A Benchmark Approach to Quantitative Finance

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2006, 1st
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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 optimisation, derivative pricing, integrated risk managemetn and insurance risk modeling. Th 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 fromprobability theory, statistics, stochastic calculus and the theory of stochastic differential equations with jumps. The second part of devoted to financial modeling by the benchmark approach. Various quajtitative methods for the real-world 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 methematically rigorous introduction to quantitative finance for readers that have a reasonable mathematical or quantitative background. Finally, the book hsould stimulate inetrest in the benchmark approach by describing some of its power and wide applicability.
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