Empirical Performance of Option Pricing Models Based on Time-Changed Lévy Processes

Abstract

In reaction to the well-known stylized facts observed in market data for stocks and options, a multitude of option pricing models beyond Black-Scholes (BS) have been developed relaxing the strict BS assumptions. While these models by construction outperform the BS model in terms of fitting observed option prices, there is only little knowledge on which models are best with respect to other – practically relevant – criteria such as hedging performance or stability. In order to close this gap, we conduct a comprehensive empirical comparison of a wide range of option pricing models based on time-changed Levy processes. This broad and flexible model class unifies the strands of affine jump-diffusion models and pure jump models and therefore allows to consistently construct models including general jump structures, a stochastic volatility and the leverage effect. In contrast to most existing studies, our model assessment is not restricted to the fitting performance, but also takes into account aspects like hedging, model stability, the exposure to risks arising from the model calibration and the ability to explain observed prices of exotic options. The main findings of this paper are: (i) Complex models including jumps, a stochastic volatility and the leverage effect tend to be over-parameterized leading to unstable prices of exotic options and expensive hedging procedures. (ii) The protection against jump risks leads to a weaker minimum variance hedging performance putting the use of jump models into question. (iii) Observed market prices for exotic options indicate to be built by models without jumps. (iv) The overall best results are achieved in the model of Heston.