- 13 Ağu 2019

- 81

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Finans Mühendisliği

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:

Bu linki görmek için izniniz yok Giriş yap veya üye ol.. 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.

Rar Password: alghaform.comPreface 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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