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Asymmetry in Stochastic Volatility Models: Threshold or Correlation?

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  • Smith Daniel R

    () (Simon Fraser University)

Abstract

We compare the ability of correlation and threshold effects in a stochastic volatility model to capture the asymmetric relationship between stock returns and volatility. The parameters are estimated using maximum likelihood based on the extended Kalman filter and uses numerical integration over the latent volatility process. The stochastic volatility model with only correlation does a better job of capturing asymmetry than a threshold stochastic volatility model even though it has fewer parameters. We develop a stochastic volatility model that includes both threshold effects and correlated innovations. We find that the general model with both threshold effects and correlated innovations dominates purely threshold and correlated models. In this augmented model volatility and returns are negatively correlated, and volatility is more persistent, less volatile and higher following negative returns even after counting for the negative correlation.

Suggested Citation

  • Smith Daniel R, 2009. "Asymmetry in Stochastic Volatility Models: Threshold or Correlation?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-36, May.
  • Handle: RePEc:bpj:sndecm:v:13:y:2009:i:3:n:1
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    References listed on IDEAS

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    1. Smith, Daniel R, 2002. "Markov-Switching and Stochastic Volatility Diffusion Models of Short-Term Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 183-197, April.
    2. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
    3. Friedman, Moshe & Harris, Lawrence, 1998. "A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 284-291, July.
    4. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    5. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
    6. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
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    1. repec:eee:intfor:v:33:y:2017:i:4:p:1105-1123 is not listed on IDEAS
    2. Lopes Moreira Da Veiga, María Helena & Ruiz Ortega, Esther & Mao, Xiuping, 2013. "One for all : nesting asymmetric stochastic volatility models," DES - Working Papers. Statistics and Econometrics. WS ws131110, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Dendramis, Yiannis & Kapetanios, George & Tzavalis, Elias, 2015. "Shifts in volatility driven by large stock market shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 55(C), pages 130-147.
    4. Montero, José M. & García-Centeno, Maria C. & Fernández-Avilés, Gema, 2011. "Modelling the Volatility of the Spanish Wholesale Electricity Spot Market. Asymmetric GARCH Models vs. Threshold ARSV model/Modelización de la volatilidad en el mercado eléctrico español. Modelos GARC," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 29, pages 597-616, Agosto.
    5. Listorti, Giulia & Esposti, Roberto, 2012. "Horizontal Price Transmission in Agricultural Markets: Fundamental Concepts and Open Empirical Issues," Bio-based and Applied Economics Journal, Italian Association of Agricultural and Applied Economics (AIEAA), issue 1, April.

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