The Stochastic Dominance Violation of Index Call Options in the Presence of Market Makers

Abstract

Finance researchers have been debating over whether index options are overpriced. Most debates have focused on expensive out-of-the-money put options. However, the stochastic dominance literature has argued that S & P 500 Index call options are frequently overpriced in the sense that every rational agent can improve her expected utility by writing these call options that violate the stochastic dominance upper bound. Hence, expensive index call options are also an unsolved puzzle in the finance literature. On the other hand, recent finance papers find that market makers play an important role in the pricing of index options. In this paper, I explore how constrained market makers interact with heterogeneity in beliefs and index option prices. Specifically, I develop an equilibrium model that accommodates previous empirical/theoretical results related to heterogeneity in beliefs, limits or arbitrage, and the role of market makers. The incremental findings from my model can be summarized as follows. First, even with the presence of market makers, the stochastic dominance upper bound violation of index call options occurs when heterogeneity in beliefs is sufficiently large. This result is novel, insomuch as someone may argue that if heterogeneous end-users share the risk themselves, heterogeneity in the presence of constrained market makers may not lead to option mispricing. Second, as the market maker is more constrained, the stochastic dominance upper bound violation becomes more severe. This paper is related to and contributes to the growing literature on the puzzle of index options. In addition, this paper complements the literature on the role of market makers in index option markets and the stochastic dominance literature.