In a previous post, we presented a methodology for pricing European options using a closed-form formula. In this installment, we price these options using a numerical method. Specifically, we will use Monte Carlo simulation. Recall that,
where ST denotes the stock price at expiration and K is the strike price. To price these options, we first simulate the price paths using the following Stochastic Differential Equation: where
The simulation is carried out until the options’ maturity. We then apply the terminal payoff functions and calculate the mean values of all the payoffs. Finally, we discount the mean values to the present and thus obtain the option values. For a more detailed presentation of the Monte Carlo method, see Reference [1]. The picture below shows the call and put option prices using 100000 simulations. All other parameters are the same as in the previous post. We compare the above results to the ones obtained by using a third-party software and notice that they are in good agreement. In the next installment, we will present a methodology for pricing American options using Monte Carlo simulation. References [1] Glasserman, Paul; Monte Carlo Methods in Financial Engineering, Springer; 2003
Follow the link below to download the Python program. Post Source Here: Valuing European Options Using Monte Carlo Simulation-Derivative Pricing in Python
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