‘Finance’ is one of the fastest developing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods; the area is an expanding source for novel and relevant ‘real-world’ mathematics. The demand from financial institutions for well-qualified mathematicians is substantial, and there is a corresponding need for professional training of existing staff. Since 1992 the authors of this book have, in response, given graduate and undergraduate level courses on the subject. We have also organised a series of professional development courses for practitioners, held in Oxford and New York, with the assistance of Oxford University's Department for Continuing Education and the Oxford Centre for Industrial and Applied Mathematics. The material and notes from these courses became a book, Option Pricing: Mathematical Models and Computation, an advanced yet accessible account of applied and numerical techniques in the area of derivatives pricing.

Following the success of Option Pricing among financial practitioners, we have written this student-oriented version as an introduction to the subject. Our aim in The Mathematics of Financial Derivatives: A Student Introduction is to introduce the principles in a clear and readable way while leaving the more advanced topics and detailed practicalities, especially numerical issues, to the earlier book.

In what follows we describe the modelling of financial derivative products from an applied mathematician's viewpoint, from modelling through analysis to elementary computation.