding yield curves associated to the underlying rate tenors, and their net present value is calculated through discount factors front a single discounting yield curve.
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Cheng, Lap-yan, and 鄭立仁. "Extension of price-trend models with applications in finance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B37428408.
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Song, Na, and 宋娜. "Mathematical models and numerical algorithms for option pricing and optimal trading." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50662168.
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Research conducted in mathematical finance focuses on the quantitative modeling of financial markets. It allows one to solve financial problems by using mathematical methods and provides understanding and prediction of the complicated financial behaviors. In this thesis, efforts are devoted to derive and extend stochastic optimization models in financial economics and establish practical algorithms for representing and solving problems in mathematical finance.
An option gives the holder the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before a specified date. In this thesis, a valuation model for a perpetual convertible bond is developed when the price dynamics of the underlying share are governed by Markovian regime-switching models. By making use of the relationship between the convertible bond and an American option, the valuation of a perpetual convertible bond can be transformed into an optimal stopping problem. A novel approach is also proposed to discuss an optimal inventory level of a retail product from a real option perspective in this thesis. The expected present value of the net profit from selling the product which is the objective function of the optimal inventory problem can be given by the actuarial value of a real option. Hence, option pricing techniques are adopted to solve the optimal inventory problem in this thesis.
The goal of risk management is to eliminate or minimize the level of risk associated with a business operation. In the risk measurement literature, there is relatively little amount of work focusing on the risk measurement and management of interest rate instruments. This thesis concerns about building a risk measurement framework based on some modern risk measures, such as Value-at-Risk (VaR) and Expected Shortfall (ES), for describing and quantifying the risk of interest rate sensitive instruments. From the lessons of the recent financial turmoils, it is understood that maximizing profits is not the only objective that needs to be taken into account. The consideration for risk control is of primal importance. Hence, an optimal submission problem of bid and ask quotes in the presence of risk constraints is studied in this thesis. The optimal submission problem of bid and ask quotes is formulated as a stochastic optimal control problem.
Portfolio management is a professional management of various securities and assets in order to match investment objectives and balance risk against performance. Different choices of time series models for asset price may lead to different portfolio management strategies. In this thesis, a discrete-time dynamic programming approach which is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system is explored. It’s also interesting to analyze the implications of the heteroscedastic effect described by a continuous-time stochastic volatility model for evaluating risk of a cash management problem. In this thesis, a continuous-time dynamic programming approach is employed to investigate the cash management problem under stochastic volatility model and constant volatility model respectively.published_or_final_version
Mathematics
Doctoral
Doctor of Philosophy
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Tokwe, Thabo. "Kalman Filtering and the Estimation of Multi-factor Affine Term Structure Models." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29465.
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When optimising the likelihood function one often encounters various stationary points and sometimes discontinuities in the parameter space (Gupta and Mehra, 1974). This is certainly true for a majority of multi-factor affine term structure models. Practitioners often recover different parameter optimisations depending on the initial parameters. If these parameters result in different option prices, the implications would be severe. This paper examines these implications through numerical experiments on the three-factor Vasicek and Arbitrage-free Nelson-Siegel (AFNS) models. The numerical experiments involve Kalman filtering as well as likelihood optimisation for parameter estimation. It was found that the parameter sets lead to the same short rate process and thus the same model. Moreover, likelihood optimisation in the AFNS does not result in different parameter sets irrespective of the starting point.
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Zhou, Junhua, and 周俊华. "To survive and succeed in the risky financial world: applications of mathematical optimization in finance andinsurance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44407579.
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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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Lopes, Marcio Ferrao. "Bias-Free Joint Simulation of Multi-Factor Short Rate Models and Discount Factor." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29396.
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This dissertation explores the use of single- and multi-factor Gaussian short rate models for the valuation of interest rate sensitive European options. Specifically, the focus is on deriving the joint distribution of the short rate and the discount factor, so that an exact and unbiased simulation scheme can be derived for risk-neutral valuation. We see that the derivation of the joint distribution remains tractable when working with the class of Gaussian short rate models. The dissertation compares three joint and exact simulation schemes for the short rate and the discount factor in the single-factor case; and two schemes in the multifactor case. We price European floor options and European swaptions using a twofactor Gaussian short rate model and explore the use of variance reduction techniques. We compare the exact and unbiased schemes to other solutions available in the literature: simulating the short rate under the forward measure and approximating the discount factor using quadrature.
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Mazviona, Batsirai Winmore. "Volatility forecasting using Double-Markov switching GARCH models under skewed Student-t distribution." Master's thesis, University of Cape Town, 2012. http://hdl.handle.net/11427/12344.
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Includes bibliographical references.This thesis focuses on forecasting the volatility of daily returns using a double Markov switching GARCH model with a skewed Student-t error distribution. The model was applied to individual shares obtained from the Johannesburg Stock Exchange (JSE). The Bayesian approach which uses Markov Chain Monte Carlo was used to estimate the unknown parameters in the model. The double Markov switching GARCH model was compared to a GARCH(1,1) model. Value at risk thresholds and violations ratios were computed leading to the ranking of the GARCH and double Markov switching GARCH models. The results showed that double Markov switching GARCH model performs similarly to the GARCH model based on the ranking technique employed in this thesis.
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Jin, Shusong, and 金曙松. "Nonlinear time series modeling with application to finance and other fields." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B3199605X.
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Dharmawan, Komang School of Mathematics UNSW. "Superreplication method for multi-asset barrier options." Awarded by:University of New South Wales. School of Mathematics, 2005. http://handle.unsw.edu.au/1959.4/30169.
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The aim of this thesis is to study multi-asset barrier options, where the volatilities of the stocks are assumed to define a matrix-valued bounded stochastic process. The bounds on volatilities may represent, for instance, the extreme values of the volatilities of traded options. As the volatilities are not known exactly, the value of the option can not be determined. Nevertheless, it is possible to calculate extreme values. We show that these values correspond to the best and the worst case scenarios of the future volatilities for short positions and long positions in the portfolio of the options. Our main tool is the equivalence of the option pricing and a certain stochastic control problem and the resulting concept of superhedging. This concept has been well known for some time but never applied to barrier options. First, we prove the dynamic programming principle (DPP) for the control problem. Next, using rather standard arguments we derive the Hamilton-Jacobi-Bellman equation for the value function. We show that the value function is a unique viscosity solution of the Hamilton-Jacobi-Bellman equation. Then we define the super price and superhedging strategy for the barrier options and show equivalence with the control problem studied above. The superprice price can be found by solving the nonlinear Hamilton-Jacobi-Equation studied above. It is called sometimes the Black-Scholes-Barenblatt (BSB) equation. This is the Hamilton-Jacobi-Bellman equation of the exit control problem. The sup term in the BSB equation is determined dynamically: it is either the upper bound or the lower bound of the volatility matrix, according to the convexity or concavity of the value function with respect to the stock prices. By utilizing a probabilistic approach, we show that the value function of the exit control problem is continuous. Then, we also obtain bounds for the first derivative of the value function with respect to the space variable. This derivative has an important financial interpretation. Namely, it allows us to define the superhedging strategy. We include an example: pricing and hedging of a single-asset barrier option and its numerical solution using the finite difference method.
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Mimouni, Karim. "Three essays on volatility specification in option valuation." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103274.
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Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the empirical shortcomings of this model. In the first essay, we investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on a long sample of S& P500 returns. Finally, we employ nonlinear least squares on a time series of cross sections of option data. In the estimations on returns and options data, we use the particle filtering technique to retrieve the spot volatility path. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of alternative volatility specifications is a model we refer to as the VAR model, which is of the GARCH diffusion type.In the second essay, we estimate the Constant Elasticity of Variance (CEV) model in order to study the level of nonlinearity in the volatility dynamic. We also estimate a CEV process combined with a jump process (CEVJ) and analyze the effects of the jump component on the nonlinearity coefficient. Estimation is performed using the particle filtering technique on a long series of S&P500 returns and on options data. We find that both returns data and returns-and-options data favor nonlinear specifications for the volatility dynamic, suggesting that the extensive use of linear models is not supported empirically. We also find that the inclusion of jumps does not affect the level of nonlinearity and does not improve the CEV model fit.
The third essay provides an empirical comparison of two classes of option valuation models: continuous-time models and discrete-time models. The literature provides some theoretical limit results for these types of dynamics, and researchers have used these limit results to argue that the performance of certain discrete-time and continuous-time models ought to be very similar. This interpretation is somewhat contentious, because a given discrete-time model can have several continuous-time limits, and a given continuous-time model can be the limit for more than one discrete-time model. Therefore, it is imperative to investigate whether there exist similarities between these specifications from an empirical perspective. Using data on S&P500 returns and call options, we find that the discrete-time models investigated in this paper have the same performance in fitting the data as selected continuous-time models both in and out-of-sample.
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Alluri, Chandra M. "Testing calculation engines using input space partitioning and automation." Fairfax, VA : George Mason University, 2008. http://hdl.handle.net/1920/3228.
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Thesis (M.S.)--George Mason University, 2008.Vita: p. 158. Thesis director: Jeff Offutt. Submitted in partial fulfillment of the requirements for the degree of Master of Science in Software Engineering. Title from PDF t.p. (viewed Aug. 27, 2008). Includes bibliographical references (p. 156-157). Also issued in print.
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Liu, Qiang. "Inference of Spot Volatility in the presence of Infinite Variation Jumps." Thesis, University of Macau, 2018. http://umaclib3.umac.mo/record=b3952482.
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Welihockyj, Alexander. "The cost of using misspecified models to exercise and hedge American options on coupon bearing bonds." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/20532.
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This dissertation investigates the cost of using single-factor models to exercise and hedge American options on South African coupon bearing bonds, when the simulated market term structure is driven by a two-factor model. Even if the single factor models are re-calibrated on a daily basis to the term structure, we find that the exercise and hedge strategies can be suboptimal and incur large losses. There is a vast body of research suggesting that real market term structures are in actual fact driven by multiple factors, so suboptimal losses can be largely reduced by simply employing a well-specified multi-factor model.
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Glover, Elistan Nicholas. "Analytic pricing of American put options." Thesis, Rhodes University, 2009. http://hdl.handle.net/10962/d1002804.
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American options are the most commonly traded financial derivatives in the market. Pricing these options fairly, so as to avoid arbitrage, is of paramount importance. Closed form solutions for American put options cannot be utilised in practice and so numerical techniques are employed. This thesis looks at the work done by other researchers to find an analytic solution to the American put option pricing problem and suggests a practical method, that uses Monte Carlo simulation, to approximate the American put option price. The theory behind option pricing is first discussed using a discrete model. Once the concepts of arbitrage-free pricing and hedging have been dealt with, this model is extended to a continuous-time setting. Martingale theory is introduced to put the option pricing theory in a more formal framework. The construction of a hedging portfolio is discussed in detail and it is shown how financial derivatives are priced according to a unique riskneutral probability measure. Black-Scholes model is discussed and utilised to find closed form solutions to European style options. American options are discussed in detail and it is shown that under certain conditions, American style options can be solved according to closed form solutions. Various numerical techniques are presented to approximate the true American put option price. Chief among these methods is the Richardson extrapolation on a sequence of Bermudan options method that was developed by Geske and Johnson. This model is extended to a Repeated-Richardson extrapolation technique. Finally, a Monte Carlo simulation is used to approximate Bermudan put options. These values are then extrapolated to approximate the price of an American put option. The use of extrapolation techniques was hampered by the presence of non-uniform convergence of the Bermudan put option sequence. When convergence was uniform, the approximations were accurate up to a few cents difference.
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Osei, Ofosuhene. "Level Crossing Times in Mathematical Finance." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/etd/1126.
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Level crossing times and their applications in finance are of importance, given certain threshold levels that represent the "desirable" or "sell" values of a stock. In this thesis, we make use of Wald's lemmas and various deep results from renewal theory, in the context of finance, in modelling the growth of a portfolio of stocks. Several models are employed .
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任尚智 and Sheung-chi Phillip Yam. "Algebraic methods on some problems in finance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B3122698X.
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Wei, Zhenghong. "Empirical likelihood based evaluation for value at risk models." HKBU Institutional Repository, 2007. http://repository.hkbu.edu.hk/etd_ra/896.
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Wei, Yong, and 卫勇. "The real effects of S&P 500 Index additions: evidence from corporate investment." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B4490681X.
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Le, Truc. "Stochastic volatility models." Monash University, School of Mathematical Sciences, 2005. http://arrow.monash.edu.au/hdl/1959.1/5181.
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De, Scheemaekere Xavier. "Essays in mathematical finance and in the epistemology of finance." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209938.
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The goal of this thesis in finance is to combine the use of advanced mathematical methods with a return to foundational economic issues. In that perspective, I study generalized rational expectations and asset pricing in Chapter 2, and a converse comparison principle for backward stochastic differential equations with jumps in Chapter 3. Since the use of stochastic methods in finance is an interesting and complex issue in itself - if only to clarify the difference between the use of mathematical models in finance and in physics or biology - I also present a philosophical reflection on the interpretation of mathematical models in finance (Chapter 4). In Chapter 5, I conclude the thesis with an essay on the history and interpretation of mathematical probability - to be read while keeping in mind the fundamental role of mathematical probability in financial models.Doctorat en Sciences économiques et de gestion
info:eu-repo/semantics/nonPublished
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Lee, Boram. "Risk perceptions and financial decisions of individual investors." Thesis, University of Stirling, 2013. http://hdl.handle.net/1893/16951.
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Standard finance theory portrays investors as rational utility maximisers. Persisting market anomalies and observed investor practice, however, have led to widespread recognition that the fundamental axioms of rationality are often violated. In response to the limitations inherent in standard theory, the Behavioural Finance approach relaxes the rationality assumption and takes account of psychological influences on individuals’ decision-making processes. Adopting the behavioural approach, this thesis, which includes two empirical studies, examines why, and to what extent, investors depart from rational or optimal investment practices. The thesis examines the effect of Myopic Loss Aversion (MLA) suggested by Benartzi and Thaler (1995) as a response to the Equity Premium Puzzle highlighted by Mehra and Prescott (1985). While previous studies are almost exclusively based on experiments in a laboratory setting, this approach provides more compelling empirical evidence by investigating the effects of MLA on real individual investors’ portfolio allocations through the use of the Dutch National Bank Household Survey. For the first time, the concept of MLA is identified through the interaction of two separate effects, firstly, individuals’ myopia, reflected in portfolio evaluation and rebalancing frequencies, and secondly, loss aversion. The thesis finds that individuals who are less affected by MLA invest more in risky financial assets. Further, individuals who are less myopic increase their share of risky assets invested in their financial portfolios over time, although this is unrelated to their loss aversion. These findings support the prediction of MLA theory that short investment horizons and high loss aversion lead to a significantly lower share of risky investments. In summary, the high equity premium can be explained by the notion of MLA. If individuals evaluate their investment performance over the long-term, they perceive much smaller risks relative to stockholding returns; consequently, they will be prepared to accept smaller equity premiums. The findings suggest possible interventions by policy makers and investment advisors to encourage individuals to remain in the stock market, such as providing long-term investment instruments, or restricting evaluation frequency to the annual reporting of investment performance. In response to the stockholding puzzle (Haliassos and Bertaut, 1995), this thesis also investigates individuals’ stock market returns expectations and their varying levels of risk aversion. Previous studies find that individuals’ heterogeneous stock market expectations determine variations in their stockholdings. The thesis accounts for the effect of risk aversion on stock market expectations, as well as on stockholding decisions. Additionally, the causality issue as between individuals’ expectations and stockholding status is controlled. The thesis finds that more risk averse individuals hold lower stock market expectations, and that the stock market return expectations of more risk averse individuals affect their stock market participation decisions negatively. The portfolio allocation decisions of individuals who already hold stocks are only affected by their expectations, with risk aversion being no longer significant. The thesis argues that persistent risk aversion effects cause individuals to hold pessimistic views of stock market returns, thus contributing to the enduring stockholding puzzle. The thesis reinforces existing perceptions that individuals in the real world may not make fully rational decisions due to their judgments which are based on heuristics and affected by cognitive biases. Individual investors often fail to maximise their utility given their preferences and constraints. Consequently, this thesis draws attention to the possible role of institutions, policy makers, and financial advisory bodies in providing effective interventions and guidelines to improve individuals’ financial decisions.
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Wang, Yintian 1976. "Three essays on volatility long memory and European option valuation." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102851.
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This dissertation is in the form of three essays on the topic of component and long memory GARCH models. The unifying feature of the thesis is the focus on investigating European index option evaluation using these models.The first essay presents a new model for the valuation of European options. In this model, the volatility of returns consists of two components. One of these components is a long-run component that can be modeled as fully persistent. The other component is short-run and has zero mean. The model can be viewed as an affine version of Engle and Lee (1999), allowing for easy valuation of European options. The model substantially outperforms a benchmark single-component volatility model that is well established in the literature. It also fits options better than a model that combines conditional heteroskedasticity and Poisson normal jumps. While the improvement in the component model's performance is partly due to its improved ability to capture the structure of the smirk and the path of spot volatility, its most distinctive feature is its ability to model the term structure. This feature enables the component model to jointly model long-maturity and short-maturity options.
The second essay derives two new GARCH variance component models with non-normal innovations. One of these models has an affine structure and leads to a closed-form option valuation formula. The other model has a non-affine structure and hence, option valuation is carried out using Monte Carlo simulation. We provide an empirical comparison of these two new component models and the respective special cases with normal innovations. We also compare the four component models against GARCH(1,1) models which they nest. All eight models are estimated using MLE on S&P500 returns. The likelihood criterion strongly favors the component models as well as non-normal innovations. The properties of the non-affine models differ significantly from those of the affine models. Evaluating the performance of component variance specifications for option valuation using parameter estimates from returns data also provides strong support for component models. However, support for non-normal innovations and non-affine structure is less convincing for option valuation.
The third essay aims to investigate the impact of long memory in volatility on European option valuation. We mainly compare two groups of GARCH models that allow for long memory in volatility. They are the component Heston-Nandi GARCH model developed in the first essay, in which the volatility of returns consists of a long-run and a short-run component, and a fractionally integrated Heston-Nandi GARCH (FIHNGARCH) model based on Bollerslev and Mikkelsen (1999). We investigate the performance of the models using S&P500 index returns and cross-sections of European options data. The component GARCH model slightly outperforms the FIGARCH in fitting return data but significantly dominates the FIHNGARCH in capturing option prices. The findings are mainly due to the shorter memory of the FIHNGARCH model, which may be attributed to an artificially prolonged leverage effect that results from fractional integration and the limitations of the affine structure.
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Ezzine, Ahmed. "Some topics in mathematical finance. Non-affine stochastic volatility jump diffusion models. Stochastic interest rate VaR models." Doctoral thesis, Universite Libre de Bruxelles, 2004. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211156.
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Lin, Zhongli, and 林中立. "On the statistical inference of some nonlinear time series models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B43757625.
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Kwan, Chun-kit, and 關進傑. "Statistical inference for some financial time series models with conditional heteroscedasticity." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B39794027.
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Zhao, Jing Ya. "Numerical methods for pricing Bermudan barrier options." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592939.
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Arroyo, Jorge M. "Money and the dispersion of relative prices in the drug and apparel industries." Thesis, Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/28574.
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劉伯文 and Pak-man Lau. "Option pricing: a survey." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31977911.
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Lee, Mou Chin. "An empirical test of variance gamma options pricing model on Hang Seng index options." HKBU Institutional Repository, 2000. http://repository.hkbu.edu.hk/etd_ra/263.
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Chan, Ka Hou. "European call option pricing under partial information." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691380.
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Campbell, Alyce. "An empirical study of a financial signalling model." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26969.
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Brennan and Kraus (1982,1986) developed a costless signalling model which can explain why managers issue hybrid securities—convertibles(CB's) or bond-warrant packages(BW's). The model predicts that when the true standard deviation (σ) of the distribution of future firm value is unknown to the market, the firm's managers will issue a hybrid with specific characteristics such that the security's full information value is at a minimum at the firm's true σ. In this fully revealing equilibrium market price is equal to this minimum value.
In this study, first the mathematical properties of the hypothesized bond-valuation model were examined to see if specific functions could have a minimum not at σ = 0 or σ = ∞ as required for signalling. The Black-Scholes-Merton model was the valuation model chosen because of ease of use, supporting empirical evidence, and compatibility with the Brennan-Kraus model. Three different variations, developed from Ingersoll(1977a); Geske( 1977,1979) and Geske and Johnson(1984); and Brennan and Schwartz(1977,1978), were examined. For all hybrids except senior CB's, pricing functions with a minimum can be found for plausible input parameters. However, functions with an interior maximum are also plausible. A function with a maximum cannot be used for signalling.
Second, bond pricing functions for 105 hybrids were studied. The two main hypotheses were: (1) most hybrids have functions with an interior minimum; (2) market price equals minimum theoretical value. The results do not support the signalling model, although the evidence is ambiguous. For the σ range 0.05-0.70, for CB's (BW's) 15(8) Brennan-Schwartz functions were everywhere positively sloping, 11(2) had an interior minimum, 22(0) were everywhere negatively sloping, and 35(12) had an interior maximum. Market prices did lie closer to minima than maxima from the Brennan-Schwartz solutions, but the results suggest that the solution as implemented overpriced the CB's. BW's were unambiguously overpriced. With consistent overpricing, market prices would naturally lie closer to minima. Average variation in theoretical values was, however, only about 5 percent for CB's and about 10 percent for BW's. This, coupled with the shape data, suggests that firms were choosing securities with theoretical values relatively insensitive to a rather than choosing securities to signal σ unambiguously.Business, Sauder School of
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Sood, Premlata Khetan. "Profit sharing, unemployment, and inflation in Canada : a simulation analysis." Thesis, McGill University, 1996. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=34459.
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The thesis examines the impact of a partial switch to a share system in Canada on unemployment and inflation. Simulations with an independent Canadian macro model and Canadian data for the period 1973-1983 show that profit sharing will not always resolve unemployment and inflation, as claimed by Martin Weitzman. Some combinations of the share parameters resolve them, while others aggravate them. Thus, the combinations of the share parameters play a key role in terms of impact of the profit sharing on unemployment and inflation.
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Haven, Emmanuel. "The use of fuzzy set theory in economics : applications in micro-economics and finance." Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=23335.
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This paper attempts to show how fuzzy set theory can be used to weaken some of the stringent, rationality assumptions used in classical micro-economics. The objective of the paper is to see whether by introducing fuzziness we arrive to new results or just only generalizations of classical micro-economic results. We discover that the axiom of completeness is not needed anymore. Using fuzziness will also allow us to better explain the existing gap between delimiting possible choices and making the actual choice. We also introduce the notions of a fuzzy indifference set with a measurable area. The fuzzy utility surface is also discussed. The demand curve is now 'thick'.In the producer area, the classical hypothesis that maximum profit entails maximum utility of profit is now substantially weakened when introducing fuzziness.
Finally, we consider revealed preference within a fuzzy context.
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Yuksel, Hasan Zafer. "Performance measures: Traditional versus new models." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3086.
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The thesis analyzed the performance of 5,987 mutual funds using a database called Steele Mutual Fund Experts and compared the predicting ability of various measures of performance. The measures discussed in the thesis are Treynor Ratio, Sharpe Ratio, Jensen's Alpha, Graham-Harvey-1 (GH-1), and Graham-Harvey-2 (GH-2). The performance measures are mostly used by professional money managers and scholars for literary purposes.