This node deals with Monte Carlo simulations in the field of finance, more specifically option pricing. There are many other applications of this concept in many other fields.

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The Monte Carlo simluation is used in Finance to estimate the value of a European-style derivative security. In other words, to solve differential equations numerically through trial and error.

Suppose that the value of the option is dependent on two underliers, a stock index and an exchange rate. Monte Carlo simulation might be used to price such an option as follows:

• Randomly generate 10,000 scenarios for the value, on the option's expiration date, of the two underliers. Do so in a manner that is consistent with an assumed (risk neutral) joint probability distribution of the two variables.
• Determine what the option's expiration value would be under each of the 10,000 scenarios.
• Form a histogram of those results. This represents a discrete approximation for the probability distribution of the option's expiration value. The discounted mean of the histogram is the estimated option price.

This simulation is numerically efficient when there are multiple variables, as the time it takes to execute a Monte Carlo simulation increases linearly as the number of variables increase, whereas for most other procedures it increases exponentially. One of the drawbacks is that it can only be used with European options.