This paper evaluates the application of two well-known asymmetric stochastic volatility (ASV) models to option price forecasting and dynamic delta hedging. They are specified in discrete time in contrast to the classical stochastic volatility models used in option pricing. There is some related literature, but little is known about the empirical implications of volatility asymmetry on option pricing. The objectives of this paper are to estimate ASV option pricing models using a Bayesian approach unknown in this type of literature, and to investigate the effect of volatility asymmetry on option pricing for different size equity sectors and periods of volatility. Using the S&P MidCap 400 and S&P 500 European call option quotes, results show that volatility asymmetry benefits the accuracy of option price forecasting and hedging cost effectiveness in the large-cap equity sector. However, ASV models do not improve the option price forecasting and dynamic hedging in the mid-cap equity sector.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Leverage implies volatility asymmetry, but not all types of volatility asymmetry imply leverage. Hereafter, we refer to the broader concept of volatility asymmetry.
Note that the p values of the tests of kurtosis and skewness have been obtained using the procedure by Premaratne and Bera (2017), which allows us to test kurtosis in the presence of asymmetry and skewness in the presence of excess of kurtosis.
Hereafter, figures do not include “OP” in the model names due to lack of space.
Asai, M. (2008). Autoregressive stochastic volatility models with heavy-tailed distributions: A comparison with multifactor volatility models. Journal of Empirical Finance, 15(2), 332–341.
Asai, M., & McAleer, M. (2006). Asymmetric multivariate stochastic volatility. Econometric Reviews, 25(2–3), 453–473.
Asai, M., & McAleer, M. (2011). Alternative asymmetric stochastic volatility models. Econometric Reviews, 30, 548–564.
Badescu, A., Elliot, R., Grigoryeva, L., & Ortega, J. P. (2016). Option pricing and hedging under non-affine autoregressive stochastic volatility models. https://cdi-icd.org/wp-content/uploads/2018/03/DR-16-08_Badescu_Elliott_Grigoryeva_Ortega_Option-pricing-and-hedging.pdf
Bakshi, G., Cao, C., & Chen, Z. (1997). Empirical performance of alternative option pricing models. Journal of Finance, 53, 499–547.
Bates, D. (2000). Post-87 crash fears in S&P 500 futures options. Journal of Econometrics, 94, 181–238.
Benzoni, L. (2002). Pricing options under stochastic volatility: An empirical investigation. Technical report, Carlson School of Management
Black, F. (1976). Studies in stock price volatility changes. In Proceedings of the 1976 business meeting of the business and economics statistics section, American Statistical Association pp (177–181).
Bormetti, G., Casarin, R., Corsi, F., & Livieri, G. (2020). A stochastic volatility model with realized measures for option pricing. Journal of Business & Economic Statistics. https://doi.org/10.1080/07350015.2019.1604371
Breidt, F. (1996). A threshold autoregressive stochastic volatility model. In VI Latin American congress of probability and mathematical statistics (CLAPEM), Valparaiso, Chile, Citeseer.
Broadie, M., & Detemple, J. (2004). Option pricing: Valuation models and applications. Management Science, 50(9), 1145–1177.
Carnero, M., Peña, D., & Ruiz, E. (2004). Persistence and kurtosis in garch and stochastic volatility models. Journal of Financial Econometrics, 2(2), 319–342.
Catania, L., & Bernardi, M. (2017). MCS: Model confidence set procedure. https://CRAN.R-project.org/package=MCS, r package version 0.1.3.
Chernov, M., & Ghysels, E. (2000). A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of option valuation. Journal of Financial Economics, 56, 407–458.
Christie, A. (1982). The stochastic behavior of common stock variances. Journal of Financial Economics, 10(4), 407–432.
Christoffersen, P., Heston, S., & Jacobs, K. (2009). The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well. Management Science, 55, 1914–1932.
Christoffersen, P., & Jacobs, K. (2004). Which garch model for option valuation? Management Science, 50(9), 1204–1221.
Danielsson, J. (1994). Stochastic volatility in asset prices: Estimation with simulated maximum likelihood. Journal of Econometrics, 64, 375–400.
Duan, J. (1995). The GARCH option pricing model. Mathematical Finance, 5, 13–32.
Durbin, J., & Koopman, S. (1997). Monte Carlo maximum likelihood estimation for non-Gaussian state space models. Biometrika, 84, 669–684.
Engle, R., & Ng, V. (1993). Measuring and testing the impact of news on volatility. The Journal of Finance, 48(5), 1779–1801.
Esperança, J. P., Gama, A. P. M., & Gulamhussen, M. A. (2003). Corporate debt policy of small firms: An empirical (re)examination. Journal of Small Business and Enterprise Development, 10(1), 62–80.
Fridman, M., & Harris, L. (1998). A maximum likelihood approach for non-Gaussian stochastic volatility models. Journal of Business & Economic Statistics, 16(3), 284–291.
Giovanni, D., Ortobelli, S., & Rachev, S. (2008). Delta hedging strategies comparison. European Journal of Operational Research, 185, 1615–1631.
Glosten, L., Jaganathan, R., & Runkle, D. (1993). On the relation between the expected value and the volatility of the nominal excess returns on stocks. Journal of Finance, 48, 1779–1801.
Hansen, P., Lunde, A., & Nason, J. (2011). The model confidence set. Econometrica, 79, 453–497.
Harvey, A., & Shephard, N. (1996). Estimation of an asymmetric stochastic volatility model for asset returns. Journal of Business & Economic Statistics, 14(4), 429–34.
Heston, S., & Nandi, S. (2000). A closed form garch option pricing model. Review of Financial Studies, 13, 585–625.
Jacquier, E., Polson, N., & Rossi, P. (2004). Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Journal of Econometrics, 122(1), 185–212.
Jiang, G. J., & van der Sluis, P. J. (1999). Index option pricing models with stochastic volatility and stochastic interest rates. Review of Finance, 3(3), 273–310.
Jones, C. (2003). The dynamics of stochastic volatility: Evidence from underlying and options markets. Journal of Econometrics, 116, 181–224.
Kim, S., Shephard, N., & Chib, S. (1998). Stochastic volatility: Likelihood inference and comparison with ARCH models. The Review of Economic Studies, 65(3), 361–393.
Liesenfeld, R., & Jung, R. C. (2000). Stochastic volatility models: Conditional normality versus heavy-tailed distributions. Journal of Applied Econometrics, 15(2), 137–160.
Mao, X., Czellar, V., Ruiz, E., & Veiga, H. (2020). Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation. Econometrics and Statistics, 13, 84–105.
Mao, X., Ruiz, E., & Veiga, H. (2017). Threshold stochastic volatility: Properties and forecasting. International Journal of Forecasting, 33(4), 1105–1123.
McAleer, M. (2005). Automated inference and learning in modeling financial volatility. Econometric Theory, 21(1), 232–261.
Meyer, R., & Yu, J. (2000). BUGS for a Bayesian analysis of stochastic volatility models. The Econometrics Journal, 3(2), 198–215.
Michaelas, N., Chittenden, F., & Poutziouris, P. (1999). Financial policy and capital structure choice in U.K. SMEs: Empirical evidence from company panel data. Small Business Economics, 12(2), 113–130.
Nandi, S. (1998). How important is the correlation between returns and volatility in a stochastic volatility model? Empirical evidence from pricing and hedging in the S&P 500 index options market. Journal of Banking & Finance, 22(5), 589–610.
Nelson, D. (1991). Conditional heteroscedasticity in asset pricing: A new approach. Econometrica, 59, 347–370.
Omori, Y., Chib, S., Shephard, N., & Nakajima, J. (2007). Stochastic volatility with leverage: Fast and efficient likelihood inference. Journal of Econometrics, 140(2), 425–449.
Pan, J. (2002). The jump-risk premia implicit in options: Evidence from a integrated time-series study. Journal of Financial Economics, 63, 3–50.
Park, Y. H. (2016). The effects of asymmetric volatility and jumps on the pricing of VIX derivatives. Journal of Econometrics, 192(1), 313–328.
Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd international workshop on distributed statistical computing.
Premaratne, G., & Bera, A. K. (2017). Adjusting the tests for skewness and kurtosis for distributional misspecifications. Communications in Statistics—Simulation and Computation, 46(5), 3599–3613.
Renault, E. (1997). Econometric models of option pricing errors. In D. Kreps & K. Wallis (Eds.), Advances in economics and econometrics: Theory and applications (Vol. 3). Cambridge University Press.
Richard, J., & Zhang, W. (2007). Efficient high-dimensional importance sampling. Journal of Econometrics, 141, 1385–1411.
Sandmann, G., & Koopman, S. (1998). Estimation of stochastic volatility models via Monte Carlo maximum likelihood. Journal of Econometrics, 87(2), 271–301.
Sayilgan, G., Karabacak, K., & Küçükkocao, G. (2006). The firm-specific determinants of corporate capital structure: Evidence from Turkish panel data. Investment Management and Financial Innovations, 3(3), 125–139.
Shephard, N., & Pitt, M. (1997). Likelihood analysis of non-Gaussian measurement time series. Biometrika, 84(3), 653–667.
So, M., Li, W., & Lam, K. (2002). A threshold stochastic volatility model. Journal of Forecasting, 21(7), 473–500.
Stentoft, L. (2011). American option pricing with discrete and continuous time models: An empirical comparison. Journal of Empirical Finance, 18, 880–902.
Su, Y., & Yajima, M. (2015). R2jags: Using R to Run JAGS. https://CRAN.R-project.org/package=R2jags, r package version 0.5-7.
Taylor, S. (1994). Modelling stochastic volatility: A review and comparative study. Mathematical Finance, 4, 183–204.
Tsiotas, G. (2012). On generalised asymmetric stochastic volatility models. Computational Statistics & Data Analysis, 56(1), 151–172.
Wu, G., & Xiao, Z. (2002). A generalized partially linear model of asymmetric volatility. Journal of Empirical Finance, 9, 287–319.
Yu, J. (2005). On leverage in a stochastic volatility model. Journal of Econometrics, 127(2), 165–178.
Yu, J. (2012). A semiparametric stochastic volatility model. Journal of Econometrics, 167(2), 473–482.
Yu, J., Yang, Z., & Zhang, X. (2006). A class of nonlinear stochastic volatility models and its implications for pricing currency options. Computational Statistics & Data Analysis, 51(4), 2218–2231.
The second author acknowledges financial support from Spanish Ministry of Economy and Competitiveness, research projects ECO2015-70331-C2-2-R and PGC2018-096977-B-I00, and FCT Grant UID/GES/00315/2019.
Conflict of interest
The authors declare that they have no conflict of interest.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
See Table 5.
About this article
Cite this article
Casas, I., Veiga, H. Exploring Option Pricing and Hedging via Volatility Asymmetry. Comput Econ (2020). https://doi.org/10.1007/s10614-020-10005-5
- Delta hedging
- Stochastic volatility
- Volatility asymmetry