Risk Arbitrage Opportunities for Stock Index Options

Abstract

Research about equity index options has shown that option prices systematically violate rational pricing bounds for the risk-averse representative investor. These results raise the question of whether profitable trading possibilities exist in this market. Standard portfolio optimization does not apply because of the large bid-ask spreads and low quote sizes in this market. Motivated by these complications, a system of linear inequalities is developed that completely characterizes all risk arbitrage opportunities in the presence of transaction costs and portfolio restrictions. The practical use of this system is illustrated with an application to front-month S&P500 stock index options. Small-scale portfolios seem to produce surprisingly large abnormal returns out of sample; outperformance, however, seems elusive for institutional investors because of the limited quote size, possibly reflecting data limitations.

Optimal measure preserving derivatives revisited

“…The results in Post and Longarela (2021) and Kleiner, Moldovanu and Strack (2021) discussed in this article establish that risk aversion is indeed the central issue relevant to understanding pricing kernel nonmonotonicity. Propositions 1 and 2 and Examples 1 and 2 in this article establish that it is the technical condition of adequacy imposed in Dybvig (1988) which broadens the set of stochastic arbitrage opportunities available under pricing kernel nonmonotonicity to include replicating portfolios.…”

“…The equivalence of conditions (ii) and (iii) in Proposition 1 is implied by Theorem 1 in Post and Longarela (2021) under the additional requirement that µ has finite support. The equivalence of conditions (i) and (iii) in Proposition 1 follows from the discussion in Section S.2.2 of the supplementary material to Kleiner, Moldovanu and Strack (2021) under the additional requirements that µ is atomless, that π is µ-essentially bounded, and that X is integrable.…”

“…This has important implications for the computation of stochastic arbitrage opportunities in practice, which necessarily involves dealing with market frictions and incompleteness. The key methodological contributions to this subject are contained in Constantinides, Jackwerth and Perrakis (2009) and Post and Longarela (2021). In the former article, a linear program was devised whose infeasibility implies the existence of opportunities for stochastic arbitrage in the sense of second-order stochastic dominance.…”

“…Two recent articles motivate my pursuit of this goal. The first is Post and Longarela (2021). Theorem 1 therein establishes, in a general setting permitting an incomplete options market and nonzero bid-ask spreads for option prices, that a necessary and sufficient condition for the existence of a stochastic arbitrage opportunity defined in the sense of second-order stochastic dominance is the nonexistence of a monotone pricing kernel implying option prices within the observed bid-ask ranges.…”

“…Two questions naturally arise. The first is the extent to which the distinction between the two characterizations of pricing kernel monotonicity hinges on the differing conditions -adequacy in Dybvig (1988) and finite support in Post and Longarela (2021) -placed on µ. Neither of these conditions on µ implies the other.…”