Stochastic arbitrage with market index options

TL;DR

This paper investigates the existence of stochastic arbitrage opportunities in options markets, develops optimization models to identify such opportunities, and applies them to 18 years of S&P 500 options data, finding no systematic arbitrage.

Contribution

It introduces linear and mixed-integer linear programming methods to detect stochastic arbitrage opportunities in options markets.

Findings

No systematic stochastic arbitrage opportunities found in 18 years of data.

Market index options pricing aligns with a skewed return distribution model.

Optimization models effectively identify potential arbitrage opportunities.

Abstract

Opportunities for stochastic arbitrage in an options market arise when it is possible to construct a portfolio of options which provides a positive option premium and which, when combined with a direct investment in the underlying asset, generates a payoff which stochastically dominates the payoff from the direct investment in the underlying asset. We provide linear and mixed-integer linear programs for computing the stochastic arbitrage opportunity providing the maximum option premium to an investor. We apply our programs to 18 years of data on monthly put and call options on the Standard & Poors 500 index, finding no evidence that stochastic arbitrage opportunities are systematically present. A skewed specification of the underlying market return distribution with a constant market risk premium and constant multiplicative variance risk premium is broadly consistent with the pricing of market index options at moderate strikes.