量子金融

前言

Financial markets have undergone tremendous growth and dramatic changes in the past two decades, with the volume of daily trading in currency markets hitting over a trillion US dollars and hundreds of billions of dollars in bond and stock markets.Deregulation and globalization have led to large-scale capital flows; this has raised new problems for finance as well as has further spurred competition among banks and financial institutions.The resulting booms, bubbles and busts of the global financial markets now directly affect the lives of hundreds of millions of people, as was witnessed during the 1998 East Asian financial crisis.The principles of banking and finance are fairly well established [ 16, 76, 87] and the challenge is to apply these principles in an increasingly complicated environment. The immense growth of financial markets, the existence of vast quantities of financial data and the growing complexity of the market, both in volume and sophistication, has made the use of powerful mathematical and computational tools in finance a necessity. In order to meet the needs of customers, complex financial instruments have been created; these instruments demand advanced valuation and risk assessment models and systems that quantify the returns and risks for investors and financial institutions [63, 100].The widespread use in finance of stochastic calculus and of partial differential equations reflects the traditional presence of probabilists and applied mathematicians in this field. The last few years has seen an increasing interest of theoretical physicists in the problems of applied and theoretical finance. In addition to the ast corpus of literature on the application of stochastic calculus to finance,concepts from theoretical physics have been finding increasing application in both theoretical and applied finance. The influx of ideas from theoretical physics, as expressed for example in [ 18] and [69], has added a whole collection of new mathematical and computational techniques to finance, from the methods of classical and quantum physics to the use of path integration, statistical mechanics and so on. This book is part of the on-going process of applying ideas from physics to finance.

內(nèi)容概要

近年來(lái)，金融數(shù)學(xué)的發(fā)展離不開(kāi)隨機(jī)微積分，而《量子金融(英文版)》提供了一種完全獨(dú)立于該方法的新方法，將量子力學(xué)和量子場(chǎng)論中的數(shù)學(xué)公式和概念運(yùn)用到期貨理論和利率模型中，重點(diǎn)講述路徑積分。相應(yīng)的得到了不少新的預(yù)期結(jié)果?！读孔咏鹑?英文版)》主要介紹了金融基本概念：金融基礎(chǔ)；衍生證券；有限自由度系統(tǒng)：哈密頓體系和股票期貨；路徑積分和股票期貨；隨機(jī)利率模型的哈密頓體系和路徑積分；利率模型的量子場(chǎng)論：利率遠(yuǎn)期合約的量子場(chǎng)論；經(jīng)驗(yàn)利率遠(yuǎn)期合約和場(chǎng)論模型；國(guó)債衍生品場(chǎng)論；利率遠(yuǎn)期合約和場(chǎng)論哈密頓體系結(jié)論。

書(shū)籍目錄

ForewordPrefaceAcknowledgments1 SynopsisPart 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 = 0Part 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 modelsPart Ⅲ Quantum field theory of interest rates modelsA Mathematical backgroundIndex

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