Quantum Finance

Path Integrals and Hmailtonians for Options and Interest Rates

Belal E. Baaquie

316 pages, parution le 03/11/2004

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Résumé

The primary aim of this book is to apply the mathematical and conceptual formalism of quantum mechanics and quantum field theory, with particular emphasis on the path integral, to the theory of options and to the modeling of interest rates.

Financial mathematics is currently almost completely dominated by stochastic calculus. What is unique about the present book is that it offers a formulation completely independent of that approach. Many new results emerge from the ideas developed by the author. Barrier options and other path-dependent options can be expressed and solved using Hamiltonians and path integration. Nonlinear processes such as stock options with stochastic volatility can be solved exactly using path integration, and yield efficient numerical algorithms.

A two-dimensional quantum field theory of forward interest rates is discussed, and a detailed empirical study shows that the field theory model is in excel lent agreement with market data. The modelling of nonlinear field theories is beyond the scope of stochastic calculus, and hence quantum field theory is indispensable in describing the behaviour of nonlinear forward rates that are given a precise mathematical formulation in terms of path integrals. A nonlinear field theory of forward interest rates with stochastic volatility is defined, and it is shown how the Hamiltonian of the forward interest rates exactly solves the martingale condition for such non linear theories.

This pioneering work will be of interest to physicists and mathematicians working in the field of finance, to quantitative analysts in banks and finance firms, to practitioners in the field of fixed income securities and foreign exchange, and can also be used as a graduate text for courses on financial physics and financial mathematics.

Sommaire

Foreword
Preface
Synopsis
Fundamental Concepts of Finance
- Introduction to finance
- Derivative securities
Systems with finite number of degrees of freedom
- Hamiltonians and stock options
- Path integrals and stock options
- Stochastic interest rates' Hamiltonians and path integrals
Quantum Field Theory of Interest Rates Models
- Quantum field theory of forward interest rates
- Empirical forward interest rates and field theory models
- Field theory of derivatives and hedging of treasury bonds
- Field theory Hamiltonian of forward interest rates
- Conclusions

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Belal E. Baaquie
Parution	03/11/2004
Nb. de pages	316
Format	18 x 25,5
Couverture	Broché
Poids	853g
Intérieur	Noir et Blanc
EAN13	9780521840453
ISBN13	978-0-521-84045-3