Jump-Diffusion Option Pricing without IID Jumps

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. We also 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 without IID jumps.