Pricing of lookback-strike put options with bounded payoff by equivalent martingale measure method

Abstract

There are many types of exotic options on underlying assets in financial markets. Payoff of lookback put option depends on the maximum asset price during the contract period as well as the terminal price, exposing the option issuer to unbounded financial risks. We consider variations of lookback options by imposing barriers or caps which limit potential payoffs. No-arbitrage prices of new options in the Black-Scholes market are derived explicitly based on equivalent martingale measure method . We examine properties of these pricing formulas and calculate fair prices under some hypothetical but realistic market parameters, finding that the price reductions made by barriers or caps are significant.