Financial Engineering and Computation : Principles, Mathematics, Algorithms / Yuh-Dauh Lyuu.

Format:

Book

Author/Creator:

Lyuu, Yuh-Dauh.

Series:

Cambridge books online.

Language:

English

Subjects (All):

Financial engineering.

Investments--Mathematical models.

Investments.

Derivative securities--Mathematical models.

Derivative securities.

Physical Description:

1 online resource (648 pages) : digital, PDF file(s)

Place of Publication:

Cambridge : Cambridge University Press, 2001.

System Details:

Mode of access: World Wide Web.

text file

PDF

Summary:

A comprehensive text and reference on the theory of financial engineering with numerous algorithms for pricing, risk management, and portfolio management.

Contents:

1.1 Modern Finance: A Brief 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

5.2 Spot Rates 46

5.3 Extracting Spot Rates from Yield Curves 47

5.4 Static Spread 49

5.5 Spot Rate Curve and Yield Curve 50

5.6 Forward Rates 50

5.7 Term Structure Theories 56

5.8 Duration and Immunization Revisited 60

6 Fundamental Statistical Concepts 64

6.2 Regression 69

6.3 Correlation 71

6.4 Parameter Estimation 72

7 Option Basics 75

7.3 Exchange-Traded Options 77

7.4 Basic Option 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 Pricing Models 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

12.2 Forward Contracts 156

12.3 Futures Contracts 161

12.4 Futures Options and Forward Options 168

12.5 Swaps 173

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

16.2 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

20.2 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

22 Term Structure Fitting 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 Term Structure Modeling 328

23.2 The Binomial Interest Rate Tree 329

23.3 Applications in Pricing and Hedging 337

23.4 Volatility Term Structures 343

24 Foundations of Term Structure Modeling 345

24.1 Terminology 345

24.2 Basic Relations 346

24.3 Risk-Neutral Pricing 348

24.4 The Term Structure 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

26.2 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

27.2 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

28.2 Mortgage Banking 416

28.3 Agencies and Securitization 417

28.4 Mortgage-Backed Securities 419

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

30.2 Floating-Rate Tranches 452

30.3 PAC Bonds 453

30.4 TAC Bonds 457

30.5 CMO Strips 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.

Notes:

Title from publishers bibliographic system (viewed on 02 Mar 2012).

Other Format:

Print version:

ISBN:

9780511546839

9780521781718

Access Restriction:

Restricted for use by site license.