Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

A new variant of estimation approach to asymmetric stochastic volatilitymodel

1 Quantitative Research, JPMorgan Chase & Co., 277 Park Avenue, New York, USA
2 Department of Statistics and Actuarial Science, University of Waterloo, 200 University AvenueWest, Waterloo, Ontario, Canada
3 School of Accounting and Finance, University of Waterloo, 200 University Avenue West, Waterloo,Ontario, Canada

Special Issues: Volatility of Prices of Financial Assets

This paper proposes a novel simulation-based inference for an asymmetric stochastic volatility model. An acceptance-rejection Metropolis-Hastings algorithm is developed for the simulation of latent states of the model. A simple and e cient algorithm is also developed for estimation of a heavy-tailed stochastic volatility model. Simulation studies show that our proposed methods give rise to reasonable parameter estimates. Our proposed estimation methods are then used to analyze a benchmark data set of asset returns.
  Article Metrics

Keywords stochastic volatility; leverage effect; Bayesian inference; acceptance-rejection; Metropolis-Hastings; slice sampler

Citation: Zhongxian Men, Tony S. Wirjanto. A new variant of estimation approach to asymmetric stochastic volatilitymodel
. Quantitative Finance and Economics, 2018, 2(2): 325-347. doi: 10.3934/QFE.2018.2.325


  • 1.Bollerslev T (1986) Generalized autoregressive conditional heteroskedasticity. J Econometrics 31: 307–327.    
  • 2.Bauwens L, Lubrano M (1998) Bayesian inference on GARCH models using the Gibbs sampler. Economet J 1: C23–C26.    
  • 3.Broto C, Ruiz E (2004) Estimation methods for stochastic volatility models: a survey. J Econ Surv 18: 613–649.    
  • 4.Carnero A, Pena D, Ruiz E (2003) Persistence and kurtosis in GARCH and stochastic volatility models J Financ Economet 2: 319–342.
  • 5.Chib S, Greenberg E (1995) Understanding the Metropolis-Hastings Algorithm. American Statistician 49: 327–335.
  • 6.Chib S, Nardarib F, Shephard N (2006) Analysis of high dimensional multivariate stochastic volatility models. J Econometrics 134: 341–371.    
  • 7.Dobigeon N, Tourneret J (2010) Bayesian orthogonal component analysis for sparse representation. IEEE T Signal Proces 58: 2675–2685.    
  • 8.Diebold FX, Guther TA, Tay AS (1998) Evaluating density forecasts with applications to financial risk management. Int Econ Rev 39: 863–883.    
  • 9.Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50: 987–1007.    
  • 10.Eraker B, Johannes M, Polson N (2003) The Impact ofJumps inVolatility and Returns. J Financ 58: 1269–1300.    
  • 11.Geweke J (1993) Bayesian treatment of the independent Student-t linear model. J Appl Econom 8: S19–S40.    
  • 12.Harvey AC, Shephard N (1996) Estimation of an asymmetric stochastic volatility model for asset returns. J Bus Econ Stat 14: 42-434.
  • 13.Jacquier E, Polson NG, Rossi PE (2004) Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. J Econometrics 122: 185–212.    
  • 14.Kawakatsu H (2007) Numerical integration-based Gaussian mixture filters for maximum likelihood estimation of asymmetric stochastic volatility models. Economet 10: 342–358.    
  • 15.Kim S, Shephard N, Chib S (1998) Stochastic volatility: Likelihood inference and comparison with ARCH models. Rev Econ Stud 65: 361–393.    
  • 16.Liesenfeld R, Richard J (2003) Univariate and multivariate stochastic volatility models: estimation and diagnostics. J Empiri Financ 45: 505–531.
  • 17.Melino A, Turnbull SM (1990) Pricing foreign currencyoptions with stochastic volatility. J Econometrics 45: 239–265.    
  • 18.Men Z (2012) Bayesian Inference for Stochastic Volatility Models. Ph.D. thesis, Department of Statistics and Actuarial Science at the University of Waterloo.
  • 19.Men Z, McLeish D, Kolkiewicz A, et al. (2017) Comparison of Asymmetric Stochastic Volatility Models under Di erent Correlation Structures. J Appl Stat 44: 1350–1368.    
  • 20.Men Z, Kolkiewicz A, Wirjanto TS (2015) Bayesian Analysis of Asymmetric Stochastic Conditional Duration Model. J Forecasting 34: 36–56.    
  • 21.Mira A, Tierney L (2002) E ciency and Convergence Properties of Slice Samplers. Scand J Stat 29: 1–12.    
  • 22.Neal RN (2003) Slice sampling. Annals Stat 31: 705–767.    
  • 23.Omori Y, Chib S, Shephard N, et al. (2007) Stochastic volatility with leverage: Fast and e cient likelihood inference. J Econometrics 140: 425–449.    
  • 24.Pitt MK, Shephard N (1999a) Time varying covariances: A factor stochastic volatility approach. Bayesian Stat 6: 547–570.
  • 25.Pitt M, Shephard N (1999b) Filtering via simulation: Auxiliary particle filters. J Am Stat Assoc 94: 590–599.
  • 26.Roberts GO, Rosenthal JS (1999) Convergence of Slice Sampler Markov Chains. J R Stat Soc B 61: 643–660.    
  • 27.Shephard N, Pitt MK (1997) Likelihood Analysis of non-Gaussian Measurement Time Series. Biometrika 84: 653–667.    
  • 28.Taylor SJ (1986) Modelling Financial Time Series, Chichester: Wiley.
  • 29.Wirjanto TS, Kolkiewicz A, Men Z (2016) Bayesian Analysis of a Threshold Stochastic Volatility Model. J Forecasting 35: 462–476.    
  • 30.Yu J (2005) On leverage in a stochastic volatility model. J Econometrics 127: 165–178.    
  • 31.Yu J, Meyer R (2006) Multivariate stochastic volatility models: Bayesian estimation and model comparison. Economet Rev 51: 2218–2231.
  • 32.Zhang X, King L (2008) Box-Cox stochastic volatility models with heavy-tails and correlated errors. J Empiri Financ 15: 549–566.    


This article has been cited by

  • 1. Nancy McCormack, When Canadian Courts Cite the Major Philosophers: Who Cites Whom in Canadian Caselaw, SSRN Electronic Journal , 2017, 10.2139/ssrn.2973877

Reader Comments

your name: *   your email: *  

© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved