Risk-neutral valuation. Pricing and hedging of financial derivatives.
type: Item
instance of: scholarly article
title: Risk-neutral valuation. Pricing and hedging of financial derivatives.
zbMATH Open document ID: 1058.91029
published in: Springer Finance
publication date: 2004-10-12T00:00:00Z
review text: This book is for students of economics, finance, financial engineering, mathematics and statistics with a preknowledge in statistics and probability theory. It has nine 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, interest rate models, and credit risks. Chapter 1 (Derivative Background) describes the financial markets and instruments, arbitrage, arbitrage relationships, and single period market models. Chapter 2 (Probability Background) begins with measure, integral, probability, equivalent measures and Radon-Nikodym derivatives. Conditional expectations, modes of convergence, convolution and characteristic functions follow. It closes with the central limit theorem, asset return distributions, infinite divisibility and the Lévy-Klintchine formula, elliptically contoured and hyperbolic distributions. Chapter 3 (Stochastic Processes in Discrete Time) begins with information and filtration, discrete-parameter stochastic processes, definition and basic properties of martingales, and martingale transforms. Further, it regards stopping times and optimal stopping, space of martingales and Markov chains. Chapter 4 (Mathematical Finance in Discrete Time) describes the model, the existence of equivalent martingale measures, complete markets, the fundamental theorem of asset pricing, the Cox-Rubinstein model, binominal approximations, american options, further contingent claim valuation in discrete time, and multifactor models. Chapter 5 (Stochastic Processes in Continuous Time) regards filtration, classes of processes, the Brownian motion, point processes, Lévy processes, stochastic integrals (Itô calculus), stochastic calculus fo…
reviewed by: Klaus Ehemann
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 91-02
zbMATH DE Number: 2107174
zbMATH Keywords: stochastic process
zbMATH Keywords: discrete time
zbMATH Keywords: continuous time
zbMATH Keywords: incomplete market
zbMATH Keywords: arbitrage
zbMATH Keywords: credit risks
author: N. H. Bingham
author: Rüdiger Kiesel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2107174