Choice Reviews Online · 2003 · 146 citations · 0 references
BusinessFinanceMathematicsDerivativesFinancial EconomicsStochastic ProcessesBrownian MotionDerivative PricingFinancial MathematicsStochastic CalculusStochastic Differential EquationsStochastic VolatilityBlack-scholes ModelJump DynamicsJump Risk PricingJump-diffusion ModelsStochastic Processes In FinanceStochastic Volatility ModelsStochastic Volatility PricingStochastic Volatility With Jumps
Finance exemplifies the successful application of advanced mathematics to pricing financial derivatives. The book serves as a first course in financial calculus for mathematically prepared students. It introduces martingales, change of measure, Brownian motion, and stochastic calculus in discrete time, derives the Black‑Scholes formula, then expands to sophisticated models and advanced topics such as jumps and stochastic volatility. The book offers many exercises and examples that demonstrate the application of the concepts to realistic financial problems.
Finance provides a dramatic example of the successful application of advanced mathematical techniques to the practical problem of pricing financial derivatives. This self-contained 2002 text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus: proofs in the continuous-time world follow naturally. The Black-Scholes pricing formula is first derived in the simplest financial context. The second half of the book is then devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts can be applied to realistic financial questions.