During the past decade many sophisticated mathematical and computational techniques have been developed for analyzing financial markets. Students and professionals intending to work in any area of finance must not only master advanced concepts and mathematical models but must also learn how to implement these models computationally. This comprehensive text combines a thorough treatment of the theory and mathematics behind financial engineering with an emphasis on computation, in keeping with the way financial engineering is practiced in today's capital markets. Unlike most books on investments, financial engineering, or derivative securities, the book starts from basic ideas in finance and gradually builds up the theory. The advanced mathematical concepts needed in modern finance are explained at accessible levels.