Kou Jump Diffusion Model: An Application to the Standard and Poor 500, Nasdaq 100 and Russell 2000 Index Options

Abstract

This research focuses on the empirical comparative analysis of three models of option pricing: a) the implied volatility daily calibrated Black-Scholes model, b) the Cox and Ross univariate model with the volatility which is a deterministic and inverse function of the underlying asset price and c) the Kou jump diffusion model. To conduct the empirical analysis, we use a diversified sample with options written on three US indexes during 2007: large cap (SP500), Hi-Tech cap (Nasdaq100) and small cap (Russell2000). For the estimation of models parameters, we opted for the data-fitting technique using the trust region reflective algorithm on option prices, rather than the more common maximum likelihood or generalized method of moments on the history of the underlying asset. The analysis that we conducted clearly shows the supremacy of Kou model. We also notice that it provided better results for the Nasdaq100 and Russell2000 index options than for the SP500 ones. Actually, this supremacy comes from the ability of this model to be as close as possible of market participant’s behavior thanks to its double exponential distribution characterized by three main properties: a) leptokurtic feature, b) psychological specificity of investors and c) memory-less feature.

Keywords

• Jump-diffusion, Kou model, Leptokurtic feature, Trust-region-reflective algorithm, US index options