Analysis of a jump-diffusion option pricing model with serially correlated jump sizes

Xenos Chang-Shuo Lin, Daniel Wei-Chung Miao and Wan-Ling Chao

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 4, 953-979

Abstract: This paper extends the classical jump-diffusion option pricing model to incorporate serially correlated jump sizes which have been documented in recent empirical studies. We model the series of jump sizes by an autoregressive process and provide an analysis on the underlying stock return process. Based on this analysis, the European option price and the hedging parameters under the extended model are derived analytically. Through numerical examples, we investigate how the autocorrelation of jump sizes influences stock returns, option prices and hedging parameters, and demonstrate its effects on hedging portfolios and implied volatility smiles. A calibration example based on real market data is provided to show the advantage of incorporating the autocorrelation of jump sizes.

Date: 2018
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DOI: 10.1080/03610926.2017.1315731

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