Article

Arbitrage Opportunities in Misspecified Stochastic Volatility Models

arXiv.org, Quantitative Finance Papers 02/2010; 2(1002.5041). DOI: 10.1137/100786678
Source: RePEc

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.

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Peter Tankov