A Discrete-Time Hedging Framework with Multiple Factors and Fat Tails: On What Matters

Abstract

Abstract This article presents a quadratic hedging framework for a general class of discrete-time affine multi-factor models and investigates the extent to which multi-component volatility factors, fat tails, and a non-monotonic pricing kernel can improve the hedging performance. A semi-explicit hedging formula is derived for our general framework which applies to a myriad of the option pricing models proposed in the discrete-time literature. We conduct an extensive empirical study of the impact of modelling features on the hedging effectiveness of S&P 500 options. Overall, we find that fat tails can be credited for half of the hedging improvement observed, while a second volatility factor and a non-monotonic pricing kernel each contribute to a quarter of this improvement. Moreover, our study indicates that the added value of these features for hedging is different than for pricing. A robustness analysis shows that a similar conclusion can be reached when considering the Dow Jones Industrial Average. Finally, the use of a hedging-based loss function in the estimation process is investigated in an additional robustness test, and this choice has a rather marginal impact on hedging performance.