We assume that the asset S(t) follows the stochastic differential equation (Geometric Brownian Motion) we have studied in Chapter 8 under the risk-neutral probability: dS(t) = r S(t)dt + σ S(t)d 4W(t), where 4W is the Brownian motion under the risk-neutral probability.We will simulate 10 batches of 5000 paths each (NbTraj = 5000) to price a European put as well as a call. The option value corresponds to the average value of its discounted future payoffs under the risk-neutral probability. We will therefore reproduce the dynamics of future prices of the underlying asset using computers, and calculate next the future payoffs to be obtained by the option holder

PLAIN VANILLA OPTIONS EUROPEAN PUT AND CALL.pdf

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