Jump-diffusion option pricing with non-IID jumps

Lin Zou, António Câmara and Weiping Li
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Lin Zou: Civil Aviation Flight University of China, Guanghan, Sichuan Province 618307, P. R. China
António Câmara: Civil Aviation Flight University of China, Guanghan, Sichuan Province 618307, P. R. China
Weiping Li: Civil Aviation Flight University of China, Guanghan, Sichuan Province 618307, P. R. China

International Journal of Financial Engineering (IJFE), 2025, vol. 12, issue 03, 1-46

Abstract: This paper investigates how violations of the assumption that jumps are identically and independently distributed (IID) affect option prices. We characterize several types of IID jumps violations including jumps with time-varying means, time-varying variances, and time-varying autocorrelations, and analyze the combined effect of these violations on option prices. These IID violations affect option prices in different ways. Different effects of IID violations can either offset each other to eliminate the effect of isolated IID violations or can act as leverages increasing the magnitude of mispricing created by a single violation of the IID assumption. Our investigation is performed inside a new framework for the pricing of options that relaxes the assumption that jumps are IID. We derive three families of jump-diffusion option pricing formulae with non-IID jumps. Numerically and empirically, we show that the non-IID models can improve the BSM on the S&P 500 options for both in-samples and out-of-the-samples data in terms of SSE, AE and ARE.

Keywords: Jump-diffusion process; IID; option price; systematic jump risk; autocorrelated jumps; jumps with time-varying variances (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S2424786323500469

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