Recipes for hedging exotics with illiquid vanillas

TL;DR

This paper develops practical methods for optimally hedging exotic options with illiquid vanilla options, considering execution costs and complex market dynamics, using variational techniques for efficient computation.

Contribution

It introduces a novel approach combining market and stochastic volatility models with variational methods to compute optimal hedging strategies for exotic options.

Findings

Hedging strategies can be efficiently computed using simple approximations.

The approach accounts for execution costs in vanilla options trading.

Optimal hedging reduces risk in exotic options portfolios.

Abstract

In this paper, we address the question of the optimal Delta and Vega hedging of a book of exotic options when there are execution costs associated with the trading of vanilla options. In a framework where exotic options are priced using a market model (e.g. a local volatility model recalibrated continuously to vanilla option prices) and vanilla options prices are driven by a stochastic volatility model, we show that, using simple approximations, the optimal dynamic Delta and Vega hedging strategies can be computed easily using variational techniques.