Financial Enginneering Computation -Principles ,Mathematics,Algorithms-alghaform

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Financial Enginneering Computation -Principles ,Mathematics,Algorithms-alghaform
Finans Mühendisliği

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FINANCIAL ENGINEERING AND COMPUTATION
During the past decade many sophisticated mathematical and
computational techniques have been developed for analyzing
financial markets. Students and professionals intending to work in
any area of finance must not only master advanced concepts and
mathematical models but must also learn how to implement these
models computationally. This comprehensive text combines a
thorough treatment of the theory and mathematics behind
financial engineering with an emphasis on computation, in
keeping with the way financial engineering is practiced in today’s
capital markets.
Unlike most books on investments, financial engineering, or
derivative securities, the book starts from basic ideas in finance
and gradually builds up the theory. The advanced mathematical
concepts needed in modern finance are explained at accessible
levels. Thus 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.
Building on the theory, the author presents algorithms for
computational techniques in pricing, risk management, and
portfolio management, together with analyses of their efficiency.
Pricing financial and derivative securities is a central theme of the
book. A broad range of instruments is treated: 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:
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. These
programs can be executed on Windows, MacOS, or Unix
platforms.
Yuh-Dauh Lyuu received his Ph.D. in computer science from
Harvard University. His past positions include Member of
Technical Staff at Bell Labs, Research Scientist at NEC Research
Institute (Princeton), and Assistant Vice President at Citicorp
Securities (New York). He is currently Professor of Computer
Science and Information Engineering and Professor of Finance,
National Taiwan University. His previous book is Information
Dispersal and Parallel Computation.
Professor Lyuu has published works in both computer
science and finance. He also holds a U.S. patent. Professor Lyuu
received several awards for supervising outstanding graduate
students’ theses.
Preface pagexiii
Useful Abbreviations xvii
1 Introduction 1
1.1 Modern Finance:ABrief History 1
1.2 Financial Engineering and Computation 1
1.3 Financial Markets 2
1.4 Computer Technology 4
2 Analysis of Algorithms 7
2.1 Complexity 7
2.2 Analysis of Algorithms 8
2.3 Description of Algorithms 9
2.4 Software Implementation 10
3 Basic Financial Mathematics 11
3.1 Time Value of Money 11
3.2 Annuities 14
3.3 Amortization 15
3.4 Yields 17
3.5 Bonds 24
4 Bond Price Volatility 32
4.1 Price Volatility 32
4.2 Duration 34
4.3 Convexity 41
5 Term Structure of Interest Rates 45
5.1 Introduction 45
5.2 Spot Rates 46
5.3 Extracting Spot Rates fromYield Curves 47
5.4 StaticSprea d 49
5.5 Spot Rate Curve and Yield Curve 50
5.6 Forward Rates 50
5.7 TermStructure Theories 56
5.8 Duration and Immunization Revisited 60
vii
viii Contents
6 Fundamental Statistical Concepts 64
6.1 Basics 64
6.2 Regression 69
6.3 Correlation 71
6.4 Parameter Estimation 72
7 Option Basics 75
7.1 Introduction 75
7.2 Basics 76
7.3 Exchange-Traded Options 77
7.4 BasicOptio n Strategies 78
8 Arbitrage in Option Pricing 84
8.1 The Arbitrage Argument 84
8.2 Relative Option Prices 85
8.3 Put–Call Parity and Its Consequences 86
8.4 Early Exercise of American Options 88
8.5 Convexity of Option Prices 89
8.6 The Option Portfolio Property 90
9 Option PricingModel s 92
9.1 Introduction 92
9.2 The Binomial Option Pricing Model 93
9.3 The Black–Scholes Formula 104
9.4 Using the Black–Scholes Formula 111
9.5 American Puts on a Non-Dividend-Paying
Stock 113
9.6 Options on a Stock that Pays Dividends 114
9.7 Traversing the Tree Diagonally 118
10 Sensitivity Analysis of Options 123
10.1 Sensitivity Measures (“The Greeks”) 123
10.2 Numerical Techniques 127
11 Extensions of Options Theory 131
11.1 Corporate Securities 131
11.2 Barrier Options 137
11.3 Interest Rate Caps and Floors 140
11.4 Stock Index Options 141
11.5 Foreign Exchange Options 143
11.6 Compound Options 147
11.7 Path-Dependent Derivatives 148
12 Forwards, Futures, Futures Options, Swaps 155
12.1 Introduction 155
12.2 Forward Contracts 156
12.3 Futures Contracts 161
12.4 Futures Options and Forward Options 168
12.5 Swaps 173
Contents ix
13 Stochastic Processes and Brownian Motion 177
13.1 Stochastic Processes 177
13.2 Martingales (“Fair Games”) 179
13.3 Brownian Motion 183
13.4 Brownian Bridge 188
14 Continuous-Time Financial Mathematics 190
14.1 Stochastic Integrals 190
14.2 Ito Processes 193
14.3 Applications 197
14.4 Financial Applications 201
15 Continuous-Time Derivatives Pricing 206
15.1 Partial Differential Equations 206
15.2 The Black–Scholes Differential Equation 207
15.3 Applications 211
15.4 General Derivatives Pricing 220
15.5 Stochastic Volatility 221
16 Hedging 224
16.1 Introduction 224
16.2 Hedging and Futures 224
16.3 Hedging and Options 228
17 Trees 234
17.1 Pricing Barrier Options with
Combinatorial Methods 234
17.2 Trinomial Tree Algorithms 242
17.3 Pricing Multivariate Contingent Claims 245
18 Numerical Methods 249
18.1 Finite-Difference Methods 249
18.2 Monte Carlo Simulation 255
18.3 Quasi–Monte Carlo Methods 262
19 Matrix Computation 268
19.1 Fundamental Definitions and Results 268
19.2 Least-Squares Problems 273
19.3 Curve Fitting with Splines 278
20 Time Series Analysis 284
20.1 Introduction 284
20.2 Conditional Variance Models for Price Volatility 291
21 Interest Rate Derivative Securities 295
21.1 Interest Rate Futures and Forwards 295
21.2 Fixed-Income Options and Interest Rate Options 306
21.3 Options on Interest Rate Futures 310
21.4 Interest Rate Swaps 312
x Contents
22 TermStructure Fitting 321
22.1 Introduction 321
22.2 Linear Interpolation 322
22.3 Ordinary Least Squares 323
22.4 Splines 325
22.5 The Nelson–Siegel Scheme 326
23 Introduction to TermStructure Modeling 328
23.1 Introduction 328
23.2 The Binomial Interest Rate Tree 329
23.3 Applications in Pricing and Hedging 337
23.4 Volatility TermStructures 343
24 Foundations of TermStructure Modeling 345
24.1 Terminology 345
24.2 BasicRelation s 346
24.3 Risk-Neutral Pricing 348
24.4 The TermStructure Equation 350
24.5 Forward-Rate Process 353
24.6 The Binomial Model with Applications 353
24.7 Black–Scholes Models 359
25 Equilibrium Term Structure Models 361
25.1 The Vasicek Model 361
25.2 The Cox-Ingersoll-Ross Model 364
25.3 Miscellaneous Models 370
25.4 Model Calibration 371
25.5 One-Factor Short Rate Models 372
26 No-Arbitrage Term Structure Models 375
26.1 Introduction 375
26.2 The Ho–Lee Model 375
26.3 The Black–Derman–Toy Model 380
26.4 The Models According to Hull and White 384
26.5 The Heath–Jarrow–Morton Model 388
26.6 The Ritchken–Sankarasubramanian Model 395
27 Fixed-Income Securities 399
27.1 Introduction 399
27.2 Treasury, Agency, and Municipal Bonds 399
27.3 Corporate Bonds 401
27.4 Valuation Methodologies 406
27.5 Key Rate Durations 412
28 Introduction to Mortgage-Backed Securities 415
28.1 Introduction 415
28.2 Mortgage Banking 416
28.3 Agencies and Securitization 417
28.4 Mortgage-Backed Securities 419
Contents xi
28.5 Federal Agency Mortgage-Backed
Securities Programs 422
28.6 Prepayments 423
29 Analysis of Mortgage-Backed Securities 427
29.1 Cash Flow Analysis 427
29.2 Collateral Prepayment Modeling 440
29.3 Duration and Convexity 444
29.4 Valuation Methodologies 446
30 Collateralized Mortgage Obligations 451
30.1 Introduction 451
30.2 Floating-Rate Tranches 452
30.3 PAC Bonds 453
30.4 TAC Bonds 457
30.5 CMOStrips 457
30.6 Residuals 457
31 Modern Portfolio Theory 458
31.1 Mean–Variance Analysis of Risk and Return 458
31.2 The Capital Asset Pricing Model 464
31.3 Factor Models 470
31.4 Value at Risk 474
32 Software 480
32.1 Web Programming 480
32.2 Use of The Capitals Software 480
32.3 Further Topics 482
33 Answers to Selected Exercises 484
Bibliography 553
Glossary of Useful Notations 585
Index 587
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