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A European lookback option is a path-dependent option whose payo? at maturity depends on the maximum/minimum price of the underlying asset before maturity. There are two types of lookback options, namely ?xed strike and ?oating strike. The payo? at maturity T for the ?xed strike call option is (MT −K)+,and the payo? at maturity T for the ?oating strike call option is ST −mT, where MT = max 0≤t≤T{St} and mT = min 0≤t≤T{St}. Assume the price of the underlying asset follows Geometric Brownian motion with S0 = 90, r = 2%, σ = 20%. Also assume K = 100,T = 1. Use n = 100,000 samples to simulate the prices of both ?oating strike call option and ?xed strike call opton, and create 95% con?dence intervals for both.
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