Stochastic dominance bounds on American option prices in markets with frictions, Working paper

Abstract. We derive equilibrium restrictions on the range of the transaction prices of American options on the stock market index and index futures. Trading over the lifetime of the options is accounted for, in contrast to earlier single-period results. The bounds on the reservation purchase price of American puts and the reservation write price of American calls are tight. We allow the market to be incomplete and imperfect due to the presence of proportional transaction costs in trading the underlying security and due to bid-ask spreads in option prices. The bounds may be derived for any given probability distribution of the return of the underlying security and admit price jumps and stochastic volatility. We assume that at least some of the traders maximize a time- separable utility function. The bounds are derived by applying the weak notion of stochastic dominance and are independent of a trader’s particular utility function and initial portfolio position. 1