This research concerns valuing European options. The goal of this paper is to explain how to implement the Black Scholes model for option valuation. We calculate the expected value of the options and of the Radon Nikodym derivative, which is a random variable. Furthermore, we use that for large number of N (number of paths) in a Monte Carlo simulation, the call or put option price at time t under the risk neutral measure Q, is equal to the option price at time t under the probability measure P multiplied by the Radon Nikodym derivative.

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