Stochastic Dominance Bounds on Derivative Prices in a Multiperiod Economy with Proportional Transaction Costs

By applying stochastic dominance arguments, upper bounds on the reservation write price of European calls and puts and lower bounds on the reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security. The primary contribution is the derivation of bounds when intermediate trading in the underlying security is allowed over the life of the option. A tight upper bound is derived on the reservation write price of a call and a tight lower bound is derived on the reservation purchase price of a put. These results jointly impose tight upper and lower bounds on the implied volatility.