Top

Review of Derivatives Research

Published in:

01-01-2021

Bayesian estimation of the stochastic volatility model with double exponential jumps

Author: Jinzhi Li

Published in: Review of Derivatives Research | Issue 2/2021

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This paper generalizes the stochastic volatility model to allow for the double exponential jumps. To derive the jumps and time-varying volatility in returns, we implement an efficient Markov chain Monte Carlo approach based on the band and sparse matrix algorithms used in Chan and Hsiao (SSRN Electron J., 2013, https://doi.org/10.2139/ssrn.2359838) to estimate this model. We illustrate the the methodology using the daily data for the Shanghai Composite Index, Hangseng Index, Nikkei 225 Index and Kospi Index. We find that the stochastic volatility model with double exponential jumps provide better fitness in sample period.

previous article A model-free approach to multivariate option pricing

next article The value of power-related options under spectrally negative Lévy processes

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Asgharian, H., & Bengtsson, C. (2006). Jump Spillover in International Equity Mar kets. Journal of Financial Econometrics, 4(2), 167–203.CrossRef

Bates, D. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Review of Financial Studies, 9, 69–107. CrossRef

Boscher, H., Fronk, E. M., & Pigeot, I. (2000). Forecasting interest rates volatilities by GARCH (1,1) and stochastic volatility models. Statistical Papers, 41(4), 409–422.CrossRef

Chan, J. C. C., & Hsiao, C. Y. L. (2013). Estimation of Stochastic Volatility Models with Heavy Tails and Serial Dependence. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2359838.

Das, S. R., & Foresi, S. (1996). Exact Solutions for Bond and Option Prices with Systematic Jump Risk. Review of Derivatives Research, 1, 7–24.CrossRef

Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007.

Eraker, B., Johannes, M., & Polson, N. (2003). The impact of jumps in voltility and returns. Journal of Finance, 58(3), 1269–1300.

Fuh, C. D., Luo, S. F., & Yen, J. F. (2013). Pricing discrete path-dependent options under a double exponential jump-diffusion model. Journal of Banking and Finance, 37, 2702–2713.CrossRef

Heynen, R. C., & Kat, H. M. (1994). Volatility prediction: A comparison of stochastic volatility, GARCH(1,1) and EGARCH(1,1) models. The Journal of Derivatives, 2(2), 50–65.

Jacquier, E., Polson, N. G., & Rossi, P. E. (1994). Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics, 12(4), 371–417.

Johannes, M., Kumar, R. and Polson, N. (1999). State Dependent Jump Models: How do U.S. Equity Markets Jump? Working Paper.

Kou, S. G. (2002). A jump diffusion model for option pricing. Management Science, 48(8), 1086–1101.CrossRef

Kou, S. G., & Wang, H. (2004). Option pricing under a double exponential jump diffusion model. Management Science, 50, 1178–1192.CrossRef

Li, H., Wells, M., & Yu, C. (2008). A bayesian analysis of return dynamics with levy jumps. Review of Financial Studies, 21, 2345–2378.CrossRef

Chan, Joshua C. C., & Grant, Angelia L. (2016). Modeling energy price dynamics: GARCH versus stochastic volatility. Energy Economics, 54, 182–189.CrossRef

Numatsi, A., & Rengifo, E. W. (2010). Stochastic volatility model with jumps in returns and volatility: An R-Package implementation. Lecture Notes in Statistics, 196, 191–201.CrossRef

Yu, J. (2002). Forecasting volatility in the New Zealand stock market. Applied Financial Economics., 12(3), 193–202.CrossRef

Ramezani, C. A., & Zeng, Y. (2007). Maximum likelihood estimation of the double exponential jump-diffusion process. Annals of Finance, 3(4), 487–507.CrossRef

Scott, L. (1997). Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: Applications of Fourier inversion methods. Mathematical Finance, 7, 413–426.CrossRef

Taylor, S. J. (1986). Modeling Financial Time Series. New York: John Wiley.

Title: Bayesian estimation of the stochastic volatility model with double exponential jumps
Author: Jinzhi Li
Publication date: 01-01-2021
Publisher: Springer US
Published in: Review of Derivatives Research / Issue 2/2021
Print ISSN: 1380-6645
Electronic ISSN: 1573-7144
DOI: https://doi.org/10.1007/s11147-020-09173-1