Minimal Variance Hedging of Options with Student-t Underlying

TL;DR

This paper derives explicit closed-form optimal hedging strategies for European call options when the underlying asset follows a Student-t distribution, highlighting the impact of fat tails on option hedging.

Contribution

It provides the first explicit solutions for hedging strategies under Student-t distributed returns, extending classical models to account for fat-tailed risks.

Findings

Closed-form solutions for hedging strategies with Student-t underlying

Illustrates the effect of fat tails on option hedging

Serves as an example for options in heavy-tailed environments

Abstract

I explicitly work out closed form solutions for the optimal hedging strategies (in the sense of Bouchaud and Sornette) in the case of European call options, where the underlying is modeled by (unbiased) iid additive returns with Student-t distributions. The results may serve as illustrative examples for option pricing in the presence of fat tails.