"Quantum Finance. Path Integrals and Hamiltonians for Options and Interest Rates" by Belal E. Baaquie

This book applies the mathematics and concepts of quantum mechanics and quantum field theory to the modelling of interest rates and the theory of options. Particular emphasis is placed on path integrals and Hamiltonians. Financial mathematics is dominated by stochastic calculus. The present book offers a formulation that is completely independent of that approach. As such many results emerge from the ideas developed by the author. This work will be of interest to physicists and mathematicians working in the field of finance, to quantitative analysts in banks and finance firms and to practitioners in the field of fixed income securities and foreign exchange. The book can also be used as a graduate text for courses in financial physics and financial mathematics.

Financial mathematics is currently almost completely dominated by stochastic calculus. Presenting a completely independent approach, this book applies 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. Many new results, accordingly, emerge from the author's perspective. • Applies the formalism of quantum mechanics and quantum field theory to finance • Contains a detailed discussion on the empirical aspects of the forward rate curve and comparison of the field theory model with market data • Addresses many problems in finance that cannot be solved using other approaches

Contents

Foreword; Preface; Acknowledgements
1. Synopsis
Part I. Fundamental Concepts of Finance:
2. Introduction to finance
3. Derivative securities
Part II. Systems with Finite Number of Degrees of Freedom:
4. Hamiltonians and stock options
5. Path integrals and stock options
6. Stochastic interest rates' Hamiltonians and path integrals
Part III. Quantum Field Theory of Interest Rates Models:
7. Quantum field theory of forward interest rates
8. Empirical forward interest rates and field theory models
9. Field theory of Treasury Bonds' derivatives and hedging
10. Field theory Hamiltonian of forward interest rates
11. Conclusions
Appendix A:
Mathematical background
Brief glossary of financial terms
Brief glossary of physics terms
List of main symbols
References
Index