Foreword
Preface
Acknowledgments
1 Synopsis
Part I Fundamental concepts of finance
2 Introduction to finance
2.1 Efficient market: random evolution of securities
2.2 Financial markets
2.3 Risk and return
2.4 Time value of money
2.5 No arbitrage, martingales and risk-neutral measure
2.6 Hedging
2.7 Forward interest rates: fixed-income securities
2.8 Summary
3 Derivative securities
3.1 Forward and futures contracts
3.2 Options
3.3 Stochastic differential equation
3.4 Ito calculus
3.5 Black-Scholes equation: hedged portfolio
3.6 Stock price with stochastic volatility
3.7 Merton——Garman equation
3.8 Summary
3.9 Appendix: Solution for stochastic volatility with p = 0
Part Ⅱ Systems with finite number of degrees of freedom
4 Hamiltonians and stock options
4.1 Essentials of quantum mechanics
4.2 State space: completeness equation
4.3 Operators: Hamiltonian
4.4 Biack-Scholes and Merton-Garman Hamiltonians
4.5 Pricing kernel for options
4.6 Eigenfunction solution of the pricing kernel
4.7 Hamiltonian formulation of the martingale condition
4.8 Potentials in option pricing
4.9 Hamiltonian and barrier options
4.10 Summary
4.11 Appendix: Two-state quantum system （qubit）
4.12 Appendix: Hamiltonian in quantum mechanics
4.13 Appendix: Down-and-out barrier option’’s pricing kernel
4.14 Appendix: Double-knock-out barrier option’’s pricing kernel
4.15 Appendix: Schrodinger and Black-Scholes equations
5 Path integrals and stock options
5.1 Lagrangian and action for the pricing kernel
5.2 Black-Scholes Lagrangian
5.3 Path integrals for path-dependent options
5.4 Action for option-pricing Hamiltonian
5.5 Path integral for the simple harmonic oscillator
5.6 Lagrangian for stock price with stochastic volatility
5.7 Pricing kernel for stock price with stochastic volatility
5.8 Summary
5.9 Appendix: Path-integral quantum mechanics
5.10 Appendix: Heisenberg’’s uncertainty principle in finance
5.11 Appendix: Path integration over stock price
5.12 Appendix: Generating function for stochastic volatility
5.13 Appendix: Moments of stock price and stochastic volatility
5.14 Appendix: Lagrangian for arbitrary at
5.15 Appendix: Path integration over stock price for arbitrary at
5.16 Appendix: Monte Carlo algorithm for stochastic volatility
5.17 Appendix: Merton’’s theorem for stochastic volatility
6 Stochastic interest rates’’ Hamiltonians and path integrals
6.1 Spot interest rate Hamiltonian and Lagrangian
6.2 Vasicek model’’s path integral
6.3 Heath-Jarrow-Morton （HJM） model’’s path integral
6.4 Martingale condition in the HJM model
6.5 Pricing of Treasury Bond futures in the HJM model
6.6 Pricing of Treasury Bond option in the HJM model
6.7 Summary
6.8 Appendix: Spot interest rate Fokker-Planck Hamiltonian
6.9 Appendix: Affine spot interest rate models
6.10 Appendix: Black-Karasinski spot rate model
6.11 Appendix: Black-Karasinski spot rate Hamiltonian
6.12 Appendix: Quantum mechanical spot rate models
Part Ⅲ Quantum field theory of interest rates models
A Mathematical background
Index
