金融衍生工具－定价、应用与数学

Financial Derivatives - Pricing, Applications, and Mathematics

(美)巴兹(Baz,J.),查科(Chacko,G.)著

本书对金融衍生工具定价的基本原理做了简单论述。第一章向读者展示了基本的随机微积分，并就不确定性与时间、随机游走和几何布朗运动等概念相关的定理进行了讨论。第二章讲述了对资产和衍生工具的一般定价方法。 第三章基于第二章讲述一般定价方法的应用。第四章是本书的数学附录，主要讲述的是随机过程、鞅理论\、随机控制等内容

    The first chapter provides readers with an intuitive exposition of basic random calculus. Concepts such as volatility and time, random walks, geometric Brownian motion, and Itô’s lemma are discussed heuristically.

    The second chapter develops generic pricing techniques for assts and derivatives, determining the notion of a stochastic discount factor or pricing kernel, and then uses this concept to price conventional and exotic derivatives.

    The third chapter applies the pricing concepts to the special case of interest rate markets, namely, bonds and swaps, and discuss factor models and term-structure-consistent models.

    The fourth chapter deals with a variety of mathematical topics that underlie derivatives pricing and portfolio allocation decisions, such as meanreverting processes and jump processes, and discusses related tools of stochastic calculus, such as Kolmogorov equations, martingales techniques, stochastic control, and partial differential equations.

　　　目　　　录

Chapter1 Preliminary Mathematics

• 1.1 RANDOM WALK
• 1.2 ANOTHER TAKE ON VOLATILITY AND TIME
• 1.3 A FIRST GLANCE AT ITÔ’S LEMMA
• 1.4 CONTINUOUS TIME: BROWNIAN MOTION; MORE ON ITÔ’S LEMMA
• 1.5 TWO-DEMENSIONAL BROWNIAN MOTION
• 1.6 BIVARIATE ITÔ’S LEMMA
• 1.7 THREE PARADOXES OF FINANCE

Chapter2 Principles of Financial Valuation

• 2.1 UNCERTAINTY, UTILITY THEORY, AND RISK
• 2.2 RISK AND THE EQUILIBRIUM PRICING OF SECURITIES
• 2.3 THE BINOMIAL OPTION-PRICING MODEL
• 2.4 LIMITING OPTION-PRICING FORMULA
• 2.5 CONTINUOUS-TIME MODELS
• 2.6 EXOTIC OPTIONS

Chapter3 Interest Rate Models

• 3.1 INTEREST RATE DERVIATIVES: NOT SO SIMPLE
• 3.2 BONDS AND YIELDS
• 3.3 NAÏVE MODELS OF INTEREST RATE RISK
• 3.4 AN OVERVIEW OF INTEREST RATE DERIVATIVES
• 3.5 YIELD CURVE SWAPS
• 3.6 FACTOR MODELS
• 3.7 TERM-STRUCTURE-CONSISTENT MODELS
• 3.8 RISKY BONDS AND THEIR DERVIATIVES
• 3.9 THE HEATH, JARROW, AND MORTON APPROACH
• 3.10 INTEREST RATES AS OPTIONS

Chapter4 Mathematics of Asset Pricing

• 4.1 RANDOM WALKS
• 4.2 ARITHMETIC BROWNIAN MOTION
• 4.3 GEOMETRIC BROWNIAN MOTION
• 4.4 ITÔ CALCULUS
• 4.5 MEAN-REVERTING PROCESSES
• 4.6 JUMP PROCESS
• 4.7 KOLMOGOROV EQUATIONS
• 4.8 MARTINGALES
• 4.9 DYNAMIC PROGRAMMING
• 4.10 PARTIAL DIFFERENTIAL EQUATIONS