Question

A floating (strike) European lookback call and a floating (strike) European lookback put, on a nondividend paying stock, both expire at date T. At date t<=T, the underlying stock price approaches zero. [a] Please deduce the lookback call price at t, c(t). Please justify your reasoning without using complex formulas. [b] Please deduce the lookback put price at t, p(t). Please justify your reasoning without using complex formulas.

Answer 1

A floating lookback option is an exotic option whose strike price is determined at the time of the option's maturity, based upon the underlying assets price during the option's lifetime. Hence, in case of a floating call lookback, the option's strike price would be equal to the lowest price possessed by the underlying asset during the option's lifetime. In case of a floating put lookback, the option's strike price would be equal to the highest price possessed by the underlying asset during the option's lifetime.

(a) If the underlying asset price is close to zero at t, then call lookback price = call lookback's intrinsic value = Underlying Asset Price - Strike Price = S(t) - 0 = 0 - 0 = 0  

(b) Let the underlying asset's highest price be S(max) during the option's lifetime. Then put lookback intrinsic value = p(t) = Put Lookback strike price - Underlying asset price at t = S(max) - 0 = S(max)