A floating (strike) European lookback call and a floating (strike) European lookback put, on a nondividend paying stock, both expire at date T.

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.