#### You've reached the end of your free preview.

Want to read all 341 pages?

**Unformatted text preview: **sundaram-1810040 book February 9, 2010 8:35 Brief Contents
Author Biographies
Preface xvi
xxi 19 Exotic Options II: Path-Dependent
Options 470 1 20 Value-at-Risk Acknowledgments
1 18 Exotic Options I: Path-Independent
Options 440 xv Introduction 498 21 Convertible Bonds PART ONE
Futures and Forwards
2 Futures Markets 22 Real Options 519 548 17 PART THREE 19 Swaps 3 Pricing Forwards and Futures I:
The Basic Theory 60
4 Pricing Forwards and Futures II: Building
on the Foundations 85
5 Hedging with Futures and Forwards 101 6 Interest-Rate Forwards and Futures 122 569 23 Interest Rate Swaps and Floating-Rate
Products 571
24 Equity Swaps 613 25 Currency and Commodity Swaps 631 PART FOUR
PART TWO Interest Rate Modeling Options 26 The Term Structure of Interest Rates:
Concepts 649 153 7 Options Markets 155 27 Estimating the Yield Curve 8 Options: Payoffs and Trading
Strategies 171 29 Factor Models of the Term Structure 10 Early Exercise and Put-Call Parity 213
12 Binomial Option Pricing 228 259 13 Implementing the Binomial Model
14 The Black-Scholes Model 667 28 Modeling Term-Structure
Movements 684 9 No-Arbitrage Restrictions on
Option Prices 196
11 Option Pricing: An Introduction 647 289 308 30 The Heath-Jarrow-Morton and Libor
Market Models 731 PART FIVE
Credit Risk 769 31 Credit Derivative Products 771 15 The Mathematics of Black-Scholes 344 32 Structural Models of Default Risk 16 Options Modeling: Beyond
Black-Scholes 357 33 Reduced-Form Models of
Default Risk 829 17 Sensitivity Analysis: The Option
“Greeks” 404 34 Modeling Correlated Default vi 700 863 802 sundaram-1810040 book February 9, 2010 8:35 Brief Contents vii Bibliography
Index B-1 I-1 The following Web chapters are
available at :
PART SIX
Computation 901 35 Derivative Pricing with Finite
Differencing 903
36 Derivative Pricing with Monte Carlo
Simulation 923
37 Using Octave 945 sundaram-1810040 book February 9, 2010 8:35 Contents
Author Biographies
Preface xvi Acknowledgments
Chapter 1
Introduction
1.1
1.2
1.3
1.4
1.5
1.6 3.8 Futures Prices 72
3.9 Exercises 74
Appendix 3A Compounding Frequency 79
Appendix 3B Forward and Futures Prices with
Constant Interest Rates 81
Appendix 3C Rolling Over Futures Contracts 83 xv
xxi 1 Forward and Futures Contracts 5
Options 9
Swaps 10
Using Derivatives: Some Comments
The Structure of this Book 14
Exercises 15 Chapter 4
Pricing Forwards and Futures II: Building
on the Foundations 85
11 PART ONE
Futures and Forwards
Chapter 2
Futures Markets 17 19 2.1 Introduction 19
2.2 The Changing Face of Futures Markets 19
2.3 The Functioning of Futures Exchanges 21
2.4 The Standardization of Futures Contracts 30
2.5 Closing Out Positions 34
2.6 Margin Requirements and Default Risk 36
2.7 Case Studies in Futures Markets 39
2.8 Exercises 53
Appendix 2A Futures Trading and US Regulation:
A Brief History 57 Chapter 3
Pricing Forwards and Futures I: The Basic
Theory 60
3.1
3.2
3.3
3.4 Introduction 60
Pricing Forwards by Replication 61
Examples 63
Forward Pricing on Currencies and Related
Assets 66
3.5 Forward-Rate Agreements 69
3.6 Concept Check 69
3.7 The Marked-to-Market Value of a Forward
Contract 70
viii 4.1 Introduction 85
4.2 From Theory to Reality 85
4.3 The Implied Repo Rate 89
4.4 Transactions Costs 92
4.5 Forward Prices and Future Spot Prices 92
4.6 Index Arbitrage 93
4.7 Exercises 97
Appendix 4A Forward Prices with Convenience
Yields 100 Chapter 5
Hedging with Futures and Forwards 101 5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10 Introduction 101
A Guide to the Main Results 103
The Cash Flow from a Hedged Position 104
The Case of No Basis Risk 105
The Minimum-Variance Hedge Ratio 106
Examples 109
Implementation 111
Further Issues in Implementation 112
Index Futures and Changing Equity Risk 114
Fixed-Income Futures and Duration-Based
Hedging 115
5.11 Exercises 115
Appendix 5A Derivation of the Optimal Tailed
Hedge Ratio h ∗∗ 120 Chapter 6
Interest-Rate Forwards and Futures
6.1
6.2
6.3
6.4 Introduction 122
Eurodollars and Libor Rates 122
Forward-Rate Agreements 123
Eurodollar Futures 129 122 sundaram-1810040 book February 9, 2010 8:35 Contents 6.5 Treasury Bond Futures 136
6.6 Treasury Note Futures 139
6.7 Treasury Bill Futures 139
6.8 Duration-Based Hedging 140
6.9 Exercises 143
Appendix 6A Deriving the Arbitrage-Free
FRA Rate 147
Appendix 6B PVBP-Based Hedging Using
Eurodollar Futures 148
Appendix 6C Calculating the Conversion
Factor 149
Appendix 6D Duration as a Sensitivity
Measure 150
Appendix 6E The Duration of a Futures
Contract 151 PART TWO
Options 153 Chapter 7
Options Markets 155 7.1
7.2
7.3
7.4
7.5 Introduction 155
Definitions and Terminology 155
Options as Financial Insurance 156
Naked Option Positions 158
Options as Views on Market Direction
and Volatility 162
7.6 Exercises 165
Appendix 7A Options Markets 167 Chapter 8
Options: Payoffs and Trading
Strategies 171
8.1 Introduction 171
8.2 Trading Strategies I: Covered Calls and
Protective Puts 171
8.3 Trading Strategies II: Spreads 174
8.4 Trading Strategies III: Combinations 182
8.5 Trading Strategies IV: Other Strategies 185
8.6 Which Strategies Are the Most Widely
Used? 189
8.7 The Barings Case 189
8.8 Exercises 192
Appendix 8A Asymmetric Butterfly
Spreads 195 Chapter 9
No-Arbitrage Restrictions on Option
Prices 196
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8 Introduction 196
Motivating Examples 196
Notation and Other Preliminaries 198
Maximum and Minimum Prices for
Options 199
The Insurance Value of an Option 204
Option Prices and Contract Parameters 205
Numerical Examples 208
Exercises 210 Chapter 10
Early Exercise and Put-Call Parity
10.1
10.2
10.3
10.4
10.5 213 Introduction 213
A Decomposition of Option Prices 213
The Optimality of Early Exercise 216
Put-Call Parity 220
Exercises 226 Chapter 11
Option Pricing: An Introduction 228 11.1 Overview 228
11.2 The Binomial Model 229
11.3 Pricing by Replication in a One-Period
Binomial Model 231
11.4 Comments 235
11.5 Riskless Hedge Portfolios 237
11.6 Pricing Using Risk-Neutral
Probabilities 238
11.7 The One-Period Model in General
Notation 242
11.8 The Delta of an Option 242
11.9 An Application: Portfolio Insurance 246
11.10 Exercises 248
Appendix 11A Riskless Hedge Portfolios
and Option Pricing 252
Appendix 11B Risk-Neutral Probabilities
and Arrow Security Prices 254
Appendix 11C The Risk-Neutral Probability,
No-Arbitrage, and Market
Completeness 255
Appendix 11D Equivalent Martingale
Measures 257 ix sundaram-1810040 x book February 9, 2010 8:35 Contents Chapter 12
Binomial Option Pricing 259 12.1
12.2
12.3
12.4 Introduction 259
The Two-Period Binomial Tree 261
Pricing Two-Period European Options 262
European Option Pricing in General n-Period
Trees 269
12.5 Pricing American Options: Preliminary
Comments 269
12.6 American Puts on Non-Dividend-Paying
Stocks 270
12.7 Cash Dividends in the Binomial Tree 272
12.8 An Alternative Approach to Cash
Dividends 275
12.9 Dividend Yields in Binomial Trees 279
12.10 Exercises 282
Appendix 12A A General Representation of
European Option Prices 286 Chapter 13
Implementing the Binomial Model 289 13.1 Introduction 289
13.2 The Lognormal Distribution 289
13.3 Binomial Approximations of the
Lognormal 294
13.4 Computer Implementation of the Binomial
Model 298
13.5 Exercises 303
Appendix 13A Estimating Historical
Volatility 306 Chapter 14
The Black-Scholes Model 308 14.1 Introduction 308
14.2 Option Pricing in the Black-Scholes
Setting 310
14.3 Remarks on the Formula 313
14.4 Working with the Formulae I: Plotting Option
Prices 314
14.5 Working with the Formulae II: Algebraic
Manipulation 315
14.6 Dividends in the Black-Scholes Model 319
14.7 Options on Indices, Currencies,
and Futures 324
14.8 Testing the Black-Scholes Model: Implied
Volatility 327
14.9 The VIX and Its Derivatives 332 14.10 Exercises 335
Appendix 14A Further Properties of the
Black-Scholes Delta 338
Appendix 14B Variance and Volatility Swaps Chapter 15
The Mathematics of Black-Scholes
15.1
15.2
15.3
15.4
15.5
15.6 339 344 Introduction 344
Geometric Brownian Motion Defined 344
The Black-Scholes Formula via
Replication 348
The Black-Scholes Formula via Risk-Neutral
Pricing 351
The Black-Scholes Formula via CAPM 353
Exercises 354 Chapter 16
Options Modeling:
Beyond Black-Scholes 357 16.1
16.2
16.3
16.4
16.5
16.6 Introduction 357
Jump-Diffusion Models 358
Stochastic Volatility 368
GARCH Models 374
Other Approaches 378
Implied Binomial Trees/Local Volatility
Models 379
16.7 Summary 389
16.8 Exercises 389
Appendix 16A Program Code for JumpDiffusions 393
Appendix 16B Program Code for a Stochastic
Volatility Model 394
Appendix 16C Heuristic Comments on Option
Pricing under Stochastic
Volatility 396
Appendix 16D Program Code for Simulating
GARCH Stock Prices
Distributions 399
Appendix 16E Local Volatility Models: The Fourth
Period of the Example 400 Chapter 17
Sensitivity Analysis: The Option
“Greeks” 404
17.1
17.2 Introduction 404
Interpreting the Greeks: A Snapshot
View 404 sundaram-1810040 book February 9, 2010 8:35 Contents 17.3 The Option Delta 408
17.4 The Option Gamma 412
17.5 The Option Theta 418
17.6 The Option Vega 423
17.7 The Option Rho 426
17.8 Portfolio Greeks 429
17.9 Exercises 432
Appendix 17A Deriving the Black-Scholes
Option Greeks 436 Chapter 18
Exotic Options I: Path-Independent
Options 440
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8 Introduction 440
Forward Start Options 442
Binary Options 445
Chooser Options 450
Compound Options 453
Exchange Options 458
Quanto Options 460
Variants on the Exchange
Option Theme 462
18.9 Exercises 465 Chapter 19
Exotic Options II: Path-Dependent
Options 470
19.1 Path-Dependent Exotic
Options 470
19.2 Barrier Options 470
19.3 Asian Options 479
19.4 Lookback Options 485
19.5 Cliquets 488
19.6 Shout Options 490
19.7 Exercises 492
Appendix 19A Barrier Option Pricing
Formulae 496 Chapter 20
Value-at-Risk
20.1
20.2
20.3
20.4
20.5 498 Introduction 498
Value-at-Risk 498
Risk Decomposition 505
Coherent Risk Measures 511
Exercises 515 Chapter 21
Convertible Bonds xi 519 21.1 Introduction 519
21.2 Convertible Bond Terminology 519
21.3 Main Features of Convertible Bonds 520
21.4 Breakeven Analysis 522
21.5 Pricing Convertibles: A First Pass 523
21.6 Incorporating Credit Risk 530
21.7 Convertible Greeks 534
21.8 Convertible Arbitrage 542
21.9 Summary 542
21.10 Exercises 543
Appendix 21A Octave Code for the Blended
Discount Rate Valuation Tree 545
Appendix 21B Octave Code for the Simplified
Das-Sundaram Model 546 Chapter 22
Real Options 548 22.1 Introduction 548
22.2 Preliminary Analysis and Examples 550
22.3 A Real Options “Case Study” 554
22.4 Creating the State Space 560
22.5 Applications of Real Options 563
22.6 Summary 564
22.7 Exercises 564
Appendix 22A Derivation of Cash-Flow Value
in the “Waiting-to-Invest”
Example 568 PART THREE
Swaps 569 Chapter 23
Interest Rate Swaps and Floating-Rate
Products 571
23.1
23.2
23.3
23.4
23.5
23.6
23.7
23.8 Introduction 571
Floating-Rate Notes 571
Interest Rate Swaps 575
Uses of Swaps 576
Swap Payoffs 579
Valuing and Pricing Swaps 582
Extending the Pricing Arguments 586
Case Study: The Procter & Gamble–Bankers
Trust “5/30” Swap 589 sundaram-1810040 book February 9, 2010 8:35 xii Contents 23.9 Case Study: A Long-Term Capital
Management “Convergence Trade” 593
23.10 Credit Risk and Credit Exposure 596
23.11 Hedging Swaps 597
23.12 Caps, Floors, and Swaptions 599
23.13 The Black Model for Pricing Caps, Floors,
and Swaptions 604
23.14 Summary 609
23.15 Exercises 609 Chapter 24
Equity Swaps
24.1
24.2
24.3
24.4
24.5
24.6 613 Introduction 613
Uses of Equity Swaps 614
Payoffs from Equity Swaps 616
Valuation and Pricing of Equity Swaps
Summary 628
Exercises 628 Chapter 25
Currency and Commodity Swaps
25.1
25.2
25.3
25.4
25.5 631 27.1 Introduction 667
27.2 Bootstrapping 667
27.3 Splines 669
27.4 Polynomial Splines 670
27.5 Exponential Splines 673
27.6 Implementation Issues with Splines 674
27.7 The Nelson-Siegel-Svensson Approach 674
27.8 Summary 676
27.9 Exercises 676
Appendix 27A Bootstrapping by Matrix
Inversion 680
Appendix 27B Implementation with Exponential
Splines 681 Chapter 28
Modeling Term-Structure Movements
28.1
28.2
28.3
28.4
28.5
28.6
28.7 PART FOUR 684 Introduction 684
Interest-Rate Modeling versus Equity
Modeling 684
Arbitrage Violations: A Simple
Example 685
A Gentle Introduction to No-Arbitrage
Modeling 687
“No-Arbitrage” and “Equilibrium”
Models 693
Summary 697
Exercises 697 647 Chapter 26
The Term Structure of Interest Rates:
Concepts 649
26.1
26.2
26.3
26.4
26.5
26.6
26.7 667 622 Introduction 631
Currency Swaps 631
Commodity Swaps 639
Summary 643
Exercises 644 Interest Rate Modeling Chapter 27
Estimating the Yield Curve Introduction 649
The Yield-to-Maturity 649
The Term Structure of Interest Rates 651
Discount Functions 652
Zero-Coupon Rates 653
Forward Rates 654
Yield-to-Maturity, Zero-Coupon Rates,
and Forward Rates 656
26.8 Constructing the Yield-to-Maturity Curve:
An Empirical Illustration 657
26.9 Summary 661
26.10 Exercises 662
Appendix 26A The Raw YTM Data 664 Chapter 29
Factor Models of the Term Structure 700 29.1 Overview 700
29.2 The Black-Derman-Toy Model 701
29.3 The Ho-Lee Model 710
29.4 One-Factor Models in Continuous Time 714
29.5 Multifactor Models 720
29.6 Affine Factor Models 722
29.7 Summary 725
29.8 Exercises 726
Appendix 29A Deriving the Fundamental PDE
in Factor Models 729 Chapter 30
The Heath-Jarrow-Morton and Libor
Market Models 731
30.1 Overview 731 sundaram-1810040 book February 9, 2010 8:35 Contents 30.2 The HJM Framework: Preliminary
Comments 731
30.3
A One-Factor HJM Model 733
30.4
A Two-Factor HJM Setting 742
30.5
The HJM Risk-Neutral Drifts: An Algebraic
Derivation 746
30.6
Libor Market Models 749
30.7
Mathematical Excursion: Martingales 750
30.8
Libor Rates: Notation 751
30.9
Risk-Neutral Pricing in the LMM 753
30.10 Simulation of the Market Model 757
30.11 Calibration 757
30.12 Swap Market Models 758
30.13 Swaptions 760
30.14 Summary 761
30.15 Exercises 761
Appendix 30A Risk-Neutral Drifts
and Volatilities in HJM 765 PART FIVE
Credit Risk 769 Chapter 31
Credit Derivative Products 771 Chapter 32
Structural Models of Default Risk 802 Introduction 802
The Merton (1974) Model 803
Issues in Implementation 812
A Practitioner Model 817
Extensions of the Merton Model 819
Evaluation of the Structural Model
Approach 820
32.7 Summary 823
32.8 Exercises 824
Appendix 32A The Delianedis-Geske
Model 826 829 33.1 Introduction 829
33.2 Modeling Default I: Intensity Processes 830
33.3 Modeling Default II: Recovery Rate
Conventions 834
33.4 The Litterman-Iben Model 836
33.5 The Duffie-Singleton Result 841
33.6 Defaultable HJM Models 843
33.7 Ratings-Based Modeling: The JLT
Model 845
33.8 An Application of Reduced-Form Models:
Pricing CDS 853
33.9 Summary 855
33.10 Exercises 855
Appendix 33A Duffie-Singleton
in Discrete Time 859
Appendix 33B Derivation of the Drift-Volatility
Relationship 860 Chapter 34
Modeling Correlated Default 31.1 Introduction 771
31.2 Total Return Swaps 775
31.3 Credit Spread Options/Forwards 779
31.4 Credit Default Swaps 779
31.5 Credit-Linked Notes 788
31.6 Correlation Products 790
31.7 Summary 797
31.8 Exercises 797
Appendix 31A The CDS Big Bang 800 32.1
32.2
32.3
32.4
32.5
32.6 Chapter 33
Reduced-Form Models of Default Risk xiii 863 34.1 Introduction 863
34.2 Examples of Correlated Default
Products 863
34.3 Simple Correlated Default Math 865
34.4 Structural Models Based on
Asset Values 868
34.5 Reduced-Form Models 874
34.6 Multiperiod Correlated Default 875
34.7 Fast Computation of Credit Portfolio Loss
Distributions without Simulation 878
34.8 Copula Functions 881
34.9 Top-Down Modeling of Credit
Portfolio Loss 893
34.10 Summary 897
34.11 Exercises 898 Bibliography
Index I-1 B-1 sundaram-1810040 book February 9, 2010 8:35 xiv Contents The following Web chapters are
available at :
PART SIX
Computation 901 Chapter 35
Derivative Pricing with Finite
Differencing 903
35.1 Introduction 903
35.2 Solving Differential Equations 904
35.3 A First Approach to Pricing Equity
Options 907
35.4 Implicit Finite Differencing 913
35.5 The Crank-Nicholson Scheme 917
35.6 Finite Differencing for Term-Structure
Models 919
35.7 Summary 921
35.8 Exercises 922 Chapter 36
Derivative Pricing with Monte Carlo
Simulation 923
36.1
36.2
36.3
36.4
36.5
36.6
36.7
36.8
36.9
36.10
36.11
36.12
36.13
36.14 Introduction 923
Simulating Normal Random Variables 924
Bivariate Random Variables 925
Cholesky Decomposition 925
Stochastic Processes for Equity Prices 927
ARCH Models 929
Interest-Rate Processes 930
Estimating Historical Volatility for
Equities 932
Estimating Historical Volatility for Interest
Rates 932
Path-Dependent Options 933
Variance Reduction 935
Monte Carlo for American Options 938
Summary 942
Exercises 943 Chapter 37
Using Octave 945
37.1
37.2
37.3
37.4
37.5 Some Simple Commands 945
Regression and Integration 948
Reading in Data, Sorting, and Finding
Equation Solving 955
Screenshots 955 950 sundaram-1810040 book February 9, 2010 8:35 Preface
The two of us have worked together academically for more than a quarter century, first as
graduate students, and then as university faculty. Given our close collaboration, our common
research and teaching interests in the field of derivatives, and the frequent pedagogical
discussions we have had on the subject, this book was perhaps inevitable.
The final product grew out of many sources. About three-fourths of the book came
from notes developed by Raghu for his derivatives course at New York University as well
as for other academic courses and professional training programs at Credit Suisse, ICICI
Bank, the International Monetary Fund (IMF), Invesco-Great Wall, J.P. Morgan, Merrill
Lynch, the Indian School of Business (ISB), the Institute for Financial Management and
Research (IFMR), and New York University, among other institutions. Other parts grew
out of academic courses and professional training programs taught by Sanjiv at Harvard
University, Santa Clara University, the University of California at Berkeley, the ISB, the
IFMR, the IMF, and Citibank, among others. Some chapters were developed specifically
for this book, as were most of the end-of-chapter exercises.
The discussion below provides an overview of the book, emphasizing some of its special
features. We provide too our suggestions for various derivatives courses that may be carved
out of the book. An Overview of the Contents
The main body of this book is divided into six parts. Parts 1–3 cover, respectively, futures and
forwards; options; and swaps. Part 4 examines term-structure modeling and the pricing of
interest-rate derivatives, while Part 5 is concerned with credit derivatives and the modeling
of credit risk. Part 6 discusses computational issues. A detailed description of the book’s
contents is provided in Section 1.5; here, we confine ourselves to a brief overview of
each part.
Part 1 examines forward and futures contracts, The topics covered in this span include
the structure and characteristics of futures markets; the pricing of forwards and futures;
hedging with forwards and futures, in particular, the notion of minimum-variance hedging
and its implementation; and interest-rate-dependent forwards and futures, such as forwardrate agreements or FRAs, eurodollar futures, and Treasury futures contracts.
Part 2, the lengthiest portion of the book, is concerned mainly with options. We begin
with a discussion of option payoffs, the role of volatility, and the use of options in incorporating into a portfolio specific views on market direction and/or volatility. Then we turn
our attention to the pricing of options contracts. The binomial and Black-Scholes models
are developed in detail, and several generalizations of these models are examined. From
pricing, we move to hedging and a discussion of the option “greeks,” measures of option
sensitivity to changes in the market environment. Rounding off the pricing and hedging
material, two chapters discuss a wide range of “exotic” options and their behavior.
The remainder of Part 2 focuses on specia...

View
Full Document

- Fall '20
- Derivatives, Derivative