Quantitative finance: its development, mathematical foundations, and current scope

The treatment in the book, while quantitative, follows roughly the historicaldevelopment of the subject and accordingly becomes progressively more challenging. This approach conveys some perspective on the evolution of ideas and thesense that the fields development continues to progress. The book begins witha review of the basic arithmetic of compounding and present value as well as the relations among spot and forward interest rates and bond prices. The book then progresses through dividend discount models, Markowitz mean-variance theory, the CAPM, and static portfolio theory based on the expected-utility paradigm. Familiar probability models for marginal distributions of returns and the dynamic behavior of security prices are also discussed. A self-contained module on stochastic calculus is provided, which develops the basic tools through Itô's formula by means of elementary arguments and examples, accessible to those with a basic course in probability. Applications in dynamic portfolio theory, the theory of optimal growth, and dynamic models of equilibrium prices of primary assets is provided as well as treatment of the infuential Lucas ‘tree’ model. The more direct idea of pricing by arbitrage is then introduced as the main theme for the remainder of the book. Arbitrage pricing in a dynamic framework, beginning with the standard Black-Scholes-Merton theory of dynamic hedging and its application to option pricing in the classic setting of geometric Brownian motion follows. Option pricing models bring readers up to the early 2000s and constitute the most quantitatively challenging material in the book.

• ISBN: 978-0-470-43199-3
• Editorial: John Wiley & Sons
• Encuadernacion: Cartoné
• Páginas: 401
• Fecha Publicación: 27/03/2009
• Nº Volúmenes: 1
• Idioma: Inglés