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Journal articles on the topic 'Volatility estimation'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 March 2023

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1

Mahatma, Yudi, and Ibnu Hadi. "Stochastic Volatility Estimation of Stock Prices using the Ensemble Kalman Filter." InPrime: Indonesian Journal of Pure and Applied Mathematics 3, no. 2 (November 10, 2021): 136–43. http://dx.doi.org/10.15408/inprime.v3i2.20256.

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AbstractVolatility plays important role in options trading. In their seminal paper published in 1973, Black and Scholes assume that the stock price volatility, which is the underlying security volatility of a call option, is constant. But thereafter, researchers found that the return volatility was not constant but conditional to the information set available at the computation time. In this research, we improve a methodology to estimate volatility and interest rate using Ensemble Kalman Filter (EnKF). The price of call and put option used in the observation and the forecasting step of the EnKF algorithm computed using the solution of Black-Scholes PDE. The state-space used in this method is the augmented state space, which consists of static variables: volatility and interest rate, and dynamic variables: call and put option price. The numerical experiment shows that the EnKF algorithm is able to estimate accurately the estimated volatility and interest rates with an RMSE value of 0.0506.Keywords: stochastic volatility; call option; put option; Ensemble Kalman Filter. AbstrakVolatilitas adalah faktor penting dalam perdagangan suatu opsi. Dalam makalahnya yang dipublikasikan tahun 1973, Black dan Scholes mengasumsikan bahwa volatilitas harga saham, yang merupakan volatilitas sekuritas yang mendasari opsi beli, adalah konstan. Akan tetapi, para peneliti menemukan bahwa volatilitas pengembalian tidaklah konstan melainkan tergantung pada kumpulan informasi yang dapat digunakan pada saat perhitungan. Pada penelitian ini dikembangkan metodologi untuk mengestimasi volatilitas dan suku bunga menggunakan metode Ensembel Kalman Filter (EnKF). Harga opsi beli dan opsi jual yang digunakan pada observasi dan pada tahap prakiraan pada algoritma EnKF dihitung menggunakan solusi persamaan Black-Scholes. Ruang keadaan yang digunakan adalah ruang keadaan yang diperluas yang terdiri dari variabel statis yaitu volatilitas dan suku bunga, dan variabel dinamis yaitu harga opsi beli dan harga opsi jual. Eksperimen numerik menunjukkan bahwa algoritma ENKF dapat secara akurat mengestimasi volatiltas dan suku bunga dengan RMSE 0.0506.Kata kunci: volatilitas stokastik; opsi beli; opsi jual; Ensembel Kalman Filter.

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2

Altin, Hakan. "Volatility Analysis in International Indices." International Journal of Sustainable Economies Management 11, no. 1 (January 1, 2022): 1–17. http://dx.doi.org/10.4018/ijsem.304461.

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Modeling and the estimation of volatility in financial time series are important research subjects for which ARCH family models are recommended. These models are widely used to analyze volatility and manage risk in financial assets. In this study, share indices from the BRIC countries, Europe and the United States were analyzed to determine volatility in international indices. Current data was used to examine the period 1982-2021. Within this framework, the existence of asymmetric information, the leverage effect and the permanence of shocks were examined. Estimation results show the existence of asymmetric information. Bad news affects the system more than good news. The leverage effect is also experienced. Estimation results show that the shocks affecting the system are permanent. At the last stage, static foresight estimations were conducted on the explanatory power of the estimation results. Static foresight estimations present strong and weak evidence together. All parameters are statistically significant.

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3

Cai, Jingwei. "Nonparametric Range-Based Double Smoothing Spot Volatility Estimation for Diffusion Models." Complexity 2020 (September 21, 2020): 1–7. http://dx.doi.org/10.1155/2020/5048925.

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We consider nonparametric spot volatility estimation for diffusion models with discrete high frequency observations. Our estimator is carried out in two steps. First, using the local average of the range-based variance, we propose a crude estimator of the spot volatility. Second, we use usual nonparametric kernel smoothing to reconstruct the volatility function from the crude estimator. By inference, we find such a double smoothing operation can effectively reduce the estimation error.

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4

Pandey, Ajay. "Volatility Models and their Performance in Indian Capital Markets." Vikalpa: The Journal for Decision Makers 30, no. 2 (April 2005): 27–46. http://dx.doi.org/10.1177/0256090920050203.

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Estimation and forecasting of volatility of asset returns is important in various applications related to financial markets such as valuation of derivatives, risk management, etc. Till early eighties, it was commonly assumed that the volatility of an asset is constant and estimation procedures were based on this assumption even though some of the pioneering studies on property of stock market returns did not support this assumption. Following the pioneering work of Engle and Bollerslev in eighties on developing models (ARCH/GARCH type models) to capture time-varying characteristics of volatility and other stock return properties, extensive research has been done world over in modeling volatility for estimation and forecasting. There are broadly four possible approaches for estimating and forecasting volatility. These are: Traditional Volatility Estimators— These estimators assume that ‘true’ volatility is unconditional and constant. The estimation is based on either squared returns or standard deviation of returns over a period. Extreme Value Volatility Estimators— These estimators are similar to traditional estimators except that these also incorporate high and low prices observed unlike traditional estimators which are based on closing prices of the asset. Conditional Volatility Models— These models (ARCH/GARCH type models) take into account the time-varying nature of volatility. There have been quite a few extensions of the basic conditional volatility models to incorporate ‘observed’ characteristics of asset/stock returns. Implied Volatility— In case of options, most of the parameters relevant for their valuation can be directly observed or estimated, except volatility. Volatility is, therefore, backed out from the observed option values and is used as volatility forecast. The empirical research across countries and markets has not been equivocal about the effectiveness of using these approaches. This study compares the result of the first three approaches in estimating and forecasting Nifty returns. Based on four different criteria related to bias and efficiency of the various estimators and models, this study analysed the estimation and forecasting ability of three different traditional estimators, four extreme value estimators, and two conditional volatility models. As a benchmark, it used ‘realized’ volatility estimates. The findings of this study are as follows: For estimating the volatility, the extreme value estimators perform better on efficiency criteria that the conditional volatility models. In terms of bias, conditional volatility models perform better than the extreme value estimators. As far as predictive power is concerned, extreme value estimators estimated from sample of length equal to forecast period perform better than the conditional volatility estimators in providing five-day and month ahead volatility forecasts.

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5

Li, Jia, Viktor Todorov, and George Tauchen. "ESTIMATING THE VOLATILITY OCCUPATION TIME VIA REGULARIZED LAPLACE INVERSION." Econometric Theory 32, no. 5 (May 25, 2015): 1253–88. http://dx.doi.org/10.1017/s0266466615000171.

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We propose a consistent functional estimator for the occupation time of the spot variance of an asset price observed at discrete times on a finite interval with the mesh of the observation grid shrinking to zero. The asset price is modeled nonparametrically as a continuous-time Itô semimartingale with nonvanishing diffusion coefficient. The estimation procedure contains two steps. In the first step we estimate the Laplace transform of the volatility occupation time and, in the second step, we conduct a regularized Laplace inversion. Monte Carlo evidence suggests that the proposed estimator has good small-sample performance and in particular it is far better at estimating lower volatility quantiles and the volatility median than a direct estimator formed from the empirical cumulative distribution function of local spot volatility estimates. An empirical application shows the use of the developed techniques for nonparametric analysis of variation of volatility.

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6

Van Es, Bert, Peter Spreij, and Harry Van Zanten. "Nonparametric volatility density estimation." Bernoulli 9, no. 3 (June 2003): 451–65. http://dx.doi.org/10.3150/bj/1065444813.

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7

Kayal, Parthajit, and G. Balasubramanian. "Excess Volatility in Bitcoin: Extreme Value Volatility Estimation." IIM Kozhikode Society & Management Review 10, no. 2 (February 28, 2021): 222–31. http://dx.doi.org/10.1177/2277975220987686.

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This article investigates the excess volatility in Bitcoin prices using an unbiased extreme value volatility estimator. We capture the time-varying nature of the excess volatility using bootstrap, multi-horizon, sub-sampling and rolling-window approaches. We observe that Bitcoin price changes are almost efficient. Although Bitcoin prices exhibit high volatility and show signs of excess volatility for a few periods, it is decreasing over time. After controlling for the outliers, we also notice that the Bitcoin market shows signs of increasing maturity. Overall, Bitcoin prices show a sign of increasing efficiency with decreasing volatility. Our findings have implications for investors making investment decisions and for regulators making policy choices.

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8

Woerner, Jeannette H. C. "Estimation of integrated volatility in stochastic volatility models." Applied Stochastic Models in Business and Industry 21, no. 1 (January 2005): 27–44. http://dx.doi.org/10.1002/asmb.548.

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9

Sanfelici, Simona, Imma Valentina Curato, and Maria Elvira Mancino. "High-frequency volatility of volatility estimation free from spot volatility estimates." Quantitative Finance 15, no. 8 (May 11, 2015): 1331–45. http://dx.doi.org/10.1080/14697688.2015.1032542.

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10

Ghahramani, M., and A. Thavaneswaran. "Nonlinear recursive estimation of volatility via estimating functions." Journal of Statistical Planning and Inference 142, no. 1 (January 2012): 171–80. http://dx.doi.org/10.1016/j.jspi.2011.07.006.

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11

Li, Yicun, and Yuanyang Teng. "Estimation of the Hurst Parameter in Spot Volatility." Mathematics 10, no. 10 (May 10, 2022): 1619. http://dx.doi.org/10.3390/math10101619.

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This paper contributes in three stages in a logic of the cognitive process: we firstly propose a new estimation of Hurst exponent by changing frequency method which is purely mathematical. Then we want to check if the new Hurst is efficient, so we prove the advantages of this new Hurst in asymptotic variance in the perspective compared with other two Hurst estimator. However, a purely mathematical game is not enough, a good estimation should be proven by reality, so we apply the new Hurst estimator into truncated and non-truncated spot volatility which fills the gap of previous literatures using 5-min price data (Source: Wind Financial Terminal) of 10 Chinese A-share industry indices from 1 January 2005 until 31 December 2020.

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12

Bollerslev, Tim, Jia Li, and Zhipeng Liao. "Fixed‐ k inference for volatility." Quantitative Economics 12, no. 4 (2021): 1053–84. http://dx.doi.org/10.3982/qe1749.

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We present a new theory for the conduct of nonparametric inference about the latent spot volatility of a semimartingale asset price process. In contrast to existing theories based on the asymptotic notion of an increasing number of observations in local estimation blocks, our theory treats the estimation block size k as fixed. While the resulting spot volatility estimator is no longer consistent, the new theory permits the construction of asymptotically valid and easy‐to‐calculate pointwise confidence intervals for the volatility at any given point in time. Extending the theory to a high‐dimensional inference setting with a growing number of estimation blocks further permits the construction of uniform confidence bands for the volatility path. An empirically realistically calibrated simulation study underscores the practical reliability of the new inference procedures. An empirical application based on intraday data for the S&P 500 equity index reveals highly significant abrupt changes, or jumps, in the market volatility at FOMC news announcement times, validating recent uses of various high‐frequency‐based identification schemes in asset pricing finance and monetary economics.

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13

Alòs, Elisa, Maria Elvira Mancino, and Tai-Ho Wang. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing." Decisions in Economics and Finance 42, no. 2 (October 31, 2019): 321–49. http://dx.doi.org/10.1007/s10203-019-00271-w.

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14

Kanaya, Shin, and Dennis Kristensen. "ESTIMATION OF STOCHASTIC VOLATILITY MODELS BY NONPARAMETRIC FILTERING." Econometric Theory 32, no. 4 (April 13, 2015): 861–916. http://dx.doi.org/10.1017/s0266466615000079.

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A two-step estimation method of stochastic volatility models is proposed: In the first step, we nonparametrically estimate the (unobserved) instantaneous volatility process. In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases and variances due to the first-step estimation, but under regularity conditions we show that these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties of the proposed estimators.

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15

Xu, Ke-Li. "REWEIGHTED FUNCTIONAL ESTIMATION OF DIFFUSION MODELS." Econometric Theory 26, no. 2 (September 30, 2009): 541–63. http://dx.doi.org/10.1017/s0266466609100087.

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The local linear method is popular in estimating nonparametric continuous-time diffusion models, but it may produce negative results for the diffusion (or volatility) functions and thus lead to insensible inference. We demonstrate this using U.S. interest rate data. We propose a new functional estimation method of the diffusion coefficient based on reweighting the conventional Nadaraya–Watson estimator. It preserves the appealing bias properties of the local linear estimator and is guaranteed to be nonnegative in finite samples. A limit theory is developed under mild requirements (recurrence) of the data generating mechanism without assuming stationarity or ergodicity.

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16

Hentschel, Ludger. "Errors in Implied Volatility Estimation." Journal of Financial and Quantitative Analysis 38, no. 4 (December 2003): 779. http://dx.doi.org/10.2307/4126743.

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17

Li, Y., and P. A. Mykland. "Rounding Errors and Volatility Estimation." Journal of Financial Econometrics 13, no. 2 (February 27, 2014): 478–504. http://dx.doi.org/10.1093/jjfinec/nbu005.

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18

Elliott, Robert J., John van der Hoek, and Jorge Valencia. "Nonlinear Filter Estimation of Volatility." Stochastic Analysis and Applications 28, no. 4 (June 2, 2010): 696–710. http://dx.doi.org/10.1080/07362994.2010.482841.

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19

Rogers, L. C. G. "Volatility Estimation with Price Quanta." Mathematical Finance 8, no. 3 (July 1998): 277–90. http://dx.doi.org/10.1111/1467-9965.00056.

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20

Todorov, Viktor, George Tauchen, and Iaryna Grynkiv. "Volatility activity: Specification and estimation." Journal of Econometrics 178 (January 2014): 180–93. http://dx.doi.org/10.1016/j.jeconom.2013.08.015.

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21

Alvarez, Alexander, Fabien Panloup, Monique Pontier, and Nicolas Savy. "Estimation of the instantaneous volatility." Statistical Inference for Stochastic Processes 15, no. 1 (December 23, 2011): 27–59. http://dx.doi.org/10.1007/s11203-011-9062-2.

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22

Ma, Dan, Tianxing Yang, Liping Liu, and Yi He. "Analysis of Factors Influencing Stock Market Volatility Based on GARCH-MIDAS Model." Complexity 2022 (January 17, 2022): 1–10. http://dx.doi.org/10.1155/2022/6176451.

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This paper further extends the existing GARCH-MIDAS model to deal with the effect of microstructure noise in mixed frequency data. This paper has two highlights. First, according to the estimation of the long-term volatility components of the GARCH-MIDAS model, rAVGRV is adopted to substitute for the RV estimator. rAVGRV uses the rich data sources in tick-by-tick data and significantly corrects the impact of the microstructure noise on volatility estimation. Second, besides introducing macroeconomic variables (i.e., macroeconomic consistency index (MCI), deposits in financial institutions (DFI), industrial value-added (IVA), and M2), Chinese Economic Policy Uncertainty (CEPU) index and Infectious Disease Equity Market Volatility Tracker (EMV) are introduced in the long-run volatility component of the GARCH-MIDAS model. As indicated by the results of this paper, the rAVGRV-based GARCH-MIDAS is slightly better than the RV model-based GARCH-MIDAS. In addition to the common macroeconomic variables significantly impacting stock market volatility, CEPU also substantially impacts stock market volatility. Nevertheless, the effect of EMV on the stock market is insignificant.

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23

Renault, Eric, Cisil Sarisoy, and Bas J. M. Werker. "EFFICIENT ESTIMATION OF INTEGRATED VOLATILITY AND RELATED PROCESSES." Econometric Theory 33, no. 2 (March 15, 2016): 439–78. http://dx.doi.org/10.1017/s0266466616000013.

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We derive nonparametric efficiency bounds for regular estimators of integrated smooth transformations of instantaneous variances, in particular, integrated power variance. We find that realized variance attains the efficiency bound for integrated variance under both regular and irregular sampling schemes. For estimating higher powers such as integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds, when observation times are equidistant. Moreover, the estimator in Jacod and Rosenbaum (2013), whose efficiency was documented for the submodel assuming constant volatility, is efficient also for nonconstant volatility paths. When the observation times are possibly random but predictable, we provide an estimator, similar to that of Kristensen (2010), which can get arbitrarily close to the nonparametric bound. Finally, parametric information about the functional form of volatility leads to a lower efficiency bound, unless the volatility process is piecewise constant.

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Koo, Bonsoo, and Oliver Linton. "LET’S GET LADE: ROBUST ESTIMATION OF SEMIPARAMETRIC MULTIPLICATIVE VOLATILITY MODELS." Econometric Theory 31, no. 4 (November 5, 2014): 671–702. http://dx.doi.org/10.1017/s0266466614000516.

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We investigate a model in which we connect slowly time varying unconditional long-run volatility with short-run conditional volatility whose representation is given as a semi-strong GARCH(1,1) process with heavy tailed errors. We focus on robust estimation of both long-run and short-run volatilities. Our estimation is semiparametric since the long-run volatility is totally unspecified whereas the short-run conditional volatility is a parametric semi-strong GARCH(1,1) process. We propose different robust estimation methods for nonstationary and strictly stationary GARCH parameters with nonparametric long-run volatility function. Our estimation is based on a two-step LAD procedure. We establish the relevant asymptotic theory of the proposed estimators. Numerical results lend support to our theoretical results.

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25

Sari, Linda Karlina, Noer Azam Achsani, and Bagus Sartono. "Pemodelan Volatilitas Return Saham: Studi Kasus Pasar Saham Asia." Jurnal Ekonomi dan Pembangunan Indonesia 18, no. 1 (July 1, 2017): 35–52. http://dx.doi.org/10.21002/jepi.v18i1.717.

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Modelling Volatility of Return Stock Index: Evidence from Asian CountriesVolatility is one of the interesting phenomenon in financial market; the reason is because of its eect to the existence of global financial market. The existence of volatility closely related to the risk in stock model. This research aims to determine the right model in modeling stock return volatility taken from four Asian countries with symmetric and various asymmetric model of GARCH. The result from fitting the right model for all of four stock markets showed that asymmetric model of GARCH showing a better estimation in portraying stock return volatility. Moreover, the model can reveal the existence of asymmetric eects on those four stock markets.Keywords: GARCH Asymmetric; Stock Market; Modelling; GARCH Symmetry; Volatility AbstrakVolatilitas pada pasar keuangan merupakan salah satu fenomena yang sangat menarik karena dampaknya terhadap eksistensi pasar finansial global. Keberadaan volatilitas berhubungan dengan risiko sebuah. Tulisan ini bertujuan menentukan model terbaik dalam memodelkan volatilitas return saham pada empat negara di Asia dengan menggunakan model simetris GARCH dan berbagai macam model asimetris GARCH. Hasil dari fitting model terbaik untuk keempat pasar saham menunjukkan bahwa model asimetris GARCH menunjukkan estimasi yang lebih baik dalam menggambarkan volatilitas return saham. Lebih jauh lagi, model tersebut mengungkapkan keberadaan efek asimetris pada keempat pasar saham.

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Njeri Ngure, Josephine, and Anthony Gichuhi Waititu. "Consistency of an Estimator for Change Point in Volatility of Financial Returns." Journal of Mathematics Research 13, no. 1 (January 27, 2021): 56. http://dx.doi.org/10.5539/jmr.v13n1p56.

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A non parametric Auto-Regressive Conditional Heteroscedastic model for financial returns series is considered in which the conditional mean and volatility functions are estimated non-parametrically using Nadaraya Watson kernel. A test statistic for unknown abrupt change point in volatility which takes into consideration conditional heteroskedasticity, dependence, heterogeneity and the fourth moment of financial returns, since kurtosis is a function of the fourth moment is considered. The test is based on L2norm of the conditional variance functions of the squared residuals. A non-parametric change point estimator in volatility of financial returns is further obtained. The consistency of the estimator is shown theoretically and through simulation. An application of the estimator in change point estimation in volatility of United States Dollar/Kenya Shilling exchange rate returns data set is made. Through binary segmentation procedure, three change points in volatility of the exchange rate returns are estimated and further accounted for.

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Wilak, Kamil. "Autocorrelation of error estimations in Labour Force Surveys." Wiadomości Statystyczne. The Polish Statistician 60, no. 6 (June 29, 2015): 31–40. http://dx.doi.org/10.5604/01.3001.0016.0826.

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Rotating panel used in the Labour Force Survey (LFS) causes correlation possibility of estimations of labor markets errors. Knowledge of autocorrelation is important in the context of the trend estimation of labor market parameters. Dismissal of autocorrelation can result in the trend curve it will be fraught with volatility, characteristic of auto-regression processes. Estimation errors are not observable, thus it is not possible to estimate the autocorrelation coefficients by conventional estimators. This paper describes the adaptation of methods for estimating the errors of autocorrelation coefficients (proposed by Pfeffermanna et al.), The rotational scheme in LFS. Then, this method was used to estimate the autocorrelation coefficients in error estimation of the unemployment rate in the province. Greater Poland for six domains defined by gender and age.

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BILGIN, MEHMET HUSEYIN, GIRAY GOZGOR, and GOKHAN KARABULUT. "THE IMPACT OF WORLD ENERGY PRICE VOLATILITY ON AGGREGATE ECONOMIC ACTIVITY IN DEVELOPING ASIAN ECONOMIES." Singapore Economic Review 60, no. 01 (March 2015): 1550009. http://dx.doi.org/10.1142/s0217590815500095.

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This paper analyzes the impact of volatility in the world energy price on aggregate economic activity in an unbalanced panel data framework for 10 developing Asian countries: Bangladesh, PR China, India, Indonesia, Malaysia, Pakistan, the Philippines, Thailand, Turkey and Vietnam. We use both the realized volatility and the generalized autoregressive conditional heteroskedasticity models to measure the volatility in the world energy price. Empirical findings from dynamic panel data estimations show that the volatility in world energy price is negatively associated with the aggregate economic activity. Using the common correlated effects panel estimation techniques, we also systematically examine uncertain transmission channel of the world energy price volatility on the aggregate economic activity in each economy and obtain the most impressive negative effects in Turkey, PR China and India, respectively.

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Matei, Rovira, and Agell. "Bivariate Volatility Modeling with High-Frequency Data." Econometrics 7, no. 3 (September 15, 2019): 41. http://dx.doi.org/10.3390/econometrics7030041.

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We propose a methodology to include night volatility estimates in the day volatility modeling problem with high-frequency data in a realized generalized autoregressive conditional heteroskedasticity (GARCH) framework, which takes advantage of the natural relationship between the realized measure and the conditional variance. This improves volatility modeling by adding, in a two-factor structure, information on latent processes that occur while markets are closed but captures the leverage effect and maintains a mathematical structure that facilitates volatility estimation. A class of bivariate models that includes intraday, day, and night volatility estimates is proposed and was empirically tested to confirm whether using night volatility information improves the day volatility estimation. The results indicate a forecasting improvement using bivariate models over those that do not include night volatility estimates.

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NIELSEN, JAN NYGAARD, and MARTIN VESTERGAARD. "ESTIMATION IN CONTINUOUS-TIME STOCHASTIC VOLATILITY MODELS USING NONLINEAR FILTERS." International Journal of Theoretical and Applied Finance 03, no. 02 (April 2000): 279–308. http://dx.doi.org/10.1142/s0219024900000139.

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The stylized facts of stock prices, interest and exchange rates have led econometricians to propose stochastic volatility models in both discrete and continuous time. However, the volatility as a measure of economic uncertainty is not directly observable in the financial markets. The objective of the continuous-discrete filtering problem considered here is to obtain estimates of the stock price and, in particular, the volatility using discrete-time observations of the stock price. Furthermore, the nonlinear filter acts as an important part of a proposed method for maximum likelihood for estimating embedded parameters in stochastic differential equations. In general, only approximate solutions to the continuous-discrete filtering problem exist in the form of a set of ordinary differential equations for the mean and covariance of the state variables. In the present paper the small-sample properties of a second order filter is examined for some bivariate stochastic volatility models and the new combined parameter and state estimation method is applied to US stock market data.

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YANG, LU, and SHIGEYUKI HAMORI. "MODELING THE DYNAMICS OF INTERNATIONAL AGRICULTURAL COMMODITY PRICES: A COMPARISON OF GARCH AND STOCHASTIC VOLATILITY MODELS." Annals of Financial Economics 13, no. 03 (September 2018): 1850010. http://dx.doi.org/10.1142/s2010495218500100.

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In this study, we employ generalized autoregressive conditional heteroscedastic (GARCH) and stochastic volatility models to investigate the dynamics of wheat, corn, and soybean prices. We find that the stochastic volatility model provides the highest persistence of the volatility estimation in all cases. In addition, based on the monthly data, we find that the jump process and asymmetric effect do not exist in agricultural commodity prices. Finally, by estimating Value at risk (VaR) for these agricultural commodities, we find that the upsurge in agricultural prices in 2008 may have been caused by financialization.

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ALBANI, VINICIUS, ADRIANO DE CEZARO, and JORGE P. ZUBELLI. "CONVEX REGULARIZATION OF LOCAL VOLATILITY ESTIMATION." International Journal of Theoretical and Applied Finance 20, no. 01 (February 2017): 1750006. http://dx.doi.org/10.1142/s0219024917500066.

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We apply convex regularization techniques to the problem of calibrating Dupire’s local volatility surface model taking into account the practical requirement of discrete grids and noisy data. Such requirements are the consequence of bid and ask spreads, quantization of the quoted prices and lack of liquidity of option prices for strikes far away from the at-the-money level. We obtain convergence rates and results comparable to those obtained in the idealized continuous setting. Our results allow us to take into account separately the uncertainties due to the price noise and those due to discretization errors, thus, allowing estimating better discretization levels both in the domain and in the image of the parameter to solution operator by a Morozov’s discrepancy principle. We illustrate the results with simulated as well as real market data. We also validate the results by comparing the implied volatility prices of market data with the computed prices of the calibrated model.

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Randal 3, John A., Peter J. Thomson, and Martin T. Lally. "Non-parametric estimation of historical volatility." Quantitative Finance 4, no. 4 (August 2004): 427–40. http://dx.doi.org/10.1080/14697680400008692.

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34

Casas, Isabel. "Estimation of stochastic volatility with LRD." Mathematics and Computers in Simulation 78, no. 2-3 (July 2008): 335–40. http://dx.doi.org/10.1016/j.matcom.2008.01.040.

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Mancini, Cecilia, Vanessa Mattiussi, and Roberto Renò. "Spot volatility estimation using delta sequences." Finance and Stochastics 19, no. 2 (February 20, 2015): 261–93. http://dx.doi.org/10.1007/s00780-015-0255-1.

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Rossi, Alessandro, and Giampiero M. Gallo. "Volatility estimation via hidden Markov models." Journal of Empirical Finance 13, no. 2 (March 2006): 203–30. http://dx.doi.org/10.1016/j.jempfin.2005.09.003.

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Boyle, Phelim P., and Draviam Thangaraj. "Volatility estimation from observed option prices." Decisions in Economics and Finance 23, no. 1 (May 1, 2000): 31–52. http://dx.doi.org/10.1007/s102030050004.

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38

Renò, Roberto. "Nonparametric estimation of stochastic volatility models." Economics Letters 90, no. 3 (March 2006): 390–95. http://dx.doi.org/10.1016/j.econlet.2005.09.009.

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Samy Elkhouly, Mona. "Volatility Estimation and Forecasting of EGX30." مجلة البحوث المالیة والتجاریة 18, no. 2 (January 1, 2017): 435–55. http://dx.doi.org/10.21608/jsst.2017.59302.

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Teker, Dilek, and Suat Teker. "Estimation of Bitcoin Volatility: GARCH Implementation." International Journal of Economics and Management Studies 7, no. 1 (January 25, 2020): 169–73. http://dx.doi.org/10.14445/23939125/ijems-v7i1p120.

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Francq, Christian, and Jean-Michel Zakoïan. "Risk-parameter estimation in volatility models." Journal of Econometrics 184, no. 1 (January 2015): 158–73. http://dx.doi.org/10.1016/j.jeconom.2014.06.019.

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Bollerslev, Tim, Nour Meddahi, and Serge Nyawa. "High-dimensional multivariate realized volatility estimation." Journal of Econometrics 212, no. 1 (September 2019): 116–36. http://dx.doi.org/10.1016/j.jeconom.2019.04.023.

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Bregantini, Daniele. "Moment-based estimation of stochastic volatility." Journal of Banking & Finance 37, no. 12 (December 2013): 4755–64. http://dx.doi.org/10.1016/j.jbankfin.2013.08.008.

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Singh, Shivam, and Vipul . "Performance of Black-Scholes model with TSRV estimates." Managerial Finance 41, no. 8 (August 10, 2015): 857–70. http://dx.doi.org/10.1108/mf-06-2014-0177.

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Purpose – The purpose of this paper is to test the pricing performance of Black-Scholes (B-S) model, with the volatility of the underlying estimated with the two-scale realised volatility measure (TSRV) proposed by Zhang et al. (2005). Design/methodology/approach – The ex post TSRV is used as the volatility estimator to ensure efficient volatility estimation, without forecasting error. The B-S option prices, thus obtained, are compared with the market prices using four performance measures, for the options on NIFTY index, and three of its constituent stocks. The tick-by-tick data are used in this study for price comparisons. Findings – The B-S model shows significantly negative pricing bias for all the options, which is dependent on the moneyness of the option and the volatility of the underlying. Research limitations/implications – The negative pricing bias of B-S model, despite the use of the more efficient TSRV estimate, and post facto volatility values, confirms its inadequacy. It also points towards the possible existence of volatility risk premium in the Indian options market. Originality/value – The use of tick-by-tick data obviates the nonsynchronous error. TSRV, used for estimating the volatility, is a significantly improved estimate (in terms of efficiency and bias), as compared to the estimates based on closing data. The use of ex post realised volatility ensures that the forecasting error does not vitiate the test results. The sample is selected to be large and varied to ensure the robustness of the results.

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Asai, Manabu, and Michael McAleer. "Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes." International Journal of Statistics and Probability 6, no. 6 (September 15, 2017): 13. http://dx.doi.org/10.5539/ijsp.v6n6p13.

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The paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive asymptotic theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated asymptotic properties.

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Klebaner, Fima, Truc Le, and Robert Liptser. "On Estimation of Volatility Surface and Prediction of Future Spot Volatility." Applied Mathematical Finance 13, no. 3 (September 2006): 245–63. http://dx.doi.org/10.1080/13504860600564661.

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Alan, Chow, and Lahtinen Kyre. "Equity Risk: Measuring Return Volatility Using Historical High-Frequency Data." Studies in Business and Economics 14, no. 3 (December 1, 2019): 60–71. http://dx.doi.org/10.2478/sbe-2019-0043.

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AbstractMarket Volatility has been investigated at great lengths, but the measure of historical volatility, referred to as the relative volatility, is inconsistent. Using historical return data to calculate the volatility of a stock return provides a measure of the realized volatility. Realized volatility is often measured using some method of calculating a deviation from the mean of the returns for the stock price, the summation of squared returns, or the summation of absolute returns. We look to the stocks that make up the DJIA, using tick-by-tick data from June 2015 - May 2016. This research helps to address the question of what is the better measure of realized volatility? Several measures of volatility are used as proxies and are compared at four estimation time intervals. We review these measures to determine a closer/better fit estimator to the true realized volatility, using MSE, MAD, Diebold-Mariano test, and Pitman Closeness. We find that when using a standard deviation based on transaction level returns, shorter increments of time, while containing some levels of noise, are better estimates of volatility than longer increments.

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Hubner, Stefan, and Pavel Čížek. "Quantile-based smooth transition value at risk estimation." Econometrics Journal 22, no. 3 (June 6, 2019): 241–61. http://dx.doi.org/10.1093/ectj/utz009.

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Summary Value at risk models are concerned with the estimation of conditional quantiles of a time series. Formally, these quantities are a function of conditional volatility and the respective quantile of the innovation distribution. The former is often subject to asymmetric dynamic behaviour, e.g., with respect to past shocks. In this paper, we propose a model in which conditional quantiles follow a generalised autoregressive process governed by two parameter regimes with their weights determined by a smooth transition function. We develop a two-step estimation procedure based on a sieve estimator, approximating conditional volatility by using composite quantile regression, which is then used in the generalised autoregressive conditional quantile estimation. We show that the estimator is consistent and asymptotically normal, and we complement the results with a simulation study. In our empirical application, we consider daily returns of the German equity index (DAX) and the USD/GBP exchange rate. Although only the latter follows a two-regime model, we find that our model performs well in terms of out-of-sample prediction in both cases.

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Roy, Rahul, and Santhakumar Shijin. "The nexus of asset pricing, volatility and the business cycle." Journal of Economic Studies 48, no. 1 (May 4, 2020): 79–101. http://dx.doi.org/10.1108/jes-08-2019-0357.

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PurposeThe purpose of the study is to examine the dynamics in the troika of asset pricing, volatility, and the business cycle in the US and Japan.Design/methodology/approachThe study uses a six-factor asset pricing model to derive the realized volatility measure for the GARCH-type models.FindingsThe comprehensive empirical investigation led to the following conclusion. First, the results infer that the market portfolio and human capital are the primary discounting factors in asset return predictability during various phases of the subprime crisis phenomenon for the US and Japan. Second, the empirical estimates neither show any significant impact of past conditional volatility on the current conditional volatility nor any significant effect of subprime crisis episodes on the current conditional volatility in the US and Japan. Third, there is no asymmetric volatility effect during the subprime crisis phenomenon in the US and Japan except the asymmetric volatility effect during the post-subprime crisis period in the US and full period in Japan. Fourth, the volatility persistence is relatively higher during the subprime crisis period in the US, whereas during the subprime crisis transition period in Japan than the rest of the phases of the subprime crisis phenomenon.Originality/valueThe study argues that the empirical investigations that employed the autoregressive method to derive the realized volatility measure for the parameter estimation of GARCH-type models may result in incurring spurious estimates. Further, the empirical results of the study show that using the six-factor asset pricing model in an intertemporal framework to derive the realized volatility measure yields better estimation results while estimating the parameters of GARCH-type models.

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HAN, CHUAN-HSIANG, WEI-HAN LIU, and TZU-YING CHEN. "VaR/CVaR ESTIMATION UNDER STOCHASTIC VOLATILITY MODELS." International Journal of Theoretical and Applied Finance 17, no. 02 (March 2014): 1450009. http://dx.doi.org/10.1142/s0219024914500095.

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This paper proposes an improved procedure for stochastic volatility model estimation with an application to Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) estimation. This improved procedure is composed of the following instrumental components: Fourier transform method for volatility estimation, and importance sampling for extreme event probability estimation. The empirical analysis is based on several foreign exchange series and the S&P 500 index data. In comparison with empirical results by RiskMetrics, historical simulation, and the GARCH(1,1) model, our improved procedure outperforms on average.

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