Financial Mathematics, Financial Engineering and Risk Management

Financial Mathematics Bookshelf | Bestsellers | New Books | Trading Books | Risk Books | Fabozzi | AMS Booklist | Chicago Financial Mathematics Seminar | Chicago Financial Engineering & Risk Management Workshop | Related Seminars/Workshops | Journals | IRWIN Trader's Edge | Wiley Financial Engineering | Wiley Finance | Springer Finance | Springer Mathematics | Butterworth-Heinemann Finance | Kolmogorov-100 | Book List from the Notices of the American Mathematical Society | Conferences/Seminars/Workshops | Events | Links | Search | Amazon Coupons | Top new and future releases in Finance & Investing. Updated daily.

HULL Options, Futures & Other Derivatives, 5th Edition, US

See also HULL: Solutions Manual: Options, Futures and Other Derivatives (Solutions Manual) and HULL: Fundamentals of Futures and Options Markets

**Table of Contents**

1. Introduction

2. Mechanics of Futures and Forward Markets

3. Determination of Forward and Futures Prices

4. Hedging Strategies Using Futures

5. Interest Rate Markets

6. Swaps

7. Mechanics of Options Markets

8. Properties of Stock Options

9. Trading Strategies Involving Options

10. Introduction to Binomial Trees

11. Model of the Behavior of Stock Prices

12. The Black-Scholes Model

13. Options on Stock Indices, Currencies, and Futures

14. The Greek Letters

15. Volatility Smiles

16. Value at Risk

17. Estimating Volatilities and Correlations

18. Numerical Procedures

19. Exotic Options

20. More on Models and Numerical Procedures

21. Martingales and Measures

22. Interest Rate Derivatives: The Standard Market Models

23. Interest Rate Derivatives: Models of the Short Rate

24. Interest Rate Derivatives: More Advanced Models

25. Swaps Revisited

26. Credit Risk

27. Credit Derivatives

28. Real Options

29. Insurance, Weather, and Energy Derivatives

30. Derivatives Mishaps and What We Can Learn from Them

NEFTCI
Introduction to the Mathematics of Financial Derivatives

See also a new book NEFTCI
Principles of Financial Engineering

**Table of Contents**

Financial Derivatives: A Brief Introduction

A Primer on Arbitrage Theorem

Calculus in Deterministic and Stochastic Environments

Pricing Derivatives: Models and Notation.

Tools in Probability Theory

Martingales and Martingale Representations

Differentiation in Stochastic Environments

The Wiener Process and Rare Events in Financial Markets

Integration in Stochastic Environments: The Ito Integral

Ito's Lemma

The Dynamics of Derivative Prices: Stochastic Differential Equations.

Pricing Derivative Products: Partial Differential Equations

The Black-Scholes PDE: An Application

Pricing Derivative Products: Equivalent Martingale Measures

Equivalent Martingale Measures: Applications

New Results and Tools for Interest Sensitive Securities.

Arbitrage Theorem in a New Setting: Normalization and Random Interest Rates.

Modeling Term Structure and Related Concepts.

Classical and HJM Approaches to Fixed Income.

Classical PDE Analysis for Interest Rate Derivatives.

Relating Conditional Expectations to PDEs.

Stopping Times and American-Type Securities.

Bibliography

Index

WILMOTT
Paul Wilmott on Quantitative Finance, 2 Volume Set

**Table of Contents**

Volume 1

Chapter 1: Products and Markets

Chapter 2: Derivatives

Chapter 3: The Random Behavior of Assets

Chapter 4: Elementary Stochastic Calculus

Chapter 5: The Black-Scholes Model

Chapter 6: Partial Differential Equations

Chapter 7: The Black-Scholes Formulae and the 'Greeks'

Chapter 8: Simple Generalizations of the Black-Scholes World

Chapter 9: Early Exercise and American Options

Chapter 10: Probability Density Functions and First Exit Times

Chapter 11: Multi-asset Options

Chapter 12: The Binomial Model

Chapter 13: Predicting the Markets?

Chapter 14: The Trading Game

Chapter 15: An Introduction to Exotic and Path-dependent Options

Chapter 16: Barrier Options

Chapter 17: Strongly Path-dependent Options

Chapter 18: Asian Options

Chapter 19: Lookback Options

Chapter 20: Derivatives and Stochastic Control

Chapter 21: Miscellaneous Exotics

Chapter 22: Defects of the Black-Scholes Model

Chapter 23: Discrete Hedging

Chapter 24: Transaction Costs

Chapter 25: Volatility Smiles and Surfaces

Chapter 26: Stochastic Volatility

Chapter 21: Uncertain Parameters

Chapter 28: Empirical Analysis of Volatility

Chapter 29: Jump Diffusion

Chapter 30: Crash Modeling

Chapter 31: Speculating With Options

Chapter 32: Static Hedging

Chapter 33: The Feedback Effect of Hedging in Illiquid Markets

Chapter 34: Utility Theory

Chapter 35: More About American Options and Related Matters

Chapter 36: Stochastic Volatility and Mean-variance Analysis

Chapter 37: Advanced Dividend Modeling

Volume 2

Chapter 38: Fixed-income Products and Analysis: Yield, Duration and Convexity

Chapter 39: Swaps

Chapter 40: One-factor Interest Rate Modeling

Chapter 41: Yield Curve Fitting

Chapter 42: Interest Rate Derivatives

Chapter 43: Convertible Bonds

Chapter 44: Mortgage-backed Securities

Chapter 45: Multi-factor Interest Rate Modeling

Chapter 46: Empirical Behavior of the Spot Interest Rate

Chapter 47: Heath, Jarrow and Morton

Chapter 48: Interest-rate Modeling Without Probabilities

Chapter 49: Pricing and Optimal Hedging of Derivatives, the Non-probabilistic Model Cont'd

Chapter 50: Extensions to the Non-probabilistic Interest-rate Model

Chapter 51: Portfolio Management

Chapter 52: Asset Allocation in Continuous Time

Chapter 53: Value at Risk

Chapter 54: Value of the Firm and the Risk of Default

Chapter 55: Credit Risk

Chapter 56: Credit Derivatives

Chapter 57: RiskMetrics and CreditMetrics

Chapter 58: CrashMetrics

Chapter 59: Derivatives **** Ups

Chapter 60: Bonus Time

Chapter 61: Real Options

Chapter 62: Energy Derivatives

Chapter 63: Finite-difference Methods for One-factor Models

Chapter 64: Further Finite-difference Methods for One-factor Models

Chapter 65: Finite-difference Methods for Two-factor Models

Chapter 66: Monte Carlo Simulation and Related Methods

Chapter 67: Finite-difference Programs Appendix: All the Math You Need ... and No More (An Executive Summary)

JAECKEL
Monte Carlo Methods in Finance

**Table of Contents**

Introduction

The Mathematics behind Monte Carlo methods

Correlation

Normal, Log-Normal and Other Processes

Applications in Risk Management

Option Pricing

Value at Risk

Faster Monte Carlo 1: Various Reduction Techniques

Faster Monte Carlo 2: Low Discrepency Numbers

Monte Carlo and Professional Quantitative Research

More Hints and Tricks

New Monte Carlo Techniques

REBONATO
Volatility and Correlation : In the Pricing of Equity, Fx and Interest-Rate Options

See also a new Second Edition
Volatility and Correlation : The Perfect Hedger and the Fox

**Table of Contents**

FOUNDATIONS

Volatility: Fundamental Concepts and Definitions

Variance and Mean Reversion in the Real and the Risk-Adjusted Worlds

Instantaneous and Terminal Correlations

DEALING WITH SMILES

Pricing Options in the Presence of Smiles

Tree Methodologies for Smiley Option Prices

Efficient Extraction of the Future Local Volatility from Plain-Vanilla Option Prices

Closed-Form Solutions for Smiley Option Prices via Direct Modelling of the Density

Explaining Smiles by Means of Mixed Jump-Diffusion Processes

INTEREST RATES

The Role of Mean Reversion in Interest-Rate Models

Optimal Calibration of the Brace-Gatarek-Musiela Model

Specifying the Instantaneous Volatility of Forward Rates

References

Index

REBONATO
Interest-Rate Option Models : Understanding, Analyzing and Using Models for Exotic Interest-Rate Options, 2nd Edition

**Table of Contents**

Acknowledgements

Introduction and outline of the book

List of symbols and abbreviations

1. Definition and valuation of the underlying instruments

2. Yield curve models: a statistical approach

3. A motivation for yield curve models

4. The analytic and probabilistic tools

5. The conditions of no-arbitrage

6. Lattice methodologies

7. The partial differential equation (PDE) approach

8. Monte Carlo approaches

9. The CIR and Vasicek models

10. The Black Derman and Toy model

11. The Hull and White approach

12. The Longstaff and Schwartz model

13. The Brennan and Schwartz model

14. The Heath Jarrow and Morton approach

15. Affine models

16. Markovian and non-Markovian interest-rate models

Bibliography

Index

REBONATO
Modern Pricing of Interest-Rate Derivatives: The Libor Market Model and Beyond

**Table of Contents**

I. The Structure of the LIBOR Market Model

1. Putting the Modern Pricing Approach in Perspective

2. The Mathematical and Financial Set-up

3. Describing the Dynamics of Forward Rates

4. Characterizing and Valuing Complex LIBOR Products

5. Determining the No-Arbitrage Drifts of Forward Rates

II. The Inputs to the General Framework

6. Instantaneous Volatilities

7. Specifying the Instantaneous Correlation Function

III Calibration of the LIBOR Market Model

8. Fitting the Instantaneous Volatility Functions

9. Simultaneous Calibration to Market Caplet Prices and to an Exogenous Correlation Matrix

10 Calibrating a Forward-Rate-Based LIBOR Market Model to Swaption Prices

IV. Beyond the Standard Approach: Accounting for Smiles

11. Extending the Standard Approach - I: CEV and Displaced Diffusion

12. Extending the Standard Approach - II: Stochastic Instantaneous Volatilities

13. A Joint Empirical and Theoretical Analysis of the Stochastic-Volatility LIBOR Market Model

HAUG
The Complete Guide to Option Pricing Formulas

**Table of Contents**

Plain Vanilla Options

Exotic Options

Numerical Methods in Options Pricing

Interest-Rate Options

Volatility and Correlation

Some Useful Formulas

Distributions

Partial Derivatives of the Black-Scholes

The Option-Pricing Software

Bibliography

Index

FABOZZI
The Handbook of Fixed Income Securities

**Table of Contents**

1 Overview of the Types and Features of Fixed Income Securities 3

2 Risks Associated with Investing in Fixed Income Securities 20

3 A Review of the Time Value of Money 28

4 Bond Pricing and Return Measures 49

5 Price Volatility Characteristics of Fixed Income Securities 83

6 The Structure of Interest Rates 113

7 Treasury and Agency Securities 141

8 Municipal Bonds 155

9 Private Money Market Instruments 186

10 Corporate Bonds 203

11 Medium-Term Notes 233

12 Domestic Floating-Rate and Adjustable-Rate Debt Securities 255

13 Nonconvertible Preferred Stock 265

14 Convertible Securities 290

15 The High-Yield Corporate Bond Market 307

16 Eurocapital Markets 327

17 Stable Value Investments 354

18 Credit Analysis for Corporate Bonds 375

19 Credit Considerations in Evaluating High-Yield Bonds 411

20 Investing in Chapter 11 and Other Distressed Companies 421

21 Guidelines in the Credit Analysis of General Obligation and Revenue Municipal Bonds 443

22 Sovereign Risk from a Corporate Bond Analyst Perspective 470

23 Mortgages 483

24 Mortgage Pass-Through Securities 502

25 Collateralized Mortgage Obligations 549

26 Asset-Backed Securities 583

27 Evaluating Credit Risk of Asset-Backed Securities 602

28 Valuation of Bonds with Embedded Options 611

29 Option-Adjusted Spread Analysis 635

30 OAS and Effective Duration 665

31 New Duration Measures for Risk Management 682

32 Interest-Rate Risk Models Used in the Banking and Thrift Industries 695

33 Risk Measures for Foreign Bonds 709

34 Fixed Income Risk Modeling 720

35 Valuation and Risk Analysis of International Bonds 733

36 Valuation and Analysis of Convertible Securities 750

37 The Term Structure of Interest Rates 779

38 Bond Management: Past, Current, and Future 833

39 The Active Decisions in the Selection of Passive Management and Performance Bogeys 840

40 A Sponsor's View of Benchmark Portfolios 864

41 Indexing Fixed Income Assets 882

42 Bond Immunization: An Asset/Liability Optimization Strategy 896

43 Dedicated Bond Portfolios 927

44 Beyond Cash Matching 942

45 Improving Insurance Company Portfolio Returns 955

46 Asset/Liability Management for Property/Casualty Insurers 971

47 The Management of High-Yield Bond Portfolios 995

48 International Bond Investing and Portfolio Management 1007

49 International Fixed Income Investing: Theory and Practice 1045

50 Introduction to Interest-Rate Futures and Options Contracts 1079

51 Pricing Futures and Portfolio Applications 1106

52 Treasury Bond Futures Mechanics and Basis Valuation 1119

53 The Basics of Interest-Rate Options 1145

54 An Overview of Fixed Income Option Models 1171

55 Hedging with Futures and Options 1204

56 Interest-Rate Swaps 1236

57 Interest-Rate Caps and Floors and Compound Options 1255

58 Forecasting Interest Rates

JACKSON / STAUNTON
Advanced Modelling in Finance Using Excel and VBA

**Table of Contents**

Preface

Acknowledgements

1 Introduction 1

Pt. 1 Advanced Modelling in Excel 7

2 Advanced Excel functions and procedures 9

3 Introduction to VBA 39

4 Writing VBA user-defined functions 73

Pt. 2 Equities 99

5 Introduction to equities 101

6 Portfolio optimisation 103

7 Asset pricing 125

8 Performance measurement and attribution 139

Pt. 3 Options on Equities 155

9 Introduction to options on equities 157

10 Binomial trees 167

11 The Black-Scholes formula 185

12 Other numerical methods for European options 197

13 Non-normal distributions and implied volatility 209

Pt. 4 Options on Bonds 221

14 Introduction to valuing options on bonds 223

15 Interest rate models 231

16 Matching the term structure 243

App Other VBA functions 253

Index 259

TAVELLA
Quantitative Methods in Derivatives Pricing : An Introduction to Computational Finance

**Table of Contents**

Ch. 1 Arbitrage and Pricing 1

Ch. 2 Fundamentals of Stochastic Calculus 8

Ch. 3 Pricing in Continuous Time 41

Ch. 4 Scenario Generation 77

Ch. 5 European Pricing with Simulation 121

Ch. 6 Simulation for Early Exercise 177

Ch. 7 Pricing with Finite Differences 207

Bibliography 273

Index 277

TAVELLA / RANDALL
Pricing Financial Instruments : The Finite Difference Method

**Table of Contents**

1 Introduction 1

Stochastic Processes 3

Markov Processes 5

Stochastic Differential Equations 8

Ito's Formula 9

Ito's Formula for Processes with Jumps 10

Arbitrage Pricing Theory 13

Change of Measure 16

References 21

2 The Pricing Equations 23

European Derivatives 24

Hedging Portfolio Approach 24

Feynman-Kac Approach 27

The Pricing Equation in the Presence of Jumps 30

An Application of Jump Processes: Credit Derivatives 34

Defaultable Bonds 37

Full Protection Credit Put 38

American Derivatives 39

Relationship between European and American Derivatives 40

American Options as Dynamic Optimization Problems 42

Conditions at Exercise Boundaries 43

Linear Complementarity Formulation of American Option Pricing 44

Path Dependency 45

Discrete Sampling of Path Dependency 47

Dimensionality Reduction 48

Reformulating the Underlying Processes in a Different Measure 49

Currency Translated Options 50

Equations for the Hedging Parameters 56

Computation of Greeks by Direct Discretization 57

Computation of Greeks through Their Governing Equations 57

References 60

3 Analysis of Finite Difference Methods 61

Motivation 61

Constructing Finite Difference Approximations 67

Stability Analysis: Matrix Approach 70

Space Discretization 71

Time Discretization 73

Analysis of Specific Algorithms 77

Eigenvalue Analysis of the Black-Scholes Equation 86

Stability Analysis: Fourier Approach 90

Implementation of the Time Advancement 93

Solving Sparse Systems of Linear Equations 94

Finite Difference Approach to American Options 100

The Linear Complementarity Problem 101

Distortions Induced by Discretization 105

Strategies for Complex Derivative Structures 107

References 108

4 Special Issues 110

Effect of Payoff Discontinuities on Convergence 110

Implementing Jump Conditions 114

Boundary Conditions 120

Boundary Conditions in One Dimension 121

Boundary Conditions in Multiple Dimensions 130

Continuous and Discrete Sampling Models for Path-Dependent Options 132

Continuous Sampling 132

Discrete Sampling 136

Performance of Solvers for Multidimensional Problems 141

Numerical Solution of PIDEs: Jump-Diffusion and Pure Jump Models 147

References 155

5 Coordinate Transformations 156

One-Dimensional, Time-Independent Transformations 157

Transformations Place Grid Points at Selected Positions 160

Transformations That Concentrate Grid Points 167

One-Dimensional, Time-Dependent Transformations 172

Multidimensional, Time-Independent Transformations 173

Factored Multidimensional, Time-Independent Transformations 174

General Multidimensional, Time-Independent Transformations 175

Multidimensional Linear Transformations 177

References 182

6 Numerical Examples 183 Barrier Options 183

Time-Dependent Barriers 183

Nonuniform Grids and Discrete Sampling 187

Discretely Sampled Parisian Options 196

A Leveraged Knockin Put 202

Discretely Sampled Asian Options 206

Stochastic Volatility 212

Convertible Bond 214

Simple Fixed Income Instruments: Forward Swap 218

Credit Derivatives 223

References 228

Index 231

BROOKS
Building Financial Derivatives Applications with C++

**Table of Contents**

Preface

Introduction

Learning Objectives

Introduction

The Case for C++

Derivative Technology and Applications

Overview of C++

Summary

Appendix 1A: Brief Overview of Borland C++ Builder

Hello World Program: Windows Graphical User

Interface (GUI)

File Types

Introduction to C++

Learning Objectives

Introduction

Basic Features of C++

Object-Oriented Programming

Bond Pricing Program: Console Application

Summary

Appendix 2A: User Inputs in C++Builder

Bond Pricing Program Without Error Trapping

Bond Pricing Program With Error Trapping

Derivatives Valuation

Learning Objectives

Introduction

Review of Valuation Issues

Approaches to Valuation

Market Comparables Approach (MCA)

Cash Flow Adjusted Approach (CFAA)

Discount Factor Adjusted Approach (DFAA)

Selecting the Best Approach to Valuation

Tools of the Trade

Learning Objectives

Introduction

Secant Method

Fitting the Term Structure of Interest Rates

Monte Carlo Simulation

Lattice Procedures

Summary

Appendix 4A: C++ Builder Form for Yield to

Maturity

Valuing Forward Contracts and Interest Rate Swaps

Learning Objectives

Introduction

Valuing Forward Contracts

Valuing Futures Contracts

Valuing Interest Rate Swaps

Summary

Appendix 5A: C++Builder Form for Valuing

Forward Contracts

Valuing Stock Options

Learning Objectives

Introduction

Black-Scholes Option Pricing Model and DLLs

Implied Volatility

American-Style Option Valuation with the

Binomial Lattice

Summary

Building Interest Rate Trees

Learning Objectives

Introduction

Interest Rate Modeling

Equilibrium Swap Rates

Caps and Floors Based on the Black, Derman, and Toy Model in C++

Summary

Appendix 7A: Forward Rates from Par Bond Yields

Appendix 7B: State Contingent Claim Values

Mortgage-Backed Securities and Monte Carlo Simulation

Learning Objectives

Introduction

Mortgage-Backed Securities and Prepayment

Models

Monte Carlo Simulation

Mortgage-Backed Securities Valuation

Summary

Value-at-Risk and Summary

Learning Objectives

Introduction

Value-at-Risk

Review

Summary

Selected Readings

Index

GRINOLD / KAHN
Active Portfolio Management:
A Quantitative Approach for Producing Superior Returns and Controlling Risk

**Table of Contents**

Preface

Acknowledgments

Ch. 1 Introduction 1

Pt. 1 Foundations

Ch. 2 Consensus Expected Returns: The Capital Asset Pricing Model 11

Ch. 3 Risk 41

Ch. 4 Exceptional Return, Benchmarks, and Value Added 87

Ch. 5 Residual Risk and Return: The Information Ratio 109

Ch. 6 The Fundamental Law of Active Management 147

Pt. 2 Expected Returns and Valuation

Ch. 7 Expected Returns and the Arbitrage Pricing Theory 173

Ch. 8 Valuation in Theory 199

Ch. 9 Valuation in Practice 225

Pt. 3 Information Processing

Ch. 10 Forecasting Basics 261

Ch. 11 Advanced Forecasting 295

Ch. 12 Information Analysis 315

Ch. 13 The Information Horizon 347

Pt. 4 Implementation

Ch. 14 Portfolio Construction 377

Ch. 15 Long/Short Investing 419

Ch. 16 Transactions Costs, Turnover, and Trading 445

Ch. 17 Performance Analysis 477

Ch. 18 Asset Allocation 517

Ch. 19 Benchmark Timing 541

Ch. 20 The Historical Record for Active Management 559

Ch. 21 Open Questions 573

Ch. 22 Summary 577

App. A: Standard Notation 581

App. B: Glossary 583

App. C Return and Statistics Basics 587

Index 591

CRACK
Heard on The Street : Quantitative Questions from Wall Street Job Interviews

New! (January 2004) DOWNLOAD: ADOBE READER

**Table of Contents**

1 Introduction 1

2 Purely Quantitative & Logic Questions 7

3 Derivatives Questions 21

4 Other Financial Economics Questions 35

5 Statistics and Programming Questions 41

5.1 Statistics Questions 41

5.2 Programming Questions 47

6 Non-Quantitative Questions 49

6.1 Questions about You 50

6.2 Questions about Your Job Awareness 54

6.3 Questions about the Markets or the Economy 56

6.4 Financial Management Questions 57

6.5 Thinking Questions 58

A Purely Quantitative & Logic Answers 61

B Derivatives Answers 119

C Other Financial Economics Answers 193

D Statistics Answers 215

E Non-Quantitative Answers (Selected) 237

F Basic Option Pricing Theory 243

F.1 Logarithms and Exponentials 243

F.2 Normality and Lognormality 248

F.3 Prices, Returns and Compounding 253

F.4 Option Pricing 258

F.4.1 A Discussion of the Black-Scholes Formula 265

F.5 Deriving the Black-Scholes Formula 268

F.5.1 A Derivation of the Black-Scholes Formula 268

F.5.2 Discussion of the Derivation 272

G HP 17B and 19B Source Code 275

G.1 Black-Scholes Call and Put Prices 275

G.2 Binomial Option Pricing 279

G.3 Macaulay Duration 281

G.4 Macaulay Convexity 281

References for Further Research 285

Index 303

OSBORNE
The Stock Market and Finance From a Physicist's Viewpoint

MANTEGNA / STANLEY
An Introduction to Econophysics: Correlations and Complexity in Finance

**Table of Contents**

Preface

1 Introduction 1

2 Efficient market hypothesis 8

3 Random walk 14

4 Levy stochastic processes and limit theorems 23

5 Scales in financial data 34

6 Stationarity and time correlation 44

7 Time correlation in financial time series 53

8 Stochastic models of price dynamics 60

9 Scaling and its breakdown 68

10 ARCH and GARCH processes 76

11 Financial markets and turbulence 88

12 Correlation and anticorrelation between stocks 98

13 Taxonomy of a stock portfolio 105

14 Options in idealized markets 113

15 Options in real markets 123

App. A Notation guide 130

App. B Martingales 136

References 137

Index 145

CAMPBELL / LO / MACKINLAY
The Econometrics of Financial Markets

**Table of Contents**

List of Figures

List of Tables

Preface

1 Introduction 3

2 The Predictability of Asset Returns 27

3 Market Microstructure 83

4 Event-Study Analysis 149

5 The Capital Asset Pricing Model 181

6 Multifactor Pricing Models 219

7 Present-Value Relations 253

8 Intertemporal Equilibrium Models 291

9 Derivative Pricing Models 339

10 Fixed-Income Securities 395

11 Term-Structure Models 427

12 Nonlinearities in Financial Data 467

App. A.1 Linear Instrumental Variables 527

App. A.2 Generalized Method of Moments 532

App. A.3 Serially Correlated and Heteroskedastic Errors 534

App. A.4 GMM and Maximum Likelihood 536

References 541

Author Index 587

Subject Index 597

TALEB
Dynamic Hedging : Managing Vanilla and Exotic Options

**Table of Contents**

Introduction: Dynamic Hedging 1

1 Introduction to the Instruments 9

2 The Generalized Option 38

3 Market Making and Market Using 48

4 Liquidity and Liquidity Holes 68

5 Arbitrage and the Arbitrageurs 80

6 Volatility and Correlation 88

7 Adapting Black-Scholes-Merton: The Delta 115

8 Gamma and Shadow Gamma 132

9 Vega and the Volatility Surface 147

10 Theta and Minor Greeks 167

11 The Greeks and Their Behavior 191

12 Fungibility, Convergence, and Stacking 208

13 Some Wrinkles of Option Markets 222

14 Bucketing and Topography 229

15 Beware the Distribution 238

16 Option Trading Concepts 256

17 Binary Options: European Style 273

18 Binary Options: American Style 295

19 Barrier Options (I) 312

20 Barrier Options (II) 347

21 Compound, Choosers, and Higher Order Options 376

22 Multiasset Options 383

23 Minor Exotics: Lookback and Asian Options 403

Module A Brownian Motion on a Spreadsheet, a Tutorial 415

Module B Risk Neutrality Explained 426

Module C Numeraire Relativity and the Two-Country Paradox 431

Module D Correlation Triangles: A Graphical Case Study 438

Module E The Value-at-Risk 445

Module F Probabilistic Rankings in Arbitrage 453

Module G Option Pricing 459

Notes 479

Bibliography 490

Index 499

ALEXANDER
Market Models : A Guide to Financial Data Analysis

**Table of Contents**

Preface

Acknowledgements

Pt. I Volatility and Correlation Analysis

Ch. 1 Understanding Volatility and Correlation 3

Ch. 2 Implied Volatility and Correlation 21

Ch. 3 Moving Average Models 49

Ch. 4 GARCH Models 63

Ch. 5 Forecasting Volatility and Correlation 117

Pt. II Modelling the Market Risk of Portfolios

Ch. 6 Principal Component Analysis 143

Ch. 7 Covariance Matrices 179

Ch. 8 Risk Measurement in Factor Models 229

Ch. 9 Value-at-Risk 249

Ch. 10 Modelling Non-normal Returns 285

Pt. III Statistical Models for Financial Markets

Ch. 11 Time Series Models 315

Ch. 12 Cointegration 347

Ch. 13 Forecasting High-Frequency Data 389

Technical Appendices 409

References 453

Tables 467

Index 475

WILMOTT / HOWISON / DEWYNNE
The Mathematics of Financial Derivatives : A Student Introduction

**Table of Contents**

Preface

Pt. 1 Basic Option Theory

1 An Introduction to Options and Markets 3

2 Asset Price Random Walks 18

3 The Black-Scholes Model 33

4 Partial Differential Equations 58

5 The Black-Scholes Formulae 71

6 Variations on the Black-Scholes Model 90

7 American Options 106

Pt. 2 Numerical Methods 133

8 Finite-difference Methods 135

9 Methods for American Options 165

10 Binomial Methods 180

Pt. 3 Further Option Theory 195

11 Exotic and Path-dependent Options 197

12 Barrier Options 206

13 A Unifying Framework for Path-dependent Options 213

14 Asian Options 222

15 Lookback Options 236

16 Options with Transaction Costs 252

Pt. 4 Interest Rate Derivative Products 263

17 Interest Rate Derivatives 265

18 Convertible Bonds 286

Hints to Selected Exercises 295

Bibliography 308

Index 312

MURPHY
Technical Analysis of the Financial Markets : A Comprehensive Guide to Trading Methods and Applications

**Table of Contents**

About the Author

About the Contributors

Introduction

Acknowledgments

1 Philosophy of Technical Analysis 1

2 Dow Theory 23

3 Chart Construction 35

4 Basic Concepts of Trend 49

5 Major Reversal Patterns 99

6 Continuation Patterns 129

7 Volume and Open Interest 157

8 Long Term Charts 181

9 Moving Averages 195

10 Oscillators and Contrary Opinion 225

11 Point and Figure Charting 265

12 Japanese Candlesticks 297

13 Elliott Wave Theory 319

14 Time Cycles 343

15 Computers and Trading Systems 377

16 Money Management and Trading Tactics 393

17 The Link Between Stocks and Futures: Intermarket Analysis 413

18 Stock Market Indicators 433

19 Pulling It All Together - A Checklist 453

A Advanced Technical Indicators 463

B Market Profile 475

C The Essentials of Building a Trading System 493

D Continuous Futures Contracts 505

Glossary 511

Selected Bibliography 523

Selected Resources 527

Index 531

WOLFRAM
The Mathematica Book.
See also a new book WOLFRAM: The Mathematica Book, Fifth Edition (August 2003).

**Table of Contents**

A Tour of Mathematica 1

Pt. 1 A Practical Introduction to Mathematica

1.0 Running Mathematica 26

1.1 Numerical Calculations 29

1.2 Building Up Calculations 38

1.3 Using the Mathematica System 44

1.4 Algebraic Calculations 62

1.5 Symbolic Mathematics 78

1.6 Numerical Mathematics 100

1.7 Functions and Programs 108

1.8 Lists 113

1.9 Graphics and Sound 133

1.10 Input and Output in Notebooks 178

1.11 Files and External Operations 208

1.12 Special Topic: The Internals of Mathematica 220

Pt. 2 Principles of Mathematica

2.1 Expressions 232

2.2 Functional Operations 242

2.3 Patterns 261

2.4 Transformation Rules and Definitions 285

2.5 Evaluation of Expressions 310

2.6 Modularity and the Naming of Things 363

2.7 Strings and Characters 391

2.8 Textual Input and Output 409

2.9 The Structure of Graphics and Sound 472

2.10 Manipulating Notebooks 558

2.11 Files and Streams 613

2.12 MathLink and External Program Communication 647

2.13 Global Aspects of Mathematica Sessions 692

Pt. 3 Advanced Mathematics in Mathematica

3.1 Numbers 714

3.2 Mathematical Functions 736

3.3 Algebraic Manipulation 789

3.4 Manipulating Equations 811

3.5 Calculus 830

3.6 Series, Limits and Residues 860

3.7 Linear Algebra 871

3.8 Numerical Operations on Data 893

3.9 Numerical Operations on Functions 909

3.10 Mathematical and Other Notation 939

Formula Gallery 969

Graphics Gallery 979

Appendix Mathematica Reference Guide

Index 1381

BJORK
Arbitrage Theory in Continuous Time

See also a new Second Edition (2004)
BJORK: Arbitrage Theory in Continuous Time

**Table of Contents**

1 Introduction 1

2 The Binomial Model 6

3 Stochastic Integrals 27

4 Differential Equations 52

5 Portfolio Dynamics 69

6 Arbitrage Pricing 76

7 Completeness and Hedging 99

8 Parity Relations and Delta Hedging 108

9 Several Underlying Assets 119

10 Incomplete Markets 135

11 Dividends 154

12 Currency Derivatives 167

13 Barrier Options 182

14 Stochastic Optimal Control 198

15 Bonds and Interest Rates 228

16 Short Rate Models 243

17 Martingale Models for the Short Rate 253

18 Forward Rate Models 267

19 Change of Numeraire 275

20 Forwards and Futures 298

References 304

Index 308

NICHOLAS
Market-Neutral Investing : Long/Short Hedge Fund Strategies

**Table of Contents**

Acknowledgments

Foreword

Introduction 1

1 Investing in Relationships 5

2 Developments in the Hedge Fund Industry 19

3 Making an Investment in Market-Neutral Strategies 27

4 Convertible Arbitrage 57

5 Fixed-Income Arbitrage 89

6 Mortgage-Backed Securities Arbitrage 119

7 Merger Arbitrage 145

8 Equity Hedge 177

9 Equity Market-Neutral and Statistical Arbitrage 203

10 Relative Value Arbitrage 231

Afterword 247

Glossary 249

Index 255

NATENBERG
Option Volatility & Pricing : Advanced Trading Strategies and Techniques

**Table of Contents**

Preface to the First Edition

Preface to the Second Edition

1 The Language of Options 1

2 Elementary Strategies 13

3 Introduction to Theoretical Pricing Models 35

4 Volatility 51

5 Using an Option's Theoretical Value 81

6 Option Values and Changing Market Conditions 95

7 Introduction to Spreading 127

8 Volatility Spreads 137

9 Risk Considerations 173

10 Bull and Bear Spreads 199

11 Option Arbitrage 213

12 Early Exercise of American Options 241

13 Hedging with Options 257

14 Volatility Revisited 273

15 Stock Index Futures and Options 301

16 Intermarket Spreading 331

17 Position Analysis 353

18 Models and the Real World 385

Appendix A A Glossary of Option and Related Terminology 419

Appendix B The Mathematics of Option Pricing 431

Appendix C Characteristics of Volatility Spreads 449

Appendix D What's the Right Strategy? 451

Appendix E Synthetic and Arbitrage Relationships 453

Appendix F Recommended Reading 457

Index 463

OKSENDAL
Stochastic Differential Equations : An Introduction With Applications, 6th edition (Universitext), December 2003

**Table of Contents**

I Introduction 1

II Some Mathematical Preliminaries 5

III Ito Integrals 18

IV Ito Processes and the Ito Formula 40

V Stochastic Differential Equations 59

VI The Filtering Problem 75

VII Diffusions: Basic Properties 103

VIII Other Topics in Diffusion Theory 124

IX Applications to Boundary Value Problems 160

X Application to Optimal Stopping 183

XI Application to Stochastic Control 212

Appendix A: Normal Random Variables 236

Appendix B: Conditional Expectations 239

Appendix C: Uniform Integrability and Martingale Convergence 241

Solutions and additional hints to some of the exercises 244

Bibliography 252

List of Frequently Used Notation and Symbols 261

Index 265

PRISMAN
Pricing Derivative Securities: An Interactive, Dynamic Environment with Maple V and Matlab

**Table of Contents**

Preface xv

Software xxii

1 Theory of Arbitrage 1

1.1 A Basic One-Period Model 1

1.2 Defining the No-Arbitrage Condition 5

1.2.1 Identifying an Arbitrage Portfolio 8

1.2.2 Law of One Price 11

1.3 Pricing by Replication 13

1.3.1 Three Special Contingent Cash Flows 14

1.4 Stochastic Discount Factors (SDFs) 18

1.4.1 SDFs and Risk-Neutral Probability 22

1.5 Concluding Remarks 28

1.6 Questions and Problems 29

1.7 Appendix 32

1.7.1 Complete Market 32

1.7.2 Incomplete Market 34

1.7.3 Incomplete Market and Arbitrage Bounds 35

1.7.4 The No-Arbitrage Condition and Its Geometric Exposition 42

2 Arbitrage Pricing: Equity Markets 47

2.1 Market Structure and the Risk-Free Rate 47

2.2 One-Period Binomial Model 50

2.3 Valuing Two Propositions 57

2.4 Forwards: A First Look 61

2.4.1 Forward Contract on a Security 62

2.4.2 Forward Contract on the Exchange Rate 67

2.5 Swaps: A First Look 72

2.5.1 Currency Swaps 72

2.5.2 Equity (Asset) Swap 74

2.6 General Valuation 77

2.6.1 The Risk-Free Rate of Interest Implicit in the Market 78

2.6.2 The Two Propositions 78

2.6.3 Forwards 79

2.6.4 Swaps 83

2.7 Concluding Remarks 86

2.8 Questions and Problems 87

3 Pricing by Arbitrage: Debt Markets 91

3.1 Setting the Framework 91

3.2 Arbitrage in the Debt Market 94

3.2.1 Distinct Features of the Debt Market 99

3.2.2 Defining the No-Arbitrage Condition 101

3.3 Discount Factors 104

3.4 Discount Factors and Continuous Compounding 108

3.4.1 Continuous Compounding 108

3.5 Concluding Remarks 110

3.6 Questions and Problems 111

3.7 Appendix 113

3.7.1 No-Arbitrage Condition in the Bond Market 113

4 Fundamentals of Options 115

4.1 Extending the Simple Model 115

4.2 Two Types of Options 116

4.3 Trading Strategies 125

4.3.1 Portfolios of Calls and Puts with the Same Maturity Date 127

4.4 Payoff Diagrams and Relative Pricing 141

4.4.1 Pricing Bounds Obtained by Relative Pricing Results 143

4.4.2 Put-Call Parity 148

4.5 From Payoffs to Portfolios 154

4.6 Concluding Remarks 164

4.7 Questions and Problems 165

4.8 Appendix 168

4.8.1 Explanation of Stripay 168

4.8.2 Procedural Issues 169

5 Risk-Neutral Probability and the SDF 183

5.1 Infinite vs. Finite States of Nature 184

5.2 SDF for an Infinite [Omega] 187

5.3 Risk-Neutral Probability and the SDF 191

5.4 A First Look at Stock Prices 193

5.5 The Distribution of the Rate of Return 196

5.6 Paths of the Price Process 204

5.7 Specifying a Risk-Neutral Probability 208

5.8 Lognormal Distributions and the SDF 213

5.9 The Stochastic Discount Factor Function 215

5.10 Concluding Remarks 220

5.11 Questions and Problems 221

6 Valuation of European Options 223

6.1 Valuing a Call Option 224

6.2 Valuing a Put Option 230

6.3 Combinations across Time 234

6.4 Dividends and Option Pricing 255

6.5 Volatility and Implied Volatility 259

6.5.1 Estimating Volatility from Historical Data 259

6.5.2 Implied Volatility 261

6.6 Concluding Remarks 265

6.7 Questions and Problems 266

6.8 Appendix 268

6.8.1 Estimating Implied Volatility Using Trial and Error 268

7 Sensitivity Measures 271

7.1 The Theta Measure 272

7.2 The Delta Measure 281

7.3 The Gamma Measure 288

7.4 The Vega Measure 293

7.5 The Rho Measure 298

7.6 Concluding Remarks 302

7.7 Questions and Problems 304

7.8 Appendix 307

7.8.1 Derivation of Sensitivity Measures 307

7.8.2 Sensitivities of Other Options 312

7.8.3 Signs of the Sensitivities 317

8 Hedging with the Greeks 323

8.1 Hedging: The General Philosophy 323

8.2 Delta Hedging 326

8.2.1 Solving for a Delta Neutral Portfolio 326

8.3 Delta Neutral Portfolios 341

8.4 General Hedging 347

8.5 Optimizing Hedged Portfolios 364

8.6 Concluding Remarks 370

8.7 Questions and Problems 371

9 The Term Structure and Its Estimation 373

9.1 The Term Structure of Interest Rates 374

9.1.1 Zero-Coupon, Spot, and Yield Curves 377

9.2 Smoothing of the Term Structure 383

9.2.1 Smoothing and Continuous Compounding 389

9.3 Forward Rate 393

9.3.1 Forward Rate: A Classical Approach 393

9.3.2 Forward Rate: A Practical Approach 396

9.4 A Variable Rate Bond 399

9.5 Concluding Remarks 402

9.6 Questions and Problems 404

9.7 Appendix 408

9.7.1 Theories of the Shape of the Term Structure 408

9.7.2 Approximating Functions 411

10 Forwards, Eurodollars, and Futures 413

10.1 Forward Contracts: A Second Look 414

10.2 Valuation of Forward Contracts 415

10.3 Forward Price of Assets 423

10.3.1 Forward Contracts, Prior to Maturity, of Assets That Pay Known Cash Flows 427

10.3.2 Forward Price of a Dividend-Paying Stock 430

10.4 Eurodollar Contracts 432

10.4.1 Forward Rate Agreements (FRAs) 432

10.5 Futures Contracts: A Second Look 435

10.6 Deterministic Term Structure (DTS) 439

10.7 Futures Contracts in a DTS Environment 441

10.8 Concluding Remarks 448

10.9 Questions and Problems 449

11 Swaps: A Second Look 453

11.1 A Fixed-for-Float Swap 453

11.1.1 Valuing an Existing Swap 458

11.2 Currency Swaps 461

11.3 Commodity and Equity Swaps 472

11.3.1 Equity Swaps 475

11.4 Forwards and Swaps: A Visualization 478

11.5 Concluding Remarks 479

11.6 Questions and Problems 481

12 American Options 485

12.1 American Call Option 486

12.1.1 Arbitrage Bounds 486

12.1.2 Early Exercise Decision 487

12.2 American Put Options 488

12.2.1 Arbitrage Bounds 488

12.2.2 Early Exercise Decision 490

12.3 Put--Call Parity 492

12.4 The Effect of Dividends 495

12.4.1 A Call Option 495

12.4.2 A Put Option 501

12.5 Concluding Remarks 502

12.6 Questions and Problems 502

13 Binomial Models I 505

13.1 Setting the Premises 505

13.2 No-Arbitrage and SDFs 511

13.2.1 No-Arbitrage 511

13.2.2 SDF 512

13.3 Valuation 521

13.3.1 Valuation with SDFs 521

13.3.2 Valuation by Replication 522

13.4 Numerical Valuation 529

13.4.1 Price Evolution 529

13.4.2 European Call 530

13.4.3 European Put 539

13.4.4 American Options 546

13.5 Concluding Remarks 554

13.6 Questions and Problems 555

14 Binomial Models II 557

14.1 Binomial Model and Black-Scholes Formula 558

14.1.1 Binomial vs. Lognormal 558

14.1.2 Numerical Implementations 562

14.1.3 The Effect of Dividends 568

14.2 Risk-Neutral Probabilities 571

14.3 Futures and Forwards: A Symbolic Example 579

14.4 Brownian Motion 585

14.5 Concluding Remarks 590

14.6 Questions and Problems 592

14.7 Appendix 593

14.7.1 The Black-Scholes Formula as a Limit of the Binomial Formula 593

15 The Black-Scholes Formula 599

15.1 An Overview 599

15.2 The Price Process: A Second Look 602

15.2.1 Stochastic Evolution: The Discrete Case 605

15.3 Simulation of Stochastic Evolution 608

15.4 Stochastic Evolution 615

15.5 Ito's Lemma 621

15.5.1 Heuristic Proofs of Ito's Lemma 623

15.5.2 Examples Utilizing Ito's Lemma 628

15.6 The Black-Scholes Differential Equation 632

15.6.1 A Second Derivation 640

15.7 Reconciliation with Risk-Neutral Valuation 642

15.8 American vs. European 644

15.9 Concluding Remarks 649

15.10 Questions and Problems 651

15.11 Appendix 652

15.11.1 A Change over an Instant 652

15.11.2 The Limit of a Random Variable 656

15.11.3 A More Rigorous Insight into Ito's Lemma 666

16 Other Types of Options 673

16.1 Early Exercise, Dividends and Binomial Models 674

16.2 Indexes, Foreign Currency, and Futures 677

16.2.1 Stock Index Options 677

16.2.2 Currency Options 679

16.2.3 Options on Futures Contracts 682

16.3 Examples of Exotic Options 688

16.3.1 Binary (Digital) Options 689

16.3.2 Combinations of Binary and Plain Vanilla Options 694

16.3.3 Gap Options 695

16.3.4 Paylater (Cash on Delivery) Options 700

16.4 Interest Rate Derivatives 704

16.4.1 Black's Model 705

16.4.2 The Black, Derman, and Toy Model 714

16.5 Concluding Remarks 729

16.6 Questions and Problems 731

17 The End or the Beginning? 735

Index 743

CLEWLOW / STRICKLAND
Implementing Derivatives Models : Numerical Methods

**Table of Contents**

Preface

Acknowledgements

Notation

Pt. 1 Implementing Models in a Generalised Black-Scholes World

Ch. 1 The Black-Scholes World, Option Pricing and Numerical Techniques 3

Ch. 2 The Binomial Method 10

Ch. 3 Trinomial Trees and Finite Difference Methods 52

Ch. 4 Monte Carlo Simulation 82

Ch. 5 Implied Trees and Exotic Options 134

Pt. 2 Implementing Interest Rate Models

Ch. 6 Option Pricing and Hedging and Numerical Techniques for Pricing Interest Rate Derivatives 181

Ch. 7 Term Structure Consistent Models 208

Ch. 8 Constructing Binomial Trees for the Short Rate 233

Ch. 9 Constructing Trinomial Trees for the Short Rate 255

Ch. 10 The Heath, Jarrow and Morton Model 290

References 300

Index 304

BAXTER / RENNIE
Financial Calculus : An Introduction to Derivative Pricing

**Table of Contents**

Preface

The parable of the bookmaker 1

Ch. 1 Introduction 3

Ch. 2 Discrete processes 10

Ch. 3 Continuous processes 44

Ch. 4 Pricing market securities 99

Ch. 5 Interest rates 128

Ch. 6 Bigger models 178

App. A1: Further reading 201

App. A2: Notation 205

App. A3: Answers to exercises 209

App. A4: Glossary of technical terms 216

Index 228

JAMES / WEBBER
Interest Rate Modelling : Financial Engineering

**Table of Contents**

Part 1: Introduction to interest rate modelling

1. Introduction to interest rates

1.1 Interest rate behaviour

1.2 Basic concepts

1.3 Interest rate markets

1.4 Historical and current data

1.5 Uses of interest rate models

1.6 Conclusion

2. Interest rates in history

2.1 Interest rates in monetary history

2.2 Characteristics of interest rate behaviour

3. Introduction to interest rate modelling

3.1 Yield curve basics

3.2 Describing interest rate processes

3.3 Introducton to interest rate models

3.4 Categories of interest rate model

3.5 The role of the short rate

4. Interest rate models: theory

4.1 Summary of valuation

4.2 A theoretical market framework

4.3 Fundamentals of pricing

4.4 valuing by change of numeraire

4.5 Derivatives in the extended Vasicek model

5. Basic modelling tools

5.1 Introduction to valuation

5.2 Introduction to estimation

5.3 Statistical tests

5.4 Yield curve stripping

5.5 The convexity adjustment

6. Densities and distributions

6.1 The density function

6.2 Kernel methods

6.3 Boundary behaviour

6.4 Interest rate models at extreme values of interest rates

6.5 Tail distributions

Part II Interest rate models

7. Affine models

7.1 Affine term structure models

7.2 Interpreting the state variables

7.3 Types of affine model

7.4 Examples of one-factor affine models

7.5 Examples of n-factor affine models

7.6 A general framework for affine models

8. Market models and the Heath, Jarrow and Morton framework

8.1 Introduction to the Heath, Jarrow and Morton model

8.2 Volatility functions in HJM

8.3 Market models

8.4 General marketmodels

9. Other interest rate models

9.1 Consol models

9.2 Price kernet models

9.3 Positive interest rate models

9.4 Non-linear models

10. General formulations of interest rate models

10.1 Jump processes

10.2 Random field models

10.3 A general model

10.4 Jump models

11. Economic models

11.1 Economics and interest rates

11.2 An economically motivated financial model of interest rates

11.3 An IS-LM based model

11.4 IS-LM, hyperinflation and extended Vasicek

11.5 The general equilibrium framework

11.6 Interpreting the price kernel

Part III Valuation methods

12. Finite difference methods

12.1 The Feynman-Kac Equation

12.2 Discretising the PDE

12.3 Simplifying the PDE

12.4 Explicit methods

12.5 Implicit methods

12.6 The Crank-Nicolson method

12.7 Comparison of methods

12.8 Implicit boundary conditions

12.9 Fitting to an initial term structure

12.10 Finite difference methods in N dimensions

12.11 Operator splitting

12.12 A two-dimensional PDE

12.13 Solving a PDDE

13. Valuation: the Monte Carlo method

13.1 The basic Monte Carlo method

13.2 Speed-up methods

13.3 Sampling issues

13.4 Simulation methods for HJM models

14. Lattice methods

14.1 Introduction to lattice methods

14.2 Issues in constructing a lattice

14.3 Examples of lattice methods

14.4 Calibration to market prices

14.5 The explicit finite difference method

14.6 Lattices and the Monte Carlo method

14.7 Non-recombining lattices

14.8 Conclusions

Part IV Calibration and estimation

15. Modelling the yield curve

15.1 Stripping the yield curve

15.2 Fitting using parameterised curves

15.3 Fitting the yield curve using splines

15.4 Nelson and Siegel curves

15.5 Comparison of families of curves

15.6 Kernel methods of yield curve estimations

15.7 LP and regression methods

16. Principal components analysis

16.1 Volatility structures

16.2 Identifying empirical volatility factors

16.3 Calibrating whole yield curve methods

16.4 Processes on manifolds

16.5 Analysis of dynamical systems

16.6 Conclusions

17. Estimation methods: GMM and ML

17.1 GMM estimation

17.2 Implementation issues

17.3 The efficient method of moments (EMM)

17.4 Maximum likelihood methods

17.5 Hierarchy of procedures

18. Further estimation methods

18.1 Introduction

18.2 Filtering approaches to estimation

18.3 The extended Kalman Filter

18.4 GARCH models

18.5 Extensions of GARCH

18.6 Interest rate models and GARCH

18.7 Artificial neural nets (ANNs)

19. Interest rates and implied pricing

19.1 Problems with interest rate models

19.2 Key relationships

19.3 The interest rate case

19.4 The implied pricing method

19.5 Regularisation functions

19.6 Patching tails onto pricing densities

Afterword

Notation

Glossary of mathematical, market and model terms

References

Author Index

Subject Index

CBOT OPTIONS INSTITUTE
Options : Essential Concepts and Trading Strategies

**Table of Contents**

Preface

Acknowledgments

About the Authors

Ch. 1 The History of Options 1

Pt. 1 Essential Concepts

Ch. 2 Fundamentals of Options 19

Ch. 3 Volatility Explained 57

Ch. 4 Options Strategies: Analysis and Selection 79

Pt. 2 Investing and Trading Strategies

Ch. 5 Investing and Trading Strategies for the Individual Investor 139

Ch. 6 Strategies for Institutional Investors 171

Ch. 7 How the Trading Floor Operates 229

Ch. 8 How Market Makers Trade 253

Pt. 3 Real-Time Applications

Ch. 9 Institutional Case Studies 277

Ch. 10 The Predictive Power of Options 357

Ch. 11 Electronic Resources 389

Glossary 409

Index 425

NIELSEN
Pricing and Hedging of Derivative Securities

**Table of Contents**

1. Stochastic Processes

2. Ito Calculus

3. Gaussian Processes

4. Securities and Trading Strategies

5. The Martingale Valuation Principle

6. The Black-Scholes Model

7. Gaussian Term Structure Models

Appendix A Measure and Probability

Appendix B Lebesgue Integrals and Expectations

Appendix C The Heat Equation

Appendix D Suggested Solutions to Exercises for Chapters 1-7

Appendix E Suggested Solutions to Exercises for Appendix A and B

**Table of Contents**

Preface

Preface to the First Edition

I Corporate Finance Models 1

1 Basic Financial Calculations 3

2 Calculating the Cost of Capitol 27

App. 1 A Rule of Thumb for Calculating Debt Betas 49

App. 2 Why Is [beta] Such a Good Measure of Risk? Portfolio [beta] versus Individual Stock [beta] 51

App. 3 Getting Data from the Internet 52

3 Financial Statement Modeling 57

App. 1 Calculating the Free Cash Flows When There Are Negative Profits 83

App. 2 Accelerated Depreciation in Pro Forma Models 84

4 Using Financial Statement Models for Valuation 89

5 The Financial Analysis of Leasing 101

App The Tax and Accounting Treatment of Leases 111

6 The Financial Analysis of Leveraged Leases 115

II Portfolio Models 129

7 Portfolio Models - Introduction 131

App. 1 Adjusting for Dividends 146

App. 2 Continuously Compounded versus Geometric Returns 148

8 Calculating the Variance-Covariance Matrix 151

9 Calculating Efficient Portfolios When There Are No Short-Sale Restrictions 161

Appendix 179

10 Estimating Betas and the Security Market Line 185

11 Efficient Portfolios without Short Sales 199

12 Value at Risk (VaR) 209

App How to Bootstrap: Making a Bingo Card in Excel 219

III Option-Pricing Models 229

13 An Introduction to Options 231

14 The Binomial Option-Pricing Model 253

15 The Lognormal Distribution 277

16 The Black-Scholes Model 297

17 Portfolio Insurance 311

18 Real Options 329

19 Early Exercise Boundaries 343

App Proof 358

IV Bonds and Duration 361

20 Duration 363

21 Immunization Strategies 381

22 Modeling the Term Structure 393

23 Calculating Default-Adjusted Expected Bond Returns 401

24 Duration and the Cheapest-to-Deliver Problem for Treasury Bond Futures Contracts 417

V Technical Considerations 429

25 Random Numbers 431

26 Data Tables 443

27 Matrices 449

28 The Gauss-Seidel Method 457

29 Excel Functions 461

30 Some Excel Hints 479

VI Introduction to Visual Basic for Applications 491

31 User-Defined Functions with Visual Basic for Applications 493

App Cell Errors in Excel and VBA 516

32 Types and Loops 519

33 Macros and User Interaction 539

34 Arrays 557

35 Objects 581

App Excel Object Hierarchy 601

References 603

Index 611

BOUCHAUD / POTTERS
Theory of Financial Risks: From Statistical Physics to Risk Management

**Table of Contents**

Foreword

Preface

1 Probability theory: basic notions 1

2 Statistics of real prices 47

3 Extreme risks and optimal portfolios 91

4 Futures and options: fundamental concepts 130

5 Options: some more specific problems 186

Short glossary of financial terms 209

Index of symbols 211

Index 217

DEROSA
Options on Foreign Exchange

**Table of Contents**

Preface

Ch. 1 Introduction to Currency Options 1

The Currency Option Market 1

Option Basics 3

The Variety of Currency Options 3

The Variety of Market Participants 5

Some Additional Option Terminology 6

Ch. 2 Foreign Exchange Basics 9

The International Monetary System 9

Foreign Exchange Transactions and Market Conventions 13

The Interest Parity Theorem 14

Spot and Forward Contracts 18

Currency Futures 19

Ch. 3 Trading Currency Options 35

Over The Counter Currency Options 35

Listed Options on Actual Currency 37

Currency Futures Options 47

Listed Currency Warrants 51

Options on the USDX Futures 53

Ch. 4 Payoff Patterns at Expiration 55

Option Values at Expiration 55

Basic Analytical Concepts 56

Long and Short Positions in Futures Options 57

Option Strategies for Currency Risk Management 63

Directional Strategies 68

Volatility Biased Strategies 72

Writing Covered Calls for Income Enhancement 84

Ch. 5 Arbitrage and Parity Theorems 89

Elementary Arbitrage Theorems 89

Put-Call Parity for Currency Options 93

The Triangular Option Arbitrage Theorem 98

Synthetic Forward Contracts 98

Ch. 6 Valuation of European Currency Options 101

The Black-Scholes-Garman-Kohlhagen Model 101

Sensitivity of Option Premiums to Input Parameters 110

Remarks on Volatility 123

Ch. 7 Practical Applications of the European Currency Option Pricing Model 125

Valuation of European Currency Calls and Puts 125

Using Option Partial Derivatives 129

Topics on Volatility 138

An Example of the Analysis of a Trading Strategy 151

Ch. 8 American Currency Options 157

The General Theory of American Currency Option Pricing 157

The Economics of Early Exercise 159

The Binomial Model for American Currency Options 166

The Binomial Model for European Currency Options 175

American Option Valuation by Analytical Approximation 177

Empirical Tests of the Currency Option Pricing Model and the Behavior of Exchange Rates 180

Extensions of the Currency Option Model 188

Ch. 9 Currency Futures Options and Listed Currency Warrants 197

The Nature of Currency Futures Contracts and Their Relationships to Spot and Forward Prices 198

Arbitrage and Parity Theorems for Currency Futures Options 203

Black's Model for European Currency Futures Options 210

Synthetic Futures Contracts 216

The Valuation of American Currency Futures Options 216

Empirical Tests of the Currency Futures Option Model 221

Listed Currency Warrants 222

Ch. 10 An Introduction to Exotic Currency Options 227

Knock-out Currency Options 227

Lookback Currency Options 234

The Margrabe Option 239

Average or "Asian" Currency Options 246

Compound Options 251

Other Exotic Options 253

Selected Bibliography 257

Index 267

**Table of Contents**

Preface

1 Difference Equations 1

2 Lag Operators 25

3 Stationary ARMA Processes 43

4 Forecasting 72

5 Maximum Likelihood Estimation 117

6 Spectral Analysis 152

7 Asymptotic Distribution Theory 180

8 Linear Regression Models 200

9 Linear Systems of Simultaneous Equations 233

10 Covariance-Stationary Vector Processes 257

11 Vector Autoregressions 291

12 Bayesian Analysis 351

13 The Kalman Filter 372

14 Generalized Method of Moments 409

15 Models of Nonstationary Time Series 435

16 Processes with Deterministic Time Trends 454

17 Univariate Processes with Unit Roots 475

18 Unit Roots in Multivariate Time Series 544

19 Cointegration 571

20 Full-Information Maximum Likelihood Analysis of Cointegrated Systems 630

21 Time Series Models of Heteroskedasticity 657

22 Modeling Time Series with Changes in Regime 677

A Mathematical Review 704

B Statistical Tables 751

C Answers to Selected Exercises 769

D Greek Letters and Mathematical Symbols Used in the Text 786

Author Index 789

Subject Index 792

TAVAKOLI
Credit Derivatives: A Guide to Instruments and Applications

**Table of Contents**

Introduction

Ch. 1 Credit Derivatives Markets Overview 5

Ch. 2 Total Rate of Return Swaps - Synthetic Financing 19

Ch. 3 Credit Default Swaps of Options 73

Ch. 4 Exotic Structures 141

Ch. 5 Sovereign Risk and Emerging Markets 189

Ch. 6 Credit-Linked Notes 223

Ch. 7 Synthetic Collateralized Loan Obligations 237

Ch. 8 Selected Documentation, Regulatory, Booking, and Legal Issues 265

Ch. 9 Future of the Global Market 283

Selected Bibliography 289

Index 302

See also Second Edition (2001)
and a new book (2003)
Visit web site of the author **Janet Tavakoli** http://www.tavakolistructuredfinance.com/

KAMINSKI (formerly with ENRON)
Managing Energy Price Risk: The New Challenges and Solutions, 3rd Edition

**Table of Contents**

Preface

Contributors

Introduction

ENERGY INSTRUMENTS

1. Energy Swaps

2. Energy Options

3. Energy Exotic Options

4. Derivatives in Energy Project Finance

DEVELOPMENTS IN ENERGY MARKETS

5. The Oil Market

6. The Natural Gas Market

7. Competitive Electricity Markets Around the World: Aproaches to Prices Risk Managment

8. Regulatory and Legal Issues

RISK MEASUREMENT AND REPORTING

9. VAR, Stress-Testing and Supplementary Methodologies: Uses and Constraints in Energy Risk Managment

10. Credit Risk in Liberalised Power and Natural Gas Markets

11. Accounting for Derivative Contracts in an Energy Environment

TOOLS FOR RISK ANALYSIS

12. Power Forward Curves: A Managerial Perspective Shankar Nagarajan of Deloitte & Touche L.L.P.

13. Arbitrage-Free Valuation of Energy Derivatives

14. Volatility in Energy Prices

15. Correlation and Cointegration in Energy Markets

CHRISS Black-Scholes and Beyond : Option Pricing Models

**Table of Contents**

1 Stocks, Options, and Futures 11

2 Fundamental Mathematical Concepts 57

3 The Geometric Brownian Motion Model of Price Movements 93

4 The Black-Scholes Formula 119

5 More on the Black-Scholes Formula 185

6 Binomial Trees 219

7 Basic Option Pricing With Binomial Trees 273

8 The Volatility Smile 327

9 Implied Volatility Trees 361

10 Implied Binomial Trees 411

11 Pricing Barrier Options in the Presence of the Smile 433

Bibliography 477

Author Index 484

Index 486

DUFFIE
Dynamic Asset Pricing Theory, Third Edition

**Table of Contents**

Preface

Pt. I Discrete-Time Models 1

1 Introduction to State Pricing 3

2 The Basic Multiperiod Model 21

3 The Dynamic Programming Approach 49

4 The Infinite-Horizon Setting 65

Pt. II Continuous-Time Models 81

5 The Black-Scholes Model 83

6 State Prices and Equivalent Martingale Measures 101

7 Term-Structure Models 135

8 Derivative Pricing 167

9 Portfolio and Consumption Choice 203

10 Equilibrium 235

11 Corporate Securities 259

12 Numerical Methods 293

Appendixes 321

A Finite-State Probability 323

B Separating Hyperplanes and Optimality 326

C Probability 329

D Stochastic Integration 334

E SDE, PDE, and Feynman-Kac 340

F Ito's Formula with Jumps 347

G Utility Gradients 351

H Ito's Formula for Complex Functions 355

I Counting Processes 357

J Finite-Difference Code 363

Bibliography 373

Symbol Glossary 445

Author Index 447

Subject Index 457

KATZ / MCCORMICK The Encyclopedia of Trading Strategies

**Table of Contents**

Preface

Part One: Tools of the Trade

Chapter 1: Dat.

Chapter 2: Simulators

Chapter 3: Optimizers and Optimazation

Chapter 4: Statistics

Part Two: The Study of Entries

Chapter 5: Breakout Models

Chapter 6: Moving-Average Models

Chapter 7: Oscillator-Based Entries

Chapter 8: Seasonality

Chapter 9: Lunar and Solar Rhythms

Chapter 10: Cycle-Based Entries

Chapter 11: Neural Networks

Chapter 12: Genetic Algorithms

Part Three: The Study of Exits

Chapter 13: The Standard Exit Strategy

Chapter 14: Improvements on the Standard Exit

Chapter 15: Adding Artificial Intelligence to Exits

Conclusion

Notice

Appendix

Index

BEST Implementing Value at Risk

**Table of Contents**

Preface

Acknowledgements

1 Defining risk and VAR 1

2 Covariance 14

3 Calculating VAR using simulation 32

4 Measurement of volatility and correlation 57

5 Implementing value at risk 103

6 Stress testing 128

7 Managing risk with VAR 141

8 Risk adjusted performance measurement 149

9 Regulators and risk management 174

10 Introduction to the spreadsheets 197

References and further reading 199

Index 201

PRING Introduction to Technical Analysis

**Table of Contents**

Basic Principles

Trendlines, Support, and Resistance

Volume

Price Patterns for Traders

Moving Averages

Momentum

A Primer on Candlestick Charting

SHAW Modeling Financial Derivatives With Mathematica (Includes CD-ROM)

**Table of Contents**

Preface

1 Advanced Tools for Rocket Science 1

2 An Introduction to Mathematica 12

3 Mathematical Finance Preliminaries 68

4 Mathematical Preliminaries 85

5 Log and Power Contracts 127

6 Binary Options and the Normal Distribution 136

7 Vanilla European Calls and Puts 151

8 Barrier Options - a Case Study in Rapid Development 167

9 Analytical Models of Lookbacks 189

10 Vanilla Asian Options - Analytical Methods 200

11 Vanilla American Options - Analytical Methods 215

12 Double Barrier, Compound, Quanto Options and other Exotics 237

13 The Discipline of the Greeks and Overview of Finite-Difference Schemes 258

14 Finite-Difference Schemes for the Diffusion Equation with Smooth Initial Conditions 266

15 Finite-Difference Schemes for the Black-Scholes Equation with Nonsmooth Payoff Initial Conditions 279

16 SOR and PSOR Schemes for the Three-Time-Level Douglas Scheme and Applications to American Options 306

17 Linear Programming Alternatives to PSOR and Regression 331

18 Traditional and Supersymmetric Trees 344

19 Tree Implementation in Mathematica and Basic Tree Pathology 363

20 Turbo-charged Trees with the Mathematica Compiler 387

21 Monte Carlo and Wozniakowski Sampling 400

22 Basic Applications of Monte Carlo 420

23 Monte Carlo Simulation of Basket Options 437

24 Getting Jumpy over Dividends 454

25 Simple Deterministic and Stochastic Interest Rate Models 470

26 Building Yield Curves from Market Data 482

27 Simple Interest Rate Options 504

28 Modelling Volatility by Elasticity 515

Index 534

KARATZAS / SHREVE
Brownian Motion and Stochastic Calculus

STEELE
Stochastic Calculus and Financial Applications

MERTON
Continuous-Time Finance

**Table of Contents**

Foreward: Paul Samuelson

Part I: Introduction to Finance and the Mathematics of Continuous-time Models:

1. Modern Finance

2. Introduction to Portfolio Selection and Capital Market Theory: Static Analysis

3. On the Mathematics and Economic Assumptions of Continuous-time Financial Models

Part II: Optimum Consumption and Portfolio Selection in Continuous-time Models:

4. Lifetime Portfolio Selection under Uncertainty: The Continuous-time Case

5. Optimum Consumption and Portfolio Rules in a Continuous-time Model

6. Further Developments in Theory of Optimal Consumption and Portfolio Selection

Part III: Warrant and Option Pricing Theory:

7. A Complete Model of Warrant Pricing that Maximizes Utility

8. Theory of Rational Option Pricing

9. Option Pricing when Underlying Stock Returns are Discontinuous

10. Further Developments in Option Pricing Theory

Part IV: Contingent-Claims Analysis in the Theory of Corporate Finance and Financial Intermediation:

11. A Dynamic General Equilibrium Model of the Asset Market and its Application to the Pricing of the Capital Structure of the Firm

12. On the Pricing of Corporate Debt: The Risk Structure of Interest Rates

13. On the Pricing of Contingent Claims and the Modigliani-Miller Theorem

14. Contingent Claims Analysis in the Theory of Corporate Finance and Financial Intermediation

Part V: An Intertemporal-Equilibrium Theory of Finance:

15. An Intertemporal Capital Asset Pricing Model

16. A General Equilibrium Theory of Finance in Continuous Time

Part VI: Applications of the Continuous-Time Model to Selected Issues in Public Finance:

17. An Asymptotic Theory of Growth Under Uncertainty

18. On Consumption-Indexed Public Pension Plans

19. An Analytic Derivation of the Cost of Loan Guarantees and Deposit Insurance

20. On the Cost of Deposit Insurance when there are Surveillance Costs

WILLIAMS Probability With Martingales

ROSS
An Elementary Introduction to Mathematical Finance : Options and Other Topics, 2nd Edition

**Table of Contents**

Introduction and Preface

1 Probability

2 Normal Random Variables

3 Geometric Brownian Motion

4 Interest Rates and Present Value Analysis

5 Pricing Contracts via Arbitrage

6 The Arbitrage Theorem

7 The Black-Scholes Formula

8 Valuing by Expected Utility

9 Exotic Options

10 Beyond Geometric Brownian Motion Models

11 Autogressive Models and Mean Reversion

12 Optimization Methods in Finance

Index

ABRAMOWITZ / STEGUN
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables

Published by Dover Publications. See also some other Dover Books.

Financial Mathematics Seminar Bookshelf | Financial Mathematics Seminar | Chicago Financial Engineering & Risk Management Workshop | Related Seminars/Workshops | Journals | New Books 1999-2000-2001-2002-2003-2004++ | Bestsellers | Fabozzi | IRWIN | Financial Engineering | Wiley Finance | Trading | Risk Books | Butterworth-Heinemann | Books | State-of-the-Art | Conferences/Seminars/Workshops | FinMath | Amazon Coupons |