The use of Monte Carlo methods for option pricing

Rok Povšič (2013) The use of Monte Carlo methods for option pricing. EngD thesis.

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Abstract

An option is a contract which gives the owner (buyer) of the option the right, but not obligation, to buy or sell the underlying financial instrument at a predetermined price on a specified future date or multiple dates. They are part of a broader class of financial instruments known as derivatives. Because an option is a contract that gives the owner the right and not the obligation to buy/sell, it is intuitive that its price should be greater than 0. That is true; however, it is harder to determine exactly what the price should be. Therefore, in the last 50 years, multiple algorithms were developed, which, under certain assumptions, determine the correct option price. Monte Carlo methods are one of those algorithms, which use probability theory and pseudorandom numbers to valuate options. The aim of this thesis is to present Monte Carlo methods and their use in the valuation of options. We will describe financial markets and characteristics of derivatives. We will look at how pseudorandom numbers are generated and how to use them with Monte Carlo methods. The theory behind Monte Carlo methods will be shown, together with the assessment of their accuracy. Algorithms will be implemented in Matlab programming language.

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