Stochastic Dominance Option Bounds and Nth Order Arbitrage Opportunities

Abstract

In this paper we first derive optimal N th order stochastic dominance option bounds from concurrently expiring options. These bounds are given by pricing kernels that have piecewise constant (N − 2)th derivatives.Using numerical examples we show that option bounds are improved significantly when we raise the order of stochastic dominance rules. When these option bounds are violated there are N th order arbitrage opportunities interpreted as the comparison of (weighted average) conditional expected returns. We then establish the way to make profits from these arbitrage opportunities in option markets.

Option Bounds and Second Order Arbitrage Opportunities

“…This paper is closely related to Huang (2004bHuang ( , 2004c. Huang (2004bHuang ( , 2004c improved higher order stochastic dominance option bounds and DARA (DRRA) option bounds by using the observed prices of concurrently expiring options.…”