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Stochastic Volatility And Jump-Diffusion — Implications On Option Pricing

Author

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  • GEORGE J. JIANG

    (Schulich School of Business, York University, Canada and Faculty of Business and Economics, University of Groningen, The Netherlands)

Abstract

This paper conducts a thorough and detailed investigation on the implications of stochastic volatility and random jump on option prices. Both stochastic volatility and jump-diffusion processes admit asymmetric and fat-tailed distribution of asset returns and thus have similar impact on option prices compared to the Black–Scholes model. While the dynamic properties of stochastic volatility model are shown to have more impact on long-term options, the random jump is shown to have relatively larger impact on short-term near-the-money options. The misspecification risk of stochastic volatility as jump is minimal in terms of option pricing errors only when both the level of kurtosis of the underlying asset return distribution and the level of volatility persistence are low. While both asymmetric volatility and asymmetric jump can induce distortion of option pricing errors, the skewness of jump offers better explanations to empirical findings on implied volatility curves.

Suggested Citation

  • George J. Jiang, 1999. "Stochastic Volatility And Jump-Diffusion — Implications On Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 409-440.
    • Handle: RePEc:wsi:ijtafx:v:02:y:1999:i:04:n:s0219024999000212
    DOI: 10.1142/S0219024999000212
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    Citations

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    Cited by:

    1. Chan, Kam Fong & Gray, Philip & van Campen, Bart, 2008. "A new approach to characterizing and forecasting electricity price volatility," International Journal of Forecasting, Elsevier, vol. 24(4), pages 728-743.
    2. Robert Tompkins, 2006. "Why Smiles Exist in Foreign Exchange Options Markets: Isolating Components of the Risk Neutral Process," The European Journal of Finance, Taylor & Francis Journals, vol. 12(6-7), pages 583-603.

    More about this item

    Keywords

    Stochastic volatility; jump-diffusion; option pricing; JEL classification code G13; JEL classification code C22; JEL classification code C52;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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