I know that we can use the Black-Scholes framework to price vanilla products like a European call or put, where the payoff only depends on the share price at maturity.
But can we use it to price path dependent options - those options where the payoff depends not only on the price of the underlying at maturity, but on the entire price history over the life of the contract?
Specifically, what part of the model/derivation allows or disallows us to price such path dependent options?
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