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Testing Option Pricing Models with Stochastic Volatility, Random Jumps and Stochastic Interest Rates

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  • George J. Jiang

Abstract

In this paper, we propose a parsimonious GMM estimation and testing procedure for continuous‐time option pricing models with stochastic volatility, random jump and stochastic interest rate. Statistical tests are performed on both the underlying asset return model and the risk‐neutral option pricing model. Firstly, the underlying asset return models are estimated using GMM with valid statistical tests for model specification. Secondly, the preference related parameters in the risk‐neutral distribution are estimated from observed option prices. Our findings confirm that the implied risk premiums for stochastic volatility, random jump and interest rate are overall positive and varying over time. However, the estimated risk‐neutral processes are not unique, suggesting a segmented option market. In particular, the deep ITM call (or deep OTM put) options are clearly priced with higher risk premiums than the deep OTM call (or deep ITM put) options. Finally, while stochastic volatility tends to better price long‐term options, random jump tends to price the short‐term options better, and option pricing based on multiple risk‐neutral distributions significantly outperforms that based on a single risk‐neutral distribution.

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  • George J. Jiang, 2002. "Testing Option Pricing Models with Stochastic Volatility, Random Jumps and Stochastic Interest Rates," International Review of Finance, International Review of Finance Ltd., vol. 3(3‐4), pages 233-272, September.
    • Handle: RePEc:bla:irvfin:v:3:y:2002:i:3-4:p:233-272
    DOI: 10.1111/j.1369-412X.2002.00040.x
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    2. Liu, Dehong & Liang, Yucong & Zhang, Lili & Lung, Peter & Ullah, Rizwan, 2021. "Implied volatility forecast and option trading strategy," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 943-954.
    3. Bates, David S., 2008. "The market for crash risk," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2291-2321, July.
    4. Bing-Huei Lin & Mao-Wei Hung & Jr-Yan Wang & Ping-Da Wu, 2013. "A lattice model for option pricing under GARCH-jump processes," Review of Derivatives Research, Springer, vol. 16(3), pages 295-329, October.

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