In this tutorial we will investigate the Monte Carlo simulation method for use in valuing financial derivatives.

Monte Carlo simulations is a way of solving probabilistic problems by numerically simulating many possible scenarios so that you may calculate statistical properties of the outcomes, such as expectations, variances of probabilities of certain outcomes. In the case of Financial Derivatives, this gives us a handy tool for which to price complex derivatives for which and analytical formulae is not possible.

First used by Boyle in 1977, Monte Carlo simulation provides an easy way to deal with multiple random factors and the incorporation of more realistic asset price processes such as jumps in asset prices. Valuation of Financial Derivatives through Monte Carlo Simulations is only possible by using the Financial Mathematics of Risk-Neutral Pricing and simulating risk-neutral asset paths.

The mathematic notation and examples are from Les Clewlow and Chris Strickland's book Implementing Derivatives Models.

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00:00 Intro
01:05 What is Monte Carlo?
05:56 Accuracy Improvements
07:27 Valuation by Monte Carlo Simulation
10:00 European Call Option Modelling
14:38 Real World Example
27:02 Visualising your results

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