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An Introduction to the mathematics of financial derivatives 3rd ed

This book is an introduction to quantitative tools used in pricing financial derivatives. Hence, it is mainly about mathematics. It is a simple and heuristic introduction to mathematical concepts that have practical use in financial markets. Such an introduction requires a discussion of the logic behind asset pricing. In addition, at various points we provide examples that also require an understanding of formal asset pricing methods. All these necessitate a brief discussion of the securities under consideration. This introductory chapter has that aim. Readers can consult other books to obtain more background on derivatives. Hull (2009) is an excellent source for derivatives. Jarrow and Turnbull (1996) gives another approach. The more advanced books by Ingersoll (1987) and Duffie (1996) provide strong links to the underlying theory. The manual by Das (1994) provides a summary of the practical issues associated with derivative contracts. A comprehensive new source is Wilmott (1998). This chapter first deals with the two basic building blocks of financial derivatives: options and forwards (futures). Next, we introduce the more complicated class of derivatives known as swaps. The chapter concludes by showing that a complicated swap can be decomposed into a number of forwards and options. This decomposition is very practical. If one succeeds in pricing forwards and options, one can then reconstitute any swap and obtain its price. This chapter also introduces some formal notation that will be used throughout the book. the underlying asset St at time t. The financial derivative is sometimes assumed to yield a payout dt. At other times, the payout is zero. T will always denote the expiration date.

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