Financial Engineering and Computation

   As the title of this book suggests, a modern book on financial engineering has to

cover investment theory, financial mathematics, and computer science evenly. This

interdisciplinary emphasis is tuned more to the capital markets wherever quantitative

analysis is being practiced.

PrefaceUseful Abbreviations1 Introduction　1.1 Modern Finance: A Brief History　1.2

Financial Engineering and Computation　1.3 Financial Markets　1.4 Computer Technology2

Analysis of Algorithms　2.1 Complexity　2.2 Analysis of Algorithms　2.3 Description of

Algorithms　2.4 Software Implementation3 Basic Financial Mathematics　3.1 Time Value of

Money　3.2 Annuities　3.3 Amortization　3.4 Yields　3.5 Bonds4 Bond Price Volatility　

4.1 Price Volatility　4.2 Duration　4.3 Convexity5 Term Structure of Interest Rates　5.1

Introduction　5.2 Spot Rates　5.3 Extracting Spot Rates from Yield Curves　5.4 Static

Spread　5.5 Spot Rate Curve and Yield Curve　5.6 Forward Rates　5.7 Term Structure

Theories　5.8 Duration and Immunization Revisited6 Fundamental Statistical Concepts　6.1

Basics　6.2 Regression　6.3 Correlation　6.4 Parameter Estimation7 Option Basics　7.1

Introduction　7.2 Basics　7.3 Exchange-Traded Options　7.4 Basic Option Strategies8

Arbitrage in Option Pricing　8.1 The Arbitrage Argument　8.2 Relative Option Prices　8.3

Put-Call Parity and Its Consequences　8.4 Early Exercise of American Options　8.5

Convexity of Option Prices　8.6 The Option Portfolio Property9 Option Pricing Models　

9.1 Introduction　9.2 The Binomial Option Pricing Model　9.3 The Black-Scholes Formula　

9.4 Using the Black-Scholes Formula　9.5 American Puts on a Non-Dividend-Paying Stock　

9.6 Options on a Stock that Pays Dividends　9.7 Traversing the Tree Diagonally10

Sensitivity Analysis of Options　10.1 Sensitivity Measures ("The Greeks")　10.2

Numerical Techniques11 Extensions of Options Theory　11.1 Corporate Securities　11.2

Barrier Options　11.3 Interest Rate Caps and Floors　11.4 Stock Index Options　11.5

Foreign Exchange Options　11.6 Compound Options　11.7 Path-Dependent Derivatives12

Forwards, Futures, Futures Options, Swaps　12.1 Introduction　12.2 Forward Contracts　

12.3 Futures Contracts　12.4 Futures Options and Forward Options　12.5 Swaps13

Stochastic Processes and Brownian Motion　13.1 Stochastic Processes　13.2 Martingales

("Fair Games")　13.3 Brownian Motion　13,4 Brownian Bridge14 Continuous-Time Financial

Mathematics　14.1 Stochastic Integrals　14.2 Ito Processes　14.3 Applications　14.4

Financial Applications15 Continuous-Time Derivatives Pricing　15.1 Partial Differential

Equations　15.2 The Black-Schotes Differential Equation　15.3 Applications　15.4 General

Derivatives Pricing　15.5 Stochastic Volatility16 Hedging　16.1 Introduction　16.2

Hedging and Futures　16.3 Hedging and Options17 Trees　17.1 Pricing Barrier Options with

Combinatorial Methods　17.2 Trinomial Tree Algorithms　17.3 Pricing Multivariate

Contingent Claims18 Numerical Methods　18.1 Finite-Difference Methods　18.2 Monte Carlo

Simulation　18.3 Quasi-Monte Carlo Methods19 Matrix Computation　19.1 Fundamental

Definitions and Results　19.2 Least-Squares Problems　19.3 Curve Fitting with Splines20

Time Series Analysis　20.1 Introduction　20.2 Conditional Variance Models for Price

Volatility21 Interest Rate Derivative Securities　21.1 Interest Rate Futures and

Forwards　21.2 Fixed-Income Options and Interest Rate Options　21.3 Options on Interest

Rate Futures　21.4 Interest Rate Swaps22 Term Structure Fitting　22.1 Introduction　22.2

Linear Interpolation　22.3 Ordinary Least Squares　22.4 Splines　22.5 The Nelson-Siegel

Scheme23 Introduction to Term Structure Modeling　23.1 Introduction　23.2 The Binomial

Interest Rate Tree　23.3 Applications in Pricing and Hedging　23.4 Volatility Term

Structures24 Foundations of Term Structure Modeling　24.1 Terminology　24.2 Basic

Relations　24.3 Risk-Neutral Pricing　24.4 The Term Structure Equation　24.5 Forward-

Rate Process　24.6 The Binomial Model with Applications　24.7 Black-Scholes Models25

Equilibrium Term Structure Models　25.1 The Vasicek Model　25.2 The Cox-Ingersoll-Ross

Model　25.3 Miscellaneous Models　25.4 Model Calibration　25.5 One-Factor Short Rate

Models26 No-Arbitrage Term Structure Models　26.1 Introduction　26.2 The Ho-Lee Model　

26.3 The Black-Derman-Toy Model　26.4 The Models According to Hull and White　26.5 The

Heath-Jarrow-Morton Model　26.6 The Ritchken-Sankarasubramanian Model27 Fixed-Income

Securities　27.1 Introduction　27.2 Treasury, Agency, and Municipal Bonds　27.3

Corporate Bonds　27.4 Valuation Methodologies　27.5 Key Rate Durations28 Introduction to

Mortgage-Backed Securities　28.1 Introduction　28.2 Mortgage Banking　28.3 Agencies and

Securitization　28.4 Mortgage-Backed Securities　28.5 Federal Agency Mortgage-Backed

Securities Programs　28.6 Prepayments29 Analysis of Mortgage-Backed Securities　29.1

Cash Flow Analysis　29.2 Collateral Prepayment Modeling　29.3 Duration and Convexity　

29.4 Valuation Methodologies30 Collateralized Mortgage Obligations　30.1 Introduction　

30.2 Floating-Rate Tranches　30.3 PAC Bonds　30.4 TAC Bonds　30.5 CMO Strips　30.6

Residuals31 Modern Portfolio Theory　31.1 Mean-Variance Analysis of Risk and Return　

31.2 The Capital Asset Pricing Model　31.3 Factor Models　31.4 Value at Risk32 Software

　32.1 Web Programming　32.2 Use of The Capitals Software　32.3 Further Topics33 Answers

to Selected ExercisesBibliographyGlossary of Useful NotationsIndex