Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T14:55:19.233Z Has data issue: false hasContentIssue false
  • English
  • Français

A lattice approach for option pricing under a regime-switching GARCH-jump model

Published online by Cambridge University Press:  29 July 2021

Zhiyu Guo Open the ORCID record for Zhiyu Guo [Opens in a new window]  and
Yizhou Bai Open the ORCID record for Yizhou Bai [Opens in a new window]
Zhiyu Guo
Affiliation:
Business School, Nankai University, Tianjin 300071, China. E-mail: zhiyuguo@mail.nankai.edu.cn
Yizhou Bai
Affiliation:
College of Science, Civil Aviation University of China, Tianjin 300071, China. E-mail: baiyizhou@mail.nankai.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

In this study, we consider option pricing under a Markov regime-switching GARCH-jump (RS-GARCH-jump) model. More specifically, we derive the risk neutral dynamics and propose a lattice algorithm to price European and American options in this framework. We also provide a method of parameter estimation in our RS-GARCH-jump setting using historical data on the underlying time series. To measure the pricing performance of the proposed algorithm, we investigate the convergence of the tree-based results to the true option values and show that this algorithm exhibits good convergence. By comparing the pricing results of RS-GARCH-jump model with regime-switching GARCH (RS-GARCH) model, GARCH-jump model, GARCH model, Black–Scholes (BS) model, and Regime-Switching (RS) model, we show that accommodating jump effect and regime switching substantially changes the option prices. The empirical results also show that the RS-GARCH-jump model performs well in explaining option prices and confirm the importance of allowing for both jump components and regime switching.

Keywords

GARCH processJumpLattice algorithmOption pricingRegime switching
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 4 , October 2022 , pp. 1138 - 1170
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Avriel, M., Hilscher, J., & Raviv, A. (2013). Inflation derivatives under inflation target regimes. Journal of Futures Markets 33(10): 911–938.CrossRefGoogle Scholar
Ben-Ameur, H., Breton, M., & Martinez, J.M. (2009). Dynamic programming approach for valuing options in the GARCH model. Management Science 55(2): 252–266.CrossRefGoogle Scholar
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31(3): 307–327.CrossRefGoogle Scholar
Cakici, N. & Topyan, K. (2000). The GARCH option pricing model: a lattice approach. Journal of Computational Finance 3(4): 71–85.CrossRefGoogle Scholar
Chan, W.H. & Lee, H.-T. (2015). A regime switching correlated bivariate Poisson jump model for futures hedging. Empirical Economics 28(4): 669–685.CrossRefGoogle Scholar
Chan, W.H. & Young, D. (2009). A new look at copper markets: a regime-switching jump model. University of Alberta, Department of Economics.Google Scholar
Chen, C.C. & Hung, M.Y. (2010). Option pricing under Markov-switching GARCH processes. Journal of Futures Markets 30(5): 444–464.Google Scholar
Christoffersen, P., Elkamhi, R., Feunou, B., & Jacobs, K. (2010). Option valuation with conditional heteroskedasticity and nonnormality. The Review of Financial Studies 23(5): 2139–2183.CrossRefGoogle Scholar
Christoffersen, P., Jacobs, K., & Ornthanalai, C. (2012). Dynamic jump intensities and risk premiums: evidence from S&P500 returns and options. Journal of Financial Economics 106(3): 447–472.CrossRefGoogle Scholar
Duan, J.C. (1995). The GARCH option pricing model. Mathematical Finance 5(1): 13–32.CrossRefGoogle Scholar
Duan, J.C. & Simonato, J.G. (2001). American option pricing under GARCH by a Markov chain approximation. Journal of Economic Dynamics and Control 25(11): 1689–1718.CrossRefGoogle Scholar
Duan, J.C., Ritchken, P.H., & Sun, Z. (2006). Jump starting GARCH pricing and hedging option with jumps in returns and volatilities. FRB of Cleveland Working Paper.Google Scholar
Elliott, R.J., Siu, T.K., & Chan, L. (2006). Option pricing for GARCH models with Markov switching. International Journal of Theoretical and Applied Finance 9(06): 825–841.CrossRefGoogle Scholar
Gray, S.F. (1996). Modeling the conditional distribution of interest rates as a regime-switching process. Journal of Financial Economics 42(1): 27–62.CrossRefGoogle Scholar
Hamilton, J.D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57(2): 357–384.CrossRefGoogle Scholar
Inclán, C. & Tiao, G.C. (1994). Use of cumulative sums of squares for retrospective detection of changes of variance. Journal of the American Statistical Association 89(427): 913–923.Google Scholar
Klaassen, F. (2002). Improving GARCH volatility forecasts with regime-switching GARCH. Empirical Economics 27(2): 363–394.CrossRefGoogle Scholar
Lamoureux, C.G. & Lastrapes, W.D. (1990). Persistence in variance, structural change, and the GARCH model. Journal of Business & Economic Statistics 8(2): 225–234.Google Scholar
Lee, H.T. (2009). Optimal futures hedging under jump switching dynamics. Journal of Empirical Finance 16(3): 446–456.CrossRefGoogle Scholar
Lin, B.H. & Yeh, S.K. (2004). On the distribution and conditional heteroscedasticity in Taiwan stock prices. Journal of Multinational Financial Management 10(3): 367–395.CrossRefGoogle Scholar
Lin, B.H., Hung, M.W., Wang, J.Y., & Wu, P.D. (2013). A lattice model for option pricing under GARCH-jump processes. Review of Derivatives Research 16(3): 295–329.Google Scholar
Lyuu, Y.D. & Wu, C.N. (2005). On accurate and provably efficient GARCH option pricing algorithms. Quantitative Finance 5(2): 181–198.CrossRefGoogle Scholar
Marcucci, J. (2005). Forecasting stock market volatility with regime-switching GARCH models. Studies in Nonlinear Dynamics & Econometrics 9(4): 1–54.Google Scholar
Newey, W.K. & West, K.D. (1994). Automatic lag selection in covariance matrix estimation. The Review of Economic Studies 61(4): 631–653.CrossRefGoogle Scholar
Perez-Quiros, G. & Timmermann, A. (2001). Business cycle asymmetries in stock returns: evidence from higher order moments and conditional densities. Journal of Econometrics 103(1): 259–306.CrossRefGoogle Scholar
Rapach, D.E. & Strauss, J.K. (2008). Structural breaks and GARCH models of exchange rate volatility. Journal of Applied Econometrics 23(1): 65–90.CrossRefGoogle Scholar
Ritchken, P. & Trevor, R. (1999). Pricing options under generalized GARCH and stochastic volatility processes. Journal of Finance 54(1): 377–402.CrossRefGoogle Scholar
Rombouts, J.V.K. & Stentoft, L. (2011). Multivariate option pricing with time varying volatility and correlations. Journal of Banking & Finance 35(9): 2267–2281.CrossRefGoogle Scholar
Sansó, A., Carrion, J.L., & Aragó, V. (2004). Testing for changes in the unconditional variance of financial time series. Revista de Economía Financiera 4: 32–52.Google Scholar
Satoyoshi, K. & Mitsui, H. (2011). Empirical study of Nikkei 225 options with the Markov switching GARCH model. Asia-Pacific Financial Markets 18(1): 55–68.CrossRefGoogle Scholar
Shi, Y. & Feng, L. (2016). A discussion on the innovation distribution of the Markov regime-switching GARCH model. Economic Modelling 53: 278–288.CrossRefGoogle Scholar
Simonato, J.G. (2019). American option pricing under GARCH with non-normal innovations. Optimization and Engineering 20(3): 853–880.CrossRefGoogle Scholar