Pricing S&P 500 Index Options with L\'evy Jumps

TL;DR

This paper evaluates various jump models, including Le9vy processes, for pricing S&P 500 options, demonstrating the superior performance of the NIG model in both in-sample and out-of-sample predictions.

Contribution

It introduces a comprehensive comparison of Le9vy jump models with traditional models for S&P 500 options, highlighting the effectiveness of the NIG model.

Findings

NIG model has the lowest SSE in in-sample pricing.

NIG, SV, and SVJ models outperform others in predictive accuracy.

Le9vy jumps are empirically significant for S&P 500 options.

Abstract

We analyze various jumps for Heston model, non-IID model and three L\'evy jump models for S&P 500 index options. The L\'evy jump for the S&P 500 index options is inevitable from empirical studies. We estimate parameters from in-sample pricing through SSE for the BS, SV, SVJ, non-IID and L\'evy (GH, NIG, CGMY) models by the method of Bakshi et al. (1997), and utilize them for out-of-sample pricing and compare these models. The sensitivities of the call option pricing for the L\'evy models with respect to parameters are presented. Empirically, we show that the NIG model, SV and SVJ models with estimated volatilities outperform other models for both in-sample and out-of-sample periods. Using the in-sample optimized parameters, we find that the NIG model has the least SSE and outperforms the rest models on one-day prediction.