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Book Cover
Author Platen, Eckhard

Title A benchmark approach to quantitative finance / Eckhard Platen, David Heath
Published Berlin ; New York : Springer, 2006


Description 1 online resource (xvi, 700 pages) : illustrations
Series Springer finance
Springer finance.
Contents Preliminaries -- Statistical Methods -- Modeling via Stochastic Processes -- Diffusion Processes -- Martingales and Stochastic Integrals -- The Ito Integral or Stochastic Chain Rule -- Stochastic Differential Equations -- Continuous Benchmark Models -- Introduction to Option Pricing -- Various Approaches to Asset Pricing -- Numerical Methods for Derivatives Pricing -- Pricing of Derivatives -- Benchmark Models with Jumps
Summary The benchmark approach provides a general framework for financial market modeling, which extends beyond the standard risk neutral pricing theory. It permits a unified treatment of portfolio optimization, derivative pricing, integrated risk management and insurance risk modeling. The existence of an equivalent risk-neutral pricing measure is not required. Instead, it leads to pricing formulae with respect to the real world probability measure. This yields important modeling freedom which turns out to be necessary for the derivation of realistic, parsimonious market models. The first part of the book describes the necessary tools from probability theory, statistics, stochastic calculus and the theory of stochastic differential equations with jumps. The second part is devoted to financial modeling under the benchmark approach. Various quantitative methods for the fair pricing and hedging of derivatives are explained. The general framework is used to provide an understanding of the nature of stochastic volatility. The book is intended for a wide audience that includes quantitative analysts, postgraduate students and practitioners in finance, economics and insurance. It aims to be a self-contained, accessible but mathematically rigorous introduction to quantitative finance for readers that have a reasonable mathematical or quantitative background. Finally, the book should stimulate interest in the benchmark approach by describing some of its power and wide applicability
Bibliography Includes bibliographical references (pages 669-683)-and indexes
Notes English
Print version record
In Springer e-books
Subject Finance -- Mathematical models.
Risk -- Mathematical models
Finance -- Mathematical models.
Risk -- Mathematical models.
Finance -- Mathematical models.
Risk -- Mathematical models.
Form Electronic book
Author Heath, David
ISBN 9783540478560