Financial Engineering and Computation: Principles, Mathematics, Algorithms

by Yuh-Dauh Lyuu

• ISBN13: 9780521781718
• ISBN10: 052178171X
• eBook ISBN(s): 9780511030819
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-11-12
• Publisher: Cambridge University Press
• More Book Details

Summary

Nowadays students and professionals intending to work in any area of finance must master not only advanced concepts and mathematical models but also learn how to implement these models computationally. This comprehensive text combines the theory and mathematics behind financial engineering with an emphasis on computation, in keeping with the way financial engineering is practised in today's capital markets. Unlike most books on investments, financial engineering, or derivative securities, the book starts from very basic ideas in finance and gradually builds up the theory. It offers a thorough grounding in the subject for MBAs in finance, students of engineering and sciences who are pursuing a career in finance, researchers in computational finance, system analysts, and financial engineers. Along with the theory, the author presents numerous algorithms for pricing, risk management, and portfolio management. The emphasis is on pricing financial and derivative securities: bonds, options, futures, forwards, interest rate derivatives, mortgage-backed securities, bonds with embedded options, and more. Each instrument is treated in a short, self-contained chapter for ready reference use. Many of these algorithms are coded in Java as programs for the Web, available from the book's home page.

Author Biography

Yuh-Dauh Lyuu received his Ph.D. in computer science from Harvard University. He is currently Professor of Computer Science and Information Engineering and Professor of Finance, National Taiwan University

Table of Contents

Preface	xiii
Useful Abbreviations	xvii
Introduction	1	(6)
Modern Finance: A Brief History	1	(1)
Financial Engineering and Computation	1	(1)
Financial Markets	2	(2)
Computer Technology	4	(3)
Analysis of Algorithms	7	(4)
Complexity	7	(1)
Analysis of Algorithms	8	(1)
Description of Algorithms	9	(1)
Software Implementation	10	(1)
Basic Financial Mathematics	11	(21)
Time Value of Money	11	(3)
Annuities	14	(1)
Amortization	15	(2)
Yields	17	(7)
Bonds	24	(8)
Bond Price Volatility	32	(13)
Price Volatility	32	(2)
Duration	34	(7)
Convexity	41	(4)
Term Structure of Interest Rates	45	(19)
Introduction	45	(1)
Spot Rates	46	(1)
Extracting Spot Rates from Yield Curves	47	(2)
Static Spread	49	(1)
Spot Rate Curve and Yield Curve	50	(1)
Forward Rates	50	(6)
Term Structure Theories	56	(4)
Duration and Immunization Revisited	60	(4)
Fundamental Statistical Concepts	64	(11)
Basics	64	(5)
Regression	69	(2)
Correlation	71	(1)
Parameter Estimation	72	(3)
Options Basics	75	(9)
Introduction	75	(1)
Basics	76	(1)
Exchange-Traded Options	77	(1)
Basic Option Strategies	78	(6)
Arbitrage in Option Pricing	84	(8)
The Arbitrage Argument	84	(1)
Relative Option Prices	85	(1)
Put-Call Parity and Its Consequences	86	(2)
Early Exercise of American Options	88	(1)
Convexity of Option Prices	89	(1)
The Option Portfolio Property	90	(2)
Option Pricing Models	92	(31)
Introduction	92	(1)
The Binomial Option Pricing Model	93	(11)
The Black-Scholes Formula	104	(7)
Using the Black-Scholes Formula	111	(2)
American Puts on a Non-Dividend-Paying Stock	113	(1)
Options on a Stock that Pays Dividends	114	(4)
Traversing the Tree Diagonally	118	(5)
Sensitivity Analysis of Options	123	(8)
Sensitivity Measures (``The Greeks'')	123	(4)
Numerical Techniques	127	(4)
Extensions of Options Theory	131	(24)
Corporate Securities	131	(6)
Barrier Options	137	(3)
Interest Rate Caps and Floors	140	(1)
Stock Index Options	141	(2)
Foreign Exchange Options	143	(4)
Compound Options	147	(1)
Path-Dependent Derivatives	148	(7)
Forwards, Futures, Futures Options, Swaps	155	(22)
Introduction	155	(1)
Forward Contracts	156	(5)
Futures Contracts	161	(7)
Futures Options and Forward Options	168	(5)
Swaps	173	(4)
Stochastic Processes and Brownian Motion	177	(13)
Stochastic Processes	177	(2)
Martingales (``Fair Games'')	179	(4)
Brownian Motion	183	(5)
Brownian Bridge	188	(2)
Continuous-Time Financial Mathematics	190	(16)
Stochastic Integrals	190	(3)
Ito Processes	193	(4)
Applications	197	(4)
Financial Applications	201	(5)
Continuous-Time Derivatives Pricing	206	(18)
Partial Differential Equations	206	(1)
The Black-Scholes Differential Equation	207	(4)
Applications	211	(9)
General Derivatives Pricing	220	(1)
Stochastic Volatility	221	(3)
Hedging	224	(10)
Introduction	224	(1)
Hedging and Futures	224	(4)
Hedging and Options	228	(6)
Trees	234	(15)
Pricing Barrier Options with Combinatorial Methods	234	(8)
Trinomial Tree Algorithms	242	(3)
Pricing Multivariate Contingent Claims	245	(4)
Numerical Methods	249	(19)
Finite-Difference Methods	249	(6)
Monte Carlo Simulation	255	(7)
Quasi-Monte Carlo Methods	262	(6)
Matrix Computation	268	(16)
Fundamental Definitions and Results	268	(5)
Least-Squares Problems	273	(5)
Curve Fitting with Splines	278	(6)
Time Series Analysis	284	(11)
Introduction	284	(7)
Conditional Variance Models for Price Volatility	291	(4)
Interest Rate Derivative Securities	295	(26)
Interest Rate Futures and Forwards	295	(11)
Fixed-Income Options and Interest Rate Options	306	(4)
Options on Interest Rate Futures	310	(2)
Interest Rate Swaps	312	(9)
Term Structure Fitting	321	(7)
Introduction	321	(1)
Linear Interpolation	322	(1)
Ordinary Least Squares	323	(2)
Splines	325	(1)
The Nelson-Siegel Scheme	326	(2)
Introduction to Term Structure Modeling	328	(17)
Introduction	328	(1)
The Binomial Interest Rate Tree	329	(8)
Applications in Pricing and Hedging	337	(6)
Volatility Term Structures	343	(2)
Foundations of Term Structure Modeling	345	(16)
Terminology	345	(1)
Basic Relations	346	(2)
Risk-Neutral Pricing	348	(2)
The Term Structure Equation	350	(3)
Forward-Rate Process	353	(1)
The Binomial Model with Applications	353	(6)
Black-Scholes Models	359	(2)
Equilibrium Term Structure Models	361	(14)
The Vasicek Model	361	(3)
The Cox-Ingersoll-Ross Model	364	(6)
Miscellaneous Models	370	(1)
Model Calibration	371	(1)
One-Factor Short Rate Models	372	(3)
No-Arbitrage Term Structure Models	375	(24)
Introduction	375	(1)
The Ho-Lee Model	375	(5)
The Black-Derman-Toy Model	380	(4)
The Models According to Hull and White	384	(4)
The Health-Jarrow-Morton Model	388	(7)
The Ritchken-Sankarasubramanian Model	395	(4)
Fixed-Income Securities	399	(16)
Introduction	399	(1)
Treasury, Agency, and Municipal Bonds	399	(2)
Corporate Bonds	401	(5)
Valuation Methodologies	406	(6)
Key Rate Durations	412	(3)
Introduction to Mortgage-Backed Securities	415	(12)
Introduction	415	(1)
Mortgage Banking	416	(1)
Agencies and Securitization	417	(2)
Mortgage-Backed Securities	419	(3)
Federal Agency Mortgage-Backed Securities Programs	422	(1)
Prepayments	423	(4)
Analysis of Mortgage-Backed Securities	427	(24)
Cash Flow Analysis	427	(13)
Collateral Prepayment Modeling	440	(4)
Duration and Convexity	444	(2)
Valuation Methodologies	446	(5)
Collateralized Mortgage Obligations	451	(7)
Introduction	451	(1)
Floating-Rate Tranches	452	(1)
PAC Bonds	453	(4)
TAC Bonds	457	(1)
CMO Strips	457	(1)
Residuals	457	(1)
Modern Portfolio Theory	458	(22)
Mean-Variance Analysis of Risk and Return	458	(6)
The Capital Asset Pricing Model	464	(6)
Factor Models	470	(4)
Value at Risk	474	(6)
Software	480	(4)
Web Programming	480	(1)
Use of The Capitals Software	480	(2)
Further Topics	482	(2)
Answers to Selected Exercises	484	(69)
Bibliography	553	(32)
Glossary of Useful Notations	585	(2)
Index	587