Arbitrage Opportunities in Misspecified Stochastic volatility Models

TL;DR

This paper investigates arbitrage opportunities arising from model misspecification in stochastic volatility models, providing strategies to maximize arbitrage profits and reinterpretations of classical options in this context.

Contribution

It introduces a framework for identifying arbitrage in misspecified stochastic volatility models and offers new insights into classical options as near-optimal arbitrage strategies.

Findings

Explicit arbitrage strategies are derived for misspecified models.

Classical butterfly and risk reversal options are shown to be near-optimal arbitrage tools.

Numerical examples demonstrate the strategies' effectiveness including transaction costs.

Abstract

There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study these opportunities in a generic stochastic volatility model and exhibit the strategies which maximize the arbitrage profit. In the case when the misspecified dynamics is a classical Black-Scholes one, we give a new interpretation of the classical butterfly and risk reversal contracts in terms of their (near) optimality for arbitrage strategies. Our results are illustrated by a numerical example including transaction costs.