Short Maturity Options and Jump Memory: An Empirical Analysis

Abstract

We investigate "Jump Memory" using an extensive data base of short-term S&P 500 Index options. Jump memory refers to the attenuation of the jump intensity and magnitude parameters following a jump event. Behavioral and rational explanations for this phenomenon are posited. The pricing accuracy of the jump-diffusion model under parameter restrictions is also investigated. A restricted version of the model simplifies estimation, does not appear to degrade pricing accuracy, and permits clearer identification of components of jump memory. Further, a genetic algorithm is shown to be both robust and to produce parameter estimates that significantly improve pricing performance vis a' vis pricing performance when parameters are estimated by a gradient search technique.

Keywords: options, jump-memory, jump-diffusions, SPX, genetic

JEL Classification: G13, G14