European Option Pricing with Transaction Costs and Stochastic Volatility: an Asymptotic Analysis

TL;DR

This paper derives an asymptotic formula for European call option prices considering stochastic volatility and transaction costs, revealing corrections to the classical Black-Scholes model in the small transaction cost limit.

Contribution

It provides a novel asymptotic expansion for option pricing under combined stochastic volatility and transaction costs, including explicit optimal hedging strategies.

Findings

Black-Scholes price as leading term

Correction terms at order sqrt(ε) and ε

Explicit optimal hedging strategy in Scott's model

Abstract

In this paper the valuation problem of a European call option in presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the option price is obtained. While the dominant term in the expansion it is shown to be the classical Black and Scholes solution, the correction terms appear at $O(\varepsilon^{1/2})$ and $O(\varepsilon)$. The optimal hedging strategy is then explicitly obtained for the Scott's model.