VOLATILITY MISSPECIFICATION, OPTION PRICING AND SUPERREPLICATION VIA COUPLING

Consider the performance of an options writer who misspecifies the dyn amics of the price process of the underlying asset by overestimating a sset price volatility. When does he overprice the option? If he follow s the hedging strategy suggested by his model, when does the terminal value of his strategy dominate the option payout? We show that both th ese events happen if the option payoff is a convex function of the pri ce of the underlying at maturity. The proofs involve the simple, power ful and intuitive techniques of coupling.