ルックバック・オプションの値

最近エキゾチック・オプションの一種を勉強しています。Two forms of lookback options exist, which interestingly have payoffs based on opposite extrema of the underlying price. The pricing formula for a fixed-strike lookback call is the same as the Black-Scholes formula for a vanilla call with one additional term added. This term is exp(-rT)*(sigma^2/2r)*S(exp(rt)*N(d)-(S/K)^(-2r/(sigma^2))N(d-(2r/sigma)(sqrt(t)))).
If the vanilla call price is known, then the lookback (fixed strike) can be derived, given that sigma, T, r, S, and K are known. This is possible via a numerical method such as Octave's fsolve.
しかしこの計算式の由来が分かりにくいです。p(max of y > y) is translated to a difference of two normal cdf functions, which makes little sense. The paper, from Hong Kong, appears to assume that the log return and its max follow a joint normal distribution and then takes a variant of the cdf after normalizing with the mean and variance. The paper then performs integration on these normal cdf terms, which is even more difficult to decipher.