Discrete mathematical models and algorithms for stock options valuation

Matic Tovšak (2011) Discrete mathematical models and algorithms for stock options valuation. EngD thesis.

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Abstract

In financial markets, investors are daily exposed to all kinds of investment risks. Choices have to be made under conditions of uncertainty about future the market changes. It is possible to reduce such risks with the use of financial derivatives. These are financial instruments with a value based on some underlying security. Very common financial derivatives are stock options. Because of their complexity, much effort goes into the analysis and development of complex mathematical models. With the help of such models, stock option values can be calculated. Financial industry is therefore a major source of employment for computer engineers. The aim of this thesis is to present discrete mathematical models for stock options' valuation. Another aim is to show how these models can be implemented in the form of a computer algorithm. The first part of thesis focuses on a description of the concepts of financial markets with a general presentation of stock options. The second part provides information on more advanced aspects of valuation and development of the actual computer algorithm for a calculation of the European option value. In the end, path dependent options are presented as well. I focused on presenting how the Asian options work and I described the mathematical procedure for a calculation of the expected option payoff.

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