Title:
PLAIN-VANILLA-OPTIONS-EUROPEAN-PUT-AND-CALL
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Description: 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
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