In-Depth Guide to Simulating Paths with the Euler-Maruyama Scheme for Exotic Options Pricing
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In the world of finance, exotic options offer unique payoff structures that are highly sensitive to the path taken by the underlying asset. Traditional pricing models like Black-Scholes are not sufficient for such path-dependent options, so we turn to simulation methods. One of the most efficient methods for simulating asset prices is the Euler-Maruyama scheme, which is used to approximate solutions for stochastic differential equations (SDEs) like the geometric Brownian motion (GBM) that models asset prices.