Hedging of time discrete auto-regressive stochastic volatility options

TL;DR

This paper explores the use of Kalman filtering and hierarchical likelihood methods for pricing and hedging options within discrete auto-regressive stochastic volatility models, highlighting the effectiveness of local risk minimization strategies.

Contribution

It introduces practical implementations of volatility estimation techniques for hedging in incomplete markets modeled by ARSV, emphasizing local risk minimization.

Findings

Local risk minimization is effective for at-the-money options.

Kalman filtering improves volatility estimation accuracy.

Hedging performance varies with option moneyness and hedging frequency.

Abstract

Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor in the description of the log-returns of financial assets. The pricing and hedging of contingent products that use these models for their underlying assets is a non-trivial exercise due to the incomplete nature of the corresponding market. In this paper we apply two volatility estimation techniques available in the literature for these models, namely Kalman filtering and the hierarchical-likelihood approach, in order to implement various pricing and dynamical hedging strategies. Our study shows that the local risk minimization scheme developed by F\"ollmer, Schweizer, and Sondermann is particularly appropriate in this setup, especially for at and in the money options or for low hedging frequencies.