Prove the following put-call parity relation between the prices of the fixed strike lookback call and floating

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Prove the following put-call parity relation between the prices of the fixed strike lookback call and floating strike lookback put: 

Cfix (S, M, t; X) = Pfe (S, max(M, X), t) + S-Xe-rt. Deduce that ac fix M = 0 for M < X.

Give a financial interpretation why cfix is insensitive to M when M

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