Risk-neutral valuation: Pricing and hedging of financial derivatives
This book is for students of economics, finance, financial engineering, mathematics and statistics with pre-knowledge in statistics and probability theory. It has eight chapters. It begins with the background of financial derivatives in chapter 1, followed by the mathematical background in chapter 2. Chapter 3 describes stochastic processes in discrete time. An application to mathematical finance in discrete time follows in chapter 4. The corresponding treatment in continuous time is treated in chapter 5 and 6. The remaining chapters treat incomplete markets and interest rate models. Chapter 1 (Derivative Background) describes the financial markets and instruments, arbitrage, arbitrage relationships, and single period market models. Chapter 2 (Probability Background) treats the measure, the integral, and the probability. It follows equivalent measures, and Radon-Nikodým derivatives, conditional expectations, properties of conditional expectations. This chapter closes with modes of convergence, convolution and characteristic functions, and the central limit theorem. Chapter 3 (Stochastic Processes in Discrete Time) begins with information and filtration, discrete parameter martingales. It follows martingale transforms, stopping times and optimal stopping, and the Snell envelop. Chapter 4 (Mathematical Finance in Discrete Time) describes the model, the existence of equivalent martingale measures, complete markets, and the risk neutral pricing. Further the Cox-Rows-Rubinstein model, binominal approximations (under others the Black-Scholes option pricing formula), multifactor models, and further claim valuation in discrete time are treated. Chapter 5 (Stochastic Processes in Continuous Time) regards filtrations, finite-dimensional distributions, classes of processes, the Brownian motion, stochastic integrals, Itô calculus, Itô's lemma, and stochastic differential equations. It ends with stochastic calculus for Black-Schole models and weak convergence of stochastic processes. Chapter 6 (Mathematical Finance in Continuous Time) treats continuous time financial market models, the generalized Black-Scholes model, further contingent claim valuation (different options), discrete-versus-continuous-time models and further applications (future and currency markets. Chapter 7 (Incomplete Markets) regards pricing in incomplete markets, hedging in incomplete markets, and stochastic volatility models. Chapter 8 (Interest Rate Theory) treats the bond market, short rate models, the Heath-Jarrow-Morton methodology, and pricing and hedging contingent claims.
scientific article; zbMATH DE number 1195016