Kosowski / Neftci Principles of Financial Engineering

3. Auflage 2014
ISBN: 978-0-12-387007-0
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 896 Seiten

Principles of Financial Engineering, Third Edition, is a highly acclaimed text on the fast-paced and complex subject of financial engineering. This updated edition describes the 'engineering' elements of financial engineering instead of the mathematics underlying it. It shows how to use financial tools to accomplish a goal rather than describing the tools themselves. It lays emphasis on the engineering aspects of derivatives (how to create them) rather than their pricing (how they act) in relation to other instruments, the financial markets, and financial market practices. This volume explains ways to create financial tools and how the tools work together to achieve specific goals. Applications are illustrated using real-world examples. It presents three new chapters on financial engineering in topics ranging from commodity markets to financial engineering applications in hedge fund strategies, correlation swaps, structural models of default, capital structure arbitrage, contingent convertibles, and how to incorporate counterparty risk into derivatives pricing. Poised midway between intuition, actual events, and financial mathematics, this book can be used to solve problems in risk management, taxation, regulation, and above all, pricing. A solutions manual enhances the text by presenting additional cases and solutions to exercises. This latest edition of Principles of Financial Engineering is ideal for financial engineers, quantitative analysts in banks and investment houses, and other financial industry professionals. It is also highly recommended to graduate students in financial engineering and financial mathematics programs. - The Third Edition presents three new chapters on financial engineering in commodity markets, financial engineering applications in hedge fund strategies, correlation swaps, structural models of default, capital structure arbitrage, contingent convertibles and how to incorporate counterparty risk into derivatives pricing, among other topics - Additions, clarifications, and illustrations throughout the volume show these instruments at work instead of explaining how they should act - The solutions manual enhances the text by presenting additional cases and solutions to exercises

Robert Kosowski is Associate Professor in the Finance Group of Imperial College Business School, Imperial College London, and Director of the Risk Management Lab and Centre for Hedge Fund Research. Robert is an associate member of the Oxford-Man Institute of Quantitative Finance at Oxford University and a member of AIMA's research committee. His research interests include asset management, asset pricing, and financial econometrics with a focus on hedge and mutual funds, performance measurement, asset allocation, business cycles, and derivative trading strategies.Robert's research has been featured in 'The Financial Times' and 'The Wall Street Journal' and was awarded the European Finance Association 2007 Best Paper Award, an INQUIRE UK 2008 best paper award, an INQUIRE Europe 2009/10 and 2012/13 best paper award, and the British Academy's mid-career fellowship (2011-2012). Robert's research has been published in top peer-reviewed finance journals such as 'The Journal of Finance,' 'The Journal of Financial Economics' and the 'Review of Financial Studies.'Prior to joining Imperial College London Robert was an Assistant Professor of Finance at INSEAD, where he taught in the MBA, Executive Education, and Ph.D. programs. Robert was a visiting scholar at the UCSD Economics Department (2000) and the International Monetary Fund (2008). At Imperial Robert teaches in the MSc Finance. He won teaching prizes at Imperial College Business School in 2009 and 2014.Robert holds a BA (First Class Honours) and MA in Economics from Trinity College, Cambridge University, and a MSc in Economics and Ph.D. from the London School of Economics. He has consulted for private and public sector organizations and has worked for Goldman Sachs, the Boston Consulting Group, and Deutsche Bank. His policy related advisory work includes: Specialist Adviser to UK House of Lords (2009-2010) and Expert Technical Consultant (International Monetary Fund, USA, 2008).

Autoren/Hrsg.

Kosowski, Robert

Neftci, Salih N.

Inhaltsverzeichnis

1;Front Cover;1
2;Principles of Financial Engineering;4
3;Copyright Page;5
4;Dedication;6
5;Contents;8
6;Preface to the Third Edition;18
7;1 Introduction;20
7.1;1.1 A Unique Instrument;21
7.1.1;1.1.1 Buying a Default-Free Bond;22
7.1.2;1.1.2 Buying Stocks;24
7.1.3;1.1.3 Buying a Defaultable Bond;26
7.1.4;1.1.4 First Conclusions;29
7.2;1.2 A Money Market Problem;29
7.2.1;1.2.1 The Problem;30
7.2.2;1.2.2 Solution;30
7.2.3;1.2.3 Some Implications;32
7.3;1.3 A Taxation Example;32
7.3.1;1.3.1 The Problem;33
7.3.1.1;1.3.1.1 Another strategy;34
7.3.2;1.3.2 Implications;35
7.4;1.4 Some Caveats for What Is to Follow;36
7.5;1.5 Trading Volatility;37
7.5.1;1.5.1 A Volatility Trade;39
7.5.2;1.5.2 Recap;40
7.6;1.6 Conclusions;41
7.7;Suggested Reading;41
7.8;Exercises;41
8;2 Institutional Aspects of Derivative Markets;44
8.1;2.1 Introduction;45
8.2;2.2 Markets;45
8.2.1;2.2.1 Euromarkets;46
8.2.1.1;2.2.1.1 Eurocurrency markets;46
8.2.1.2;2.2.1.2 Eurobond markets;46
8.2.1.3;2.2.1.3 Other Euromarkets;47
8.2.2;2.2.2 Onshore Markets;47
8.2.2.1;2.2.2.1 Futures and options exchanges;48
8.2.2.2;2.2.2.2 Futures compared with forward contracts;49
8.2.3;2.2.3 Changes to the Infrastructure of Derivatives Markets Following the GFC;53
8.3;2.3 Players;54
8.4;2.4 The Mechanics of Deals;55
8.4.1;2.4.1 Orders;56
8.4.2;2.4.2 Confirmation and Settlement;57
8.4.2.1;2.4.2.1 Regulatory update following the GFC;58
8.5;2.5 Market Conventions;58
8.5.1;2.5.1 What to Quote;59
8.6;2.6 Instruments;60
8.7;2.7 Positions;60
8.7.1;2.7.1 Long and Short Positions;60
8.7.1.1;2.7.1.1 Payoff diagrams;61
8.7.1.2;2.7.1.2 Real-world complications and short selling;63
8.7.2;2.7.2 Payoff Diagrams for Forwards and Futures;64
8.7.3;2.7.3 Types of Positions;68
8.7.3.1;2.7.3.1 Arbitrage;68
8.7.3.2;2.7.3.2 Comparing performance;69
8.8;2.8 The Syndication Process;69
8.8.1;2.8.1 Selling Securities in the Primary Market;69
8.8.1.1;2.8.1.1 Syndication of a bond versus a syndicated loan;70
8.9;2.9 Conclusions;70
8.10;Suggested Reading;70
8.11;Exercises;70
9;3 Cash Flow Engineering, Interest Rate Forwards and Futures;72
9.1;3.1 Introduction;73
9.2;3.2 What Is a Synthetic?;74
9.2.1;3.2.1 Cash Flows;74
9.2.1.1;3.2.1.1 Cash flows in different currencies;76
9.2.1.2;3.2.1.2 Cash flows with different market risks;77
9.2.1.3;3.2.1.3 Cash flows with different credit risks;77
9.2.1.4;3.2.1.4 Cash flows with different volatilities;77
9.3;3.3 Engineering Simple Interest Rate Derivatives;78
9.3.1;3.3.1 A Convergence Trade;79
9.3.2;3.3.2 Yield Curve;80
9.4;3.4 LIBOR and Other Benchmarks;82
9.5;3.5 Fixed Income Market Conventions;83
9.5.1;3.5.1 How to Quote Yields;84
9.5.2;3.5.2 Day-Count Conventions;86
9.5.2.1;3.5.2.1 Holiday conventions;87
9.5.3;3.5.3 Two Examples;88
9.6;3.6 A Contractual Equation;89
9.6.1;3.6.1 Forward Loan;90
9.6.2;3.6.2 Replication of a Forward Loan;91
9.6.2.1;3.6.2.1 Bond market replication;92
9.6.2.2;3.6.2.2 Pricing;93
9.6.2.3;3.6.2.3 Arbitrage;93
9.6.2.4;3.6.2.4 Money market replication;94
9.6.2.5;3.6.2.5 Pricing;94
9.6.3;3.6.3 Contractual Equations;95
9.6.4;3.6.4 Applications;96
9.6.4.1;3.6.4.1 Application 1: creating a synthetic bond;96
9.6.4.2;3.6.4.2 Application 2: covering a mismatch;97
9.7;3.7 Forward Rate Agreements;98
9.7.1;3.7.1 Eliminating the Credit Risk;99
9.7.2;3.7.2 Definition of the FRA;100
9.7.2.1;3.7.2.1 An interpretation;101
9.7.3;3.7.3 FRA Contractual Equation;101
9.7.3.1;3.7.3.1 Application: FRA strips;101
9.8;3.8 Fixed Income Risk Measures: Duration, Convexity and Value-at-Risk;102
9.8.1;3.8.1 DV01 and PV01;103
9.8.1.1;3.8.1.1 Dollar duration DV01;103
9.8.1.2;3.8.1.2 PV01;104
9.8.2;3.8.2 Duration;104
9.8.3;3.8.3 Convexity;106
9.8.4;3.8.4 Immunization;106
9.8.5;3.8.5 Value-at-Risk, Expected Shortfall, Basel Capital Requirements and Funding Costs;107
9.9;3.9 Futures: Eurocurrency Contracts;108
9.9.1;3.9.1 Other Parameters;110
9.9.1.1;3.9.1.1 The “TED spread”;111
9.9.2;3.9.2 Comparing FRAs and Eurodollar Futures;112
9.9.2.1;3.9.2.1 Convexity differences;112
9.9.3;3.9.3 Hedging FRAs with Eurocurrency Futures;112
9.9.3.1;3.9.3.1 Some technical points;113
9.10;3.10 Real-World Complications;114
9.10.1;3.10.1 Bid-Ask Spreads;114
9.10.2;3.10.2 An Asymmetry;115
9.11;3.11 Forward Rates and Term Structure;115
9.11.1;3.11.1 Bond Prices;115
9.11.2;3.11.2 What Forward Rates Imply;116
9.11.2.1;3.11.2.1 Remark;116
9.12;3.12 Conventions;117
9.13;3.13 A Digression: Strips;118
9.14;3.14 Conclusions;118
9.15;Suggested Reading;119
9.16;Appendix—Calculating the Yield Curve;119
9.16.1;Par Yield Curve;120
9.16.2;Zero-Coupon Yield Curve;120
9.16.3;Zero-Coupon Curve from Coupon Bonds;121
9.17;Exercises;122
10;4 Introduction to Interest-Rate Swap Engineering;126
10.1;4.1 The Swap Logic;127
10.1.1;4.1.1 The Equivalent of Zero in Finance;127
10.1.2;4.1.2 A Generalization;130
10.2;4.2 Applications;130
10.2.1;4.2.1 Equity Swap;130
10.3;4.3 The Instrument: Swaps;134
10.4;4.4 Types of Swaps;136
10.4.1;4.4.1 Noninterest-Rate Swaps;136
10.4.1.1;4.4.1.1 Equity swaps;136
10.4.2;4.4.2 Interest-Rate Swaps;138
10.4.2.1;4.4.2.1 Basis swaps;141
10.4.2.2;4.4.2.2 What is an asset swap?;142
10.4.2.3;4.4.2.3 More complex swaps;143
10.4.3;4.4.3 Swap Conventions;143
10.5;4.5 Engineering Interest-Rate Swaps;143
10.5.1;4.5.1 A Horizontal Decomposition;145
10.5.1.1;4.5.1.1 A synthetic coupon bond;146
10.5.1.2;4.5.1.2 Pricing;146
10.5.1.3;4.5.1.3 Valuing fixed cash flows;147
10.5.1.4;4.5.1.4 Valuing floating cash flows;148
10.5.1.5;4.5.1.5 An important remark;149
10.5.2;4.5.2 A Vertical Decomposition;149
10.5.2.1;4.5.2.1 Pricing;152
10.6;4.6 Uses of Swaps;152
10.6.1;4.6.1 Uses of Equity Swaps;153
10.6.1.1;4.6.1.1 Fund management;153
10.6.1.2;4.6.1.2 Tax advantages;153
10.6.1.3;4.6.1.3 Regulations;154
10.6.1.4;4.6.1.4 Creating synthetic positions;155
10.6.1.5;4.6.1.5 Stripping credit risk;156
10.6.2;4.6.2 Using Interest-Rate and Other Swaps;156
10.6.3;4.6.3 Two Uses of Interest-Rate Swaps;157
10.6.3.1;4.6.3.1 Changing portfolio duration;157
10.6.3.2;4.6.3.2 Using swaps to reduce a country’s debt level;157
10.6.3.3;4.6.3.3 Technical uses;158
10.7;4.7 Mechanics of Swapping New Issues;159
10.7.1;4.7.1 All-in-Cost;161
10.8;4.8 Some Conventions;163
10.8.1;4.8.1 Quotes;163
10.9;4.9 Additional Terminology;164
10.10;4.10 Conclusions;164
10.11;Suggested Reading;164
10.12;Exercises;165
11;5 Repo Market Strategies in Financial Engineering;168
11.1;5.1 Introduction;169
11.2;5.2 Repo Details;170
11.2.1;5.2.1 Repo Terminology;171
11.2.2;5.2.2 Special Versus General Collateral;172
11.2.2.1;5.2.2.1 Why do bonds go special?;172
11.2.3;5.2.3 Summary;173
11.3;5.3 Types of Repo;173
11.3.1;5.3.1 Classic Repo;173
11.3.2;5.3.2 Sell and Buy-Back;174
11.3.3;5.3.3 Securities Lending;175
11.3.4;5.3.4 Repo and Custody Types;176
11.3.4.1;5.3.4.1 What is a matched-book repo dealer?;178
11.3.5;5.3.5 Aspects of the Repo Deal;178
11.3.6;5.3.6 Types of Collateral;179
11.3.7;5.3.7 Repo and Credit Risk;179
11.4;5.4 Equity Repos;179
11.5;5.5 Repo Market Strategies;180
11.5.1;5.5.1 Funding a Bond Position;181
11.5.1.1;5.5.1.1 A subtle risk;183
11.5.1.2;5.5.1.2 The asset swap;184
11.5.1.3;5.5.1.3 Risks and pricing aspects;184
11.5.1.4;5.5.1.4 An arbitrage approach;184
11.5.2;5.5.2 Futures Arbitrage;184
11.5.3;5.5.3 Hedging a Swap;185
11.5.4;5.5.4 Tax Strategies;185
11.6;5.6 Synthetics Using Repos;187
11.6.1;5.6.1 A Contractual Equation;187
11.6.2;5.6.2 A Synthetic Repo;188
11.6.3;5.6.3 A Synthetic Outright Purchase;188
11.6.4;5.6.4 Swaps Versus Repo;188
11.7;5.7 Differences Between Repo Markets and the Impact of the GFC;189
11.8;5.8 Conclusions;189
11.9;Suggested Reading;190
11.10;Exercises;190
12;6 Cash Flow Engineering in Foreign Exchange Markets;194
12.1;6.1 Introduction;195
12.2;6.2 Currency Forwards;197
12.2.1;6.2.1 Engineering the Currency Forward;199
12.2.2;6.2.2 Which Synthetic?;199
12.2.2.1;6.2.2.1 A money market synthetic;199
12.2.2.2;6.2.2.2 A synthetic with T-bills;201
12.2.2.3;6.2.2.3 Which synthetic should one use?;201
12.2.2.4;6.2.2.4 Credit risk;202
12.3;6.3 Synthetics and Pricing;202
12.4;6.4 A Contractual Equation;203
12.5;6.5 Applications;204
12.5.1;6.5.1 Application 1: A Withholding Tax Problem;204
12.5.2;6.5.2 Application 2: Creating Synthetic Loans;206
12.5.3;6.5.3 Application 3: Capital Controls;208
12.5.4;6.5.4 Application 4: “Cross” Currencies;208
12.6;6.6 Conventions for FX Forward and Futures;210
12.6.1;6.6.1 Quoting Conventions for FX Forward;210
12.6.2;6.6.2 FX Forward Versus FX Futures;213
12.7;6.7 Swap Engineering in FX Markets;213
12.7.1;6.7.1 FX Swaps;213
12.7.1.1;6.7.1.1 Advantages;214
12.7.1.2;6.7.1.2 Uses of FX swaps;215
12.7.1.3;6.7.1.3 Quotation conventions;216
12.8;6.8 Currency Swaps Versus FX Swaps;217
12.8.1;6.8.1 Currency Swaps;217
12.8.2;6.8.2 Differences Between Currency Swaps and FX Swaps;219
12.8.3;6.8.3 Another Difference;221
12.8.4;6.8.4 Uses of Currency Swaps;221
12.8.5;6.8.5 Relative SIZE and Liquidity of FX Swap and Currency Swap Markets;221
12.8.6;6.8.6 The Effect of the GFC on the FX Market, Margins, and Clearing;222
12.9;6.9 Mechanics of Swapping New Issues;223
12.9.1;6.9.1 Interest Rate and Currency Swap Example;223
12.10;6.10 Conclusions;225
12.11;Suggested Reading;226
12.12;Exercises;226
13;7 Cash Flow Engineering and Alternative Classes (Commodities and Hedge Funds);230
13.1;7.1 Introduction;231
13.2;7.2 Parameters of a Futures Contract;231
13.3;7.3 The Term Structure of Commodity Futures Prices;234
13.3.1;7.3.1 Backwardation and Contango;234
13.3.2;7.3.2 Contractual Equation and Synthetic Commodities;235
13.3.3;7.3.3 Convenience Yield;238
13.3.4;7.3.4 Cash and Carry Arbitrage;238
13.3.5;7.3.5 Another Interpretation of Spot–Futures Parity;240
13.4;7.4 Swap Engineering for Commodities;240
13.4.1;7.4.1 Swap Cash Flow Engineering in Commodity Markets;241
13.4.2;7.4.2 Pricing and Valuation of Commodity Swaps;241
13.4.2.1;7.4.2.1 Calculating swap prices from the futures curve;243
13.4.3;7.4.3 Real-World Complications;246
13.4.4;7.4.4 Other Commodity Swaps;247
13.5;7.5 The Hedge Fund Industry;247
13.5.1;7.5.1 Alternative Investment Funds;248
13.5.2;7.5.2 Hedge Fund Regulation;248
13.5.3;7.5.3 Hedge Fund Investment Mandate and Techniques;249
13.5.4;7.5.4 Hedge Funds’ Legal Structure;249
13.5.5;7.5.5 Incentives;250
13.5.6;7.5.6 Strategies;251
13.5.7;7.5.7 Prime Brokers;252
13.6;7.6 Conclusions;252
13.7;Suggested Reading;253
13.8;Exercises;253
14;8 Dynamic Replication Methods and Synthetics Engineering;256
14.1;8.1 Introduction;257
14.2;8.2 An Example;257
14.3;8.3 A Review of Static Replication;258
14.3.1;8.3.1 The Framework;260
14.3.2;8.3.2 Synthetics with a Missing Asset;261
14.3.2.1;8.3.2.1 A synthetic that uses Bt only;262
14.3.2.2;8.3.2.2 Synthetics that use Bt and B(t, T3);263
14.4;8.4 “Ad Hoc” Synthetics;264
14.4.1;8.4.1 Immunization;265
14.5;8.5 Principles of Dynamic Replication;267
14.5.1;8.5.1 Dynamic Replication of Options;267
14.5.2;8.5.2 Dynamic Replication in Discrete Time;269
14.5.2.1;8.5.2.1 The method;269
14.5.3;8.5.3 Binomial Trees;269
14.5.4;8.5.4 The Replication Process;270
14.5.4.1;8.5.4.1 The Bt, B(t, T3) dynamics;270
14.5.4.2;8.5.4.2 Mechanics of replication;273
14.5.4.3;8.5.4.3 Guaranteeing self-financing;274
14.5.5;8.5.5 Two Examples;274
14.5.5.1;8.5.5.1 Replicating the bond;274
14.5.6;8.5.6 Application to Options;277
14.6;8.6 Some Important Conditions;280
14.6.1;8.6.1 Arbitrage-Free Initial Conditions;280
14.6.2;8.6.2 Role of Binomial Structure;280
14.7;8.7 Real-Life Complications;281
14.7.1;8.7.1 Bid–Ask Spreads and Liquidity;281
14.7.2;8.7.2 Models and Jumps;282
14.7.3;8.7.3 Maintenance and Operational Costs;282
14.7.4;8.7.4 Changes in Volatility;282
14.8;8.8 Conclusions;282
14.9;Suggested Reading;283
14.10;Exercises;283
15;9 Mechanics of Options;286
15.1;9.1 Introduction;287
15.2;9.2 What Is an Option?;288
15.3;9.3 Options: Definition and Notation;290
15.3.1;9.3.1 Notation;290
15.3.2;9.3.2 On Retail Use of Options;294
15.3.3;9.3.3 Some Intriguing Properties of the Diagram;294
15.4;9.4 Options as Volatility Instruments;296
15.4.1;9.4.1 Initial Position and the Hedge;296
15.4.2;9.4.2 Adjusting the Hedge Over Time;300
15.4.2.1;9.4.2.1 Limiting form;303
15.4.3;9.4.3 Other Cash Flows;304
15.4.4;9.4.4 Option Gains and Losses as a PDE;304
15.4.5;9.4.5 Cash Flows at Expiration;305
15.4.6;9.4.6 An Example;306
15.4.6.1;9.4.6.1 Some caveats;307
15.5;9.5 Tools for Options;308
15.5.1;9.5.1 Solving the Fundamental PDE;308
15.5.2;9.5.2 Black–Scholes Formula;309
15.5.2.1;9.5.2.1 Black’s formula;310
15.5.3;9.5.3 Other Formulas;311
15.5.3.1;9.5.3.1 Chooser options;311
15.5.3.2;9.5.3.2 Barrier options;312
15.5.4;9.5.4 Uses of Black–Scholes Type Formulas;314
15.6;9.6 The Greeks and Their Uses;315
15.6.1;9.6.1 Delta;316
15.6.1.1;9.6.1.1 Convention;317
15.6.1.2;9.6.1.2 The exact expression;317
15.6.2;9.6.2 Gamma;319
15.6.2.1;9.6.2.1 Market use;321
15.6.3;9.6.3 Vega;322
15.6.3.1;9.6.3.1 Market use;324
15.6.3.2;9.6.3.2 Vega hedging;324
15.6.4;9.6.4 Theta;324
15.6.5;9.6.5 Omega;325
15.6.6;9.6.6 Higher-Order Derivatives;325
15.6.7;9.6.7 Greeks and PDEs;326
15.6.7.1;9.6.7.1 Gamma trading;327
15.6.7.2;9.6.7.2 Gamma trading versus Vega;327
15.6.7.3;9.6.7.3 Which expectation?;328
15.7;9.7 Real-Life Complications;328
15.7.1;9.7.1 Dealing with Option Books;329
15.7.2;9.7.2 Futures as Underlying;329
15.7.2.1;9.7.2.1 Delivery mismatch;330
15.8;9.8 Conclusion: What Is an Option?;330
15.9;Suggested Reading;330
15.10;Appendix 9.1;330
15.10.1;Derivation of Delta;330
15.10.2;Derivation of Gamma;332
15.11;Appendix 9.2;332
15.11.1;Stochastic Differential Equations;332
15.11.1.1;Examples;332
15.11.2;Ito’s Lemma;333
15.11.3;Girsanov Theorem;333
15.12;Exercises;334
16;10 Engineering Convexity Positions;338
16.1;10.1 Introduction;339
16.2;10.2 A Puzzle;339
16.3;10.3 Bond Convexity Trades;340
16.3.1;10.3.1 Delta-Hedged Bond Portfolios;344
16.3.2;10.3.2 Costs;347
16.3.3;10.3.3 A Bond PDE;347
16.3.4;10.3.4 PDEs and Conditional Expectations;349
16.3.5;10.3.5 From Black–Scholes to Bond PDE;349
16.3.6;10.3.6 Closed-Form Bond Pricing Formulas;351
16.3.6.1;10.3.6.1 Case 1;351
16.3.6.2;10.3.6.2 Case 2;351
16.3.6.3;10.3.6.3 Case 3;352
16.3.7;10.3.7 A Generalization;352
16.4;10.4 Sources of Convexity;353
16.4.1;10.4.1 Mark to Market;353
16.4.2;10.4.2 Convexity by Design;354
16.4.2.1;10.4.2.1 Swaps;354
16.4.2.2;10.4.2.2 Convexity of FRAs;357
16.4.3;10.4.3 Prepayment Options;358
16.5;10.5 A Special Instrument: Quantos;359
16.5.1;10.5.1 A Simple Example;359
16.5.1.1;10.5.1.1 Quantos in equity;361
16.5.2;10.5.2 Pricing;361
16.5.3;10.5.3 The Mechanics of Pricing;361
16.5.4;10.5.4 Where Does Convexity Come in?;364
16.5.5;10.5.5 Practical Considerations;364
16.6;10.6 Conclusions;364
16.7;Suggested Reading;365
16.8;Exercises;365
16.8.1;MATLAB Exercises;366
17;11 Options Engineering with Applications;370
17.1;11.1 Introduction;371
17.1.1;11.1.1 Payoff Diagrams;371
17.1.1.1;11.1.1.1 Examples of xt;373
17.2;11.2 Option Strategies;374
17.2.1;11.2.1 Synthetic Long and Short Positions;374
17.2.1.1;11.2.1.1 An application;376
17.2.1.2;11.2.1.2 Arbitrage opportunity?;379
17.2.2;11.2.2 A Remark on the Pin Risk;380
17.2.3;11.2.3 Risk Reversals;380
17.2.3.1;11.2.3.1 Uses of risk reversals;382
17.2.4;11.2.4 Yield Enhancement Strategies;383
17.2.4.1;11.2.4.1 Call overwriting;384
17.3;11.3 Volatility-Based Strategies;386
17.3.1;11.3.1 Strangles;388
17.3.1.1;11.3.1.1 Uses of strangles;388
17.3.2;11.3.2 Straddle;389
17.3.2.1;11.3.2.1 Static or dynamic position?;389
17.3.3;11.3.3 Butterfly;391
17.4;11.4 Exotics;392
17.4.1;11.4.1 Binary, or Digital, Options;392
17.4.1.1;11.4.1.1 A binary call;393
17.4.1.2;11.4.1.2 Replicating the binary call;393
17.4.1.3;11.4.1.3 Delta and price of binaries;395
17.4.1.4;11.4.1.4 Time value of binaries;396
17.4.1.5;11.4.1.5 Uses of the binary;396
17.4.2;11.4.2 Barrier Options;397
17.4.2.1;11.4.2.1 A contractual equation;399
17.4.2.2;11.4.2.2 Some uses of barrier options;402
17.4.3;11.4.3 New Risks;403
17.5;11.5 Quoting Conventions;403
17.5.1;11.5.1 Example 1;405
17.5.2;11.5.2 Example 2;406
17.6;11.6 Real-World Complications;406
17.6.1;11.6.1 The Role of the Volatility Smile;406
17.6.2;11.6.2 Existence of Position Limits;407
17.7;11.7 Conclusions;407
17.8;Suggested Reading;407
17.9;Exercises;408
17.9.1;EXCEL Exercises;410
17.9.2;MATLAB Exercise;410
18;12 Pricing Tools in Financial Engineering;412
18.1;12.1 Introduction;413
18.2;12.2 Summary of Pricing Approaches;414
18.3;12.3 The Framework;415
18.3.1;12.3.1 States of the World;415
18.3.2;12.3.2 The Payoff Matrix;417
18.3.3;12.3.3 The Fundamental Theorem;417
18.3.4;12.3.4 Definition of an Arbitrage Opportunity;418
18.3.5;12.3.5 Interpreting the Qi: State Prices;418
18.3.5.1;12.3.5.1 Remarks;420
18.4;12.4 An Application;420
18.4.1;12.4.1 Obtaining the .i;421
18.4.2;12.4.2 Elementary Contracts and Options;424
18.4.3;12.4.3 Elementary Contracts and Replication;425
18.5;12.5 Implications of the Fundamental Theorem;427
18.5.1;12.5.1 Result 1: Risk-Adjusted Probabilities;427
18.5.1.1;12.5.1.1 Risk-neutral probabilities;428
18.5.1.2;12.5.1.2 Other probabilities;428
18.5.1.3;12.5.1.3 A remark;430
18.5.1.4;12.5.1.4 Swap measure;431
18.5.2;12.5.2 Result 2: Martingale Property;431
18.5.2.1;12.5.2.1 Martingales under P;431
18.5.2.2;12.5.2.2 Martingales under other probabilities;432
18.5.3;12.5.3 Result 3: Expected Returns;432
18.5.3.1;12.5.3.1 Martingales and risk premia;433
18.6;12.6 Arbitrage-Free Dynamics;434
18.6.1;12.6.1 Arbitrage-Free SDEs;434
18.6.2;12.6.2 Tree Models;435
18.6.2.1;12.6.2.1 Case 1;436
18.6.2.2;12.6.2.2 Case 2;438
18.7;12.7 Which Pricing Method to Choose?;438
18.8;12.8 Conclusions;439
18.9;Suggested Reading;439
18.10;Appendix 12.1: Simple Economics of the Fundamental Theorem;439
18.11;Exercises;441
18.11.1;EXCEL Exercises;443
19;13 Some Applications of the Fundamental Theorem;446
19.1;13.1 Introduction;447
19.2;13.2 Application 1: The Monte Carlo Approach;448
19.2.1;13.2.1 Pricing with Monte Carlo;449
19.2.1.1;13.2.1.1 Pricing a call with constant spot rate;450
19.2.2;13.2.2 Pricing Binary FX Options;452
19.2.2.1;13.2.2.1 Obtaining the risk-neutral dynamics;452
19.2.2.2;13.2.2.2 Monte Carlo process;454
19.2.3;13.2.3 Path Dependency;455
19.2.4;13.2.4 Discretization Bias and Closed Forms;457
19.2.5;13.2.5 Real-Life Complications;457
19.3;13.3 Application 2: Calibration;457
19.3.1;13.3.1 Calibrating a Tree;458
19.3.2;13.3.2 Extracting a Libor Tree;458
19.3.2.1;13.3.2.1 Pricing functions;458
19.3.3;13.3.3 Obtaining the BDT Tree;460
19.3.3.1;13.3.3.1 Specifying the dynamics;460
19.3.3.2;13.3.3.2 The variance of Li;460
19.3.4;13.3.4 Calibrating the Tree;462
19.3.5;13.3.5 Uses of the Tree;464
19.3.5.1;13.3.5.1 Application: pricing a cap;464
19.3.5.2;13.3.5.2 Some assumptions of the model;466
19.3.5.3;13.3.5.3 Remarks;466
19.3.6;13.3.6 Real-World Complications;467
19.4;13.4 Application 3: Quantos;467
19.4.1;13.4.1 Pricing Quantos;467
19.4.2;13.4.2 The PDE Approach;470
19.4.2.1;13.4.2.1 A PDE for quantos;471
19.4.3;13.4.3 Quanto Forward;472
19.4.4;13.4.4 Quanto Option;472
19.4.4.1;13.4.4.1 Black–Scholes and dividends;473
19.4.5;13.4.5 How to Hedge Quantos;473
19.4.6;13.4.6 Real-Life Considerations;473
19.5;13.5 Conclusions;474
19.6;Suggested Reading;474
19.7;Exercises;474
19.7.1;EXCEL Exercises;475
19.7.2;MATLAB Exercises;476
20;14 Fixed Income Engineering;478
20.1;14.1 Introduction;479
20.2;14.2 A Framework for Swaps;480
20.2.1;14.2.1 Equivalence of Cash Flows;483
20.2.2;14.2.2 Pricing the Swap;483
20.2.2.1;14.2.2.1 Interpretation of the swap rate;485
20.2.3;14.2.3 Some Applications;487
20.2.3.1;14.2.3.1 Another formula;488
20.2.3.2;14.2.3.2 Marking to market;489
20.3;14.3 Term Structure Modeling;490
20.3.1;14.3.1 Determining the Forward Rates from Swaps;490
20.3.2;14.3.2 Determining the B(t0, ti) from Forward Rates;491
20.3.3;14.3.3 Determining the Swap Rate;491
20.3.4;14.3.4 Real-World Complications;491
20.3.4.1;14.3.4.1 Remark;492
20.4;14.4 Term Structure Dynamics;492
20.4.1;14.4.1 The Framework;493
20.4.2;14.4.2 Normalization and Forward Measure;494
20.4.2.1;14.4.2.1 Risk-neutral measure is inconvenient;494
20.4.2.2;14.4.2.2 The forward measure;496
20.4.2.3;14.4.2.3 Arbitrage-free SDEs for forward rates;497
20.4.3;14.4.3 Arbitrage-Free Dynamics;498
20.4.3.1;14.4.3.1 Review;500
20.4.4;14.4.4 A Monte Carlo Implementation;501
20.5;14.5 Measure Change Technology;502
20.5.1;14.5.1 The Mechanics of Measure Changes;504
20.5.2;14.5.2 Generalization;506
20.6;14.6 An Application;507
20.6.1;14.6.1 Another Example of Measure Change;508
20.6.2;14.6.2 Pricing CMS;512
20.7;14.7 In-Arrears Swaps and Convexity;513
20.7.1;14.7.1 Valuation;514
20.7.2;14.7.2 Special Case;516
20.8;14.8 Cross-Currency Swaps;517
20.8.1;14.8.1 Pricing;518
20.8.2;14.8.2 Conventions;519
20.9;14.9 Differential (Quanto) Swaps;519
20.9.1;14.9.1 Basis Swaps;520
20.10;14.10 Conclusions;520
20.11;Suggested Reading;521
20.12;Exercises;521
20.12.1;EXCEL Exercises;522
20.12.2;MATLAB Exercise;524
21;15 Tools for Volatility Engineering, Volatility Swaps, and Volatility Trading;526
21.1;15.1 Introduction;527
21.2;15.2 Volatility Positions;528
21.2.1;15.2.1 Trading Volatility Term Structure;528
21.2.2;15.2.2 Trading Volatility Across Instruments;529
21.3;15.3 Invariance of Volatility Payoffs;529
21.3.1;15.3.1 Imperfect Volatility Positions;530
21.3.1.1;15.3.1.1 A dynamic volatility position;531
21.3.2;15.3.2 Volatility Hedging;535
21.3.3;15.3.3 A Static Volatility Position;535
21.4;15.4 Pure Volatility Positions;537
21.4.1;15.4.1 Practical Issues;540
21.4.1.1;15.4.1.1 The smile effect;540
21.4.1.2;15.4.1.2 Liquidity problems;541
21.5;15.5 Variance Swaps;541
21.5.1;15.5.1 Uses and Users of Variance Swaps;541
21.5.1.1;15.5.1.1 Uses of variance swaps;541
21.5.1.2;15.5.1.2 Market participants with an implicit volatility exposure to hedge;542
21.5.2;15.5.2 A Framework for Variance Swaps;542
21.5.2.1;15.5.2.1 Real-world example of a variance swap;543
21.5.2.2;15.5.2.2 Real-world conventions;546
21.5.2.3;15.5.2.3 Floating leg;546
21.5.2.4;15.5.2.4 Determining the fixed variance;547
21.5.3;15.5.3 A Replicating Portfolio;548
21.5.4;15.5.4 The Hedge;549
21.6;15.6 Real-World Example of Variance Contract;550
21.7;15.7 Volatility and Variance Swaps Before and After the GFC—The Role of Convexity Adjustments?;550
21.7.1;15.7.1 The Difficulty of Hedging Variance Swaps in Practice;550
21.7.2;15.7.2 Convexity and the Difference Between Variance and Volatility Swaps;552
21.7.2.1;15.7.2.1 Source of the convexity adjustment;552
21.7.2.2;15.7.2.2 The role of convexity in the volatility trading market during the GFC;554
21.7.3;15.7.3 Introduction to Volatility as an Asset Class;554
21.7.4;15.7.4 Post-GFC Regulation, Standardization and Exchange Traded Volatility Products;555
21.7.4.1;15.7.4.1 Variance futures;555
21.7.4.2;15.7.4.2 Variance swaps;557
21.7.5;15.7.5 The Hedge;558
21.8;15.8 Which Volatility?;558
21.9;15.9 Conclusions;560
21.10;Suggested Reading;561
21.11;Exercises;561
21.11.1;MATLAB Exercises;562
22;16 Correlation as an Asset Class and the Smile;564
22.1;16.1 Introduction to Correlation as an Asset Class;565
22.1.1;16.1.1 Reasons for Trading Correlation;566
22.1.2;16.1.2 Correlation Trading Vehicles;566
22.2;16.2 Volatility as Funding;570
22.3;16.3 Smile;570
22.4;16.4 Dirac Delta Functions;571
22.5;16.5 Application to Option Payoffs;573
22.5.1;16.5.1 An Interpretation of Dynamic Hedging;575
22.6;16.6 Breeden–Litzenberger Simplified;577
22.6.1;16.6.1 The Proof;579
22.7;16.7 A Characterization of Option Prices as Gamma Gains;580
22.7.1;16.7.1 Relationship to Tanaka’s Formula;581
22.8;16.8 Introduction to the Smile;581
22.9;16.9 Preliminaries;582
22.10;16.10 A First Look at the Smile;583
22.11;16.11 What Is the Volatility Smile?;584
22.11.1;16.11.1 Some Stylized Facts;586
22.11.2;16.11.2 How Can We Define Moneyness?;589
22.11.3;16.11.3 Replicating the Smile;591
22.11.3.1;16.11.3.1 Contractual equations;592
22.12;16.12 Smile Dynamics;593
22.13;16.13 How to Explain the Smile;593
22.13.1;16.13.1 Case 1: Nongeometric Price Processes;596
22.13.2;16.13.2 Case 2: Possibility of Crash;596
22.13.2.1;16.13.2.1 Modeling crashes;599
22.13.3;16.13.3 Other Explanations;600
22.13.3.1;16.13.3.1 Structural and regulatory explanations;601
22.14;16.14 The Relevance of the Smile;601
22.15;16.15 Trading the Smile;602
22.16;16.16 Pricing with a Smile;602
22.17;16.17 Exotic Options and the Smile;603
22.17.1;16.17.1 A Hedge for a Barrier;603
22.17.2;16.17.2 Effects of the Smile;604
22.17.2.1;16.17.2.1 An example of technical difficulties;605
22.17.2.2;16.17.2.2 Pricing exotics;605
22.17.3;16.17.3 The Case of Digital Options;606
22.17.4;16.17.4 Another Application: Risk Reversals;606
22.18;16.18 Conclusions;607
22.19;Suggested Reading;607
22.20;Exercises;607
22.20.1;Excel Exercise;608
22.20.2;MATLAB Exercises;609
23;17 Caps/Floors and Swaptions with an Application to Mortgages;610
23.1;17.1 Introduction;610
23.2;17.2 The Mortgage Market;611
23.2.1;17.2.1 The Life of a Typical Mortgage;612
23.2.2;17.2.2 Hedging the Position;616
23.2.3;17.2.3 Assumptions Behind the Model;616
23.2.4;17.2.4 Two Risks;617
23.3;17.3 Swaptions;618
23.3.1;17.3.1 A Contractual Equation;620
23.4;17.4 Pricing Swaptions;620
23.4.1;17.4.1 Swap Measure;620
23.4.2;17.4.2 The Forward Swap Rate as a Martingale;623
23.4.3;17.4.3 Swaption Value;624
23.4.4;17.4.4 Real-World Complications;626
23.5;17.5 Mortgage-Based Securities;626
23.6;17.6 Caps and Floors;627
23.6.1;17.6.1 Pricing Caps and Floors;629
23.6.2;17.6.2 A Summary;631
23.6.3;17.6.3 Caplet Pricing and the Smile;631
23.7;17.7 Conclusions;632
23.8;Suggested Reading;632
23.9;Exercises;632
23.9.1;EXCEL Exercises;636
24;18 Credit Markets: CDS Engineering;638
24.1;18.1 Introduction;639
24.2;18.2 Terminology and Definitions;640
24.2.1;18.2.1 Types of Credit Derivatives;641
24.3;18.3 Credit Default Swaps;642
24.3.1;18.3.1 Creating a CDS;644
24.3.2;18.3.2 Decomposing a Risky Bond;644
24.3.3;18.3.3 A Synthetic;649
24.3.4;18.3.4 Using the Contractual Equation;649
24.3.4.1;18.3.4.1 Creating a synthetic CDS;649
24.3.4.2;18.3.4.2 Negative basis trades;650
24.3.5;18.3.5 Measuring Credit Risk of Cash Bonds;652
24.3.5.1;18.3.5.1 Asset swap;653
24.3.5.2;18.3.5.2 The Z-spread;654
24.4;18.4 Real-World Complications;655
24.4.1;18.4.1 CDS Standardization and 2009 “Big Bang”;656
24.4.1.1;18.4.1.1 Auction hardwiring;656
24.4.1.2;18.4.1.2 Standardization coupons and trading conventions;656
24.4.1.3;18.4.1.3 Central clearing;657
24.4.2;18.4.2 Restructuring;657
24.4.3;18.4.3 Fixed Recovery CDS;658
24.4.4;18.4.4 A Note on the Arbitrage Equality;659
24.5;18.5 CDS Analytics;659
24.6;18.6 Default Probability Arithmetic;660
24.6.1;18.6.1 The DVO1’s;661
24.6.2;18.6.2 Unwinding a CDS;663
24.6.3;18.6.3 Upfront Payments and CDS Unwinding;665
24.7;18.7 Pricing Single-Name CDS;665
24.7.1;18.7.1 A Simplified CDS Valuation Example;665
24.7.2;18.7.2 Real-World Complications;666
24.7.3;18.7.3 Lessons from the GFC for CDS Pricing;667
24.8;18.8 Comparing CDS to TRS and EDS;667
24.8.1;18.8.1 Total Return Swaps Versus Credit Default Swaps;667
24.8.2;18.8.2 EDS Versus CDS;668
24.9;18.9 Sovereign CDS;669
24.10;18.10 Conclusions;674
24.11;Suggested Reading;674
24.12;Exercises;674
25;19 Engineering of Equity Instruments and Structural Models of Default;678
25.1;19.1 Introduction;679
25.2;19.2 What Is Equity?;681
25.3;19.3 Equity as the Discounted Value of Future Cash Flows;682
25.4;19.4 Equity as an Option on the Assets of the Firm;682
25.4.1;19.4.1 Merton’s Structural Model of Default;682
25.4.2;19.4.2 Payoffs to Bond and Equity Holders;683
25.4.2.1;19.4.2.1 Payments to debt and equity holders under different scenarios;685
25.4.2.2;19.4.2.2 Bond and equity value in the Merton model;686
25.4.3;19.4.3 Probability of Default;689
25.4.4;19.4.4 Application of the Merton Model and Equity-to-Credit Approach;690
25.4.5;19.4.5 Assumptions of the Merton Model and Extensions;691
25.4.5.1;19.4.5.1 Extensions in published academic research;691
25.4.5.2;19.4.5.2 Evolution of structural models of default in industry;691
25.5;19.5 Capital Structure Arbitrage;692
25.5.1;19.5.1 Examples of Capital Structure Arbitrage Trades;692
25.5.2;19.5.2 Using the Merton Model to Provide Signals for Capital Structure Arbitrage Trades;693
25.5.3;19.5.3 Source of Profits from Capital;695
25.5.3.1;19.5.3.1 Capital structure arbitrage as a mispricing of bonds (or CDS) and equity;697
25.5.3.2;19.5.3.2 Capital structure arbitrage from the perspective of mispriced volatility;697
25.6;19.6 Engineering Equity Products;699
25.6.1;19.6.1 Purpose;699
25.6.2;19.6.2 Convertibles;700
25.6.3;19.6.3 Synthetic Convertible Bonds and Cash Flow Engineering;702
25.6.4;19.6.4 Real-World Example;704
25.6.5;19.6.5 Convertible Bond Pricing;705
25.6.5.1;19.6.5.1 Bond plus equity option approach;705
25.6.5.2;19.6.5.2 Multifactor model;705
25.6.6;19.6.6 Convertible Bond Arbitrage;705
25.6.7;19.6.7 Comparing the Role of Volatility in Convertible Bond Arbitrage and Capital Structure Arbitrage;707
25.6.8;19.6.8 Incorporating More Complex Structures;707
25.6.8.1;19.6.8.1 Exchange rate exposure;707
25.6.8.2;19.6.8.2 Making the convertibles callable;709
25.6.8.3;19.6.8.3 Exchangeable bond;709
25.6.9;19.6.9 Using convertibles;709
25.6.10;19.6.10 Warrants;710
25.7;19.7 Conclusions;711
25.8;Suggested Reading;711
25.9;Exercises;712
26;20 Essentials of Structured Product Engineering;714
26.1;20.1 Introduction;715
26.2;20.2 Purposes of Structured Products;716
26.2.1;20.2.1 Equity Structured Products;717
26.2.2;20.2.2 The Tools;721
26.2.2.1;20.2.2.1 Touch and digital options;723
26.2.2.2;20.2.2.2 Rainbow options;724
26.2.2.3;20.2.2.3 Reverse convertibles;724
26.2.2.4;20.2.2.4 Cliquets;728
26.2.3;20.2.3 Forward Volatility;729
26.2.4;20.2.4 Prototypes;731
26.2.4.1;20.2.4.1 Case I: A structure with built-in cliquet;732
26.2.4.2;20.2.4.2 Case II: Structures with mountain options;733
26.2.4.2.1;20.2.4.2.1 Altiplano;733
26.2.4.2.2;20.2.4.2.2 Himalaya;735
26.2.4.3;20.2.4.3 Case III: The Napoleon and Vega hedging costs;736
26.2.5;20.2.5 Similar FX Structures;737
26.3;20.3 Structured Fixed-Income Products;737
26.3.1;20.3.1 Yield Curve Strategies;737
26.3.2;20.3.2 The Tools;738
26.3.3;20.3.3 CMS;738
26.3.4;20.3.4 Yield Enhancement in Fixed-Income Products;739
26.3.4.1;20.3.4.1 Method 1: Sell cap volatility;740
26.3.4.2;20.3.4.2 Method 2: Sell swaption volatility;742
26.4;20.4 Some Prototypes;743
26.4.1;20.4.1 The Components;743
26.4.2;20.4.2 CMS-Linked Structures;744
26.4.3;20.4.3 Engineering a CMS-Linked Note;745
26.4.3.1;20.4.3.1 A contractual equation;745
26.4.4;20.4.4 Engineering a CMS Spread Note;747
26.4.5;20.4.5 The Engineering;748
26.4.5.1;20.4.5.1 A contractual equation;752
26.4.6;20.4.6 Some Other Structures;752
26.5;20.5 Conclusions;753
26.6;Suggested Reading;753
26.7;Exercises;753
27;21 Securitization, ABSs, CDOs, and Credit Structured Products;758
27.1;21.1 Introduction;759
27.2;21.2 Financial Engineering of Securitization;759
27.2.1;21.2.1 Choosing Cash Flows;760
27.2.2;21.2.2 The Critical Step: Securing the Cash Flow;761
27.2.3;21.2.3 Some Comparisons;762
27.2.3.1;21.2.3.1 Loan sales;762
27.2.3.2;21.2.3.2 Secured lending;763
27.3;21.3 ABSs Versus CDOs;764
27.3.1;21.3.1 Tranches and Some Securitization History;765
27.3.2;21.3.2 A Comparison of ABSs and CDOs;766
27.3.2.1;21.3.2.1 Credit indices;767
27.3.2.2;21.3.2.2 Synthetic CDOs;767
27.4;21.4 A Setup for Credit Indices;769
27.5;21.5 Index Arbitrage;773
27.5.1;21.5.1 Real-World Complications;773
27.5.2;21.5.2 Credit Skew Trade;774
27.6;21.6 Tranches: Standard and Bespoke;775
27.7;21.7 Tranche Modeling and Pricing;776
27.7.1;21.7.1 A Mechanical View of the Tranches;777
27.7.2;21.7.2 Tranche Values and the Default Distribution;778
27.8;21.8 The Roll and the Implications;781
27.8.1;21.8.1 Roll and Default Risk;782
27.9;21.9 Regulation, Credit Risk Management, and Tranche Pricing;783
27.9.1;21.9.1 Credit Risk Management, Default Losses, and Mark-to-Market Losses;783
27.9.2;21.9.2 Capital Requirements and CDO Activity;784
27.9.3;21.9.3 Lessons from the GFC, Post-GFC Capital Regulation and the Securitization Market;785
27.9.4;21.9.4 Can Securitization Cure Cancer?;786
27.10;21.10 New Index Markets;786
27.10.1;21.10.1 The ABX Index;787
27.10.2;21.10.2 The LCDS, LCDX;787
27.10.2.1;21.10.2.1 Cancelability;788
27.10.2.2;21.10.2.2 Quoting conventions;788
27.11;21.11 Structured Credit Products;788
27.11.1;21.11.1 Credit Options;788
27.11.2;21.11.2 Forward Start CDOs;789
27.11.3;21.11.3 The CMDS;789
27.11.4;21.11.4 Leveraged Super Senior Notes;791
27.11.5;21.11.5 CoCos;792
27.11.5.1;21.11.5.1 Cocos versus convertible bonds;792
27.11.5.2;21.11.5.2 Valuation of CoCos;793
27.11.5.3;21.11.5.3 The outlook for CoCos;794
27.12;21.12 Conclusions;795
27.13;Suggested Reading;795
27.14;Exercises;796
27.14.1;MATLAB Exercise;799
28;22 Default Correlation Pricing and Trading;800
28.1;22.1 Introduction;801
28.2;22.2 Two Simple Examples;801
28.2.1;22.2.1 Portfolio with three credit names;802
28.2.1.1;22.2.1.1 Case 1: Independence;802
28.2.1.2;22.2.1.2 Case 2: Perfect correlation;804
28.2.2;22.2.2 Sensitivity of Tranche Spreads and Basket Default Swaps to Default Correlation;805
28.2.3;22.2.3 Recent Quotation Convention for CDO Tranches and Evolution of Tranche Spreads;806
28.3;22.3 Standard Tranche Valuation Model;808
28.3.1;22.3.1 The Gaussian Copula Model;808
28.3.2;22.3.2 Implied Correlations;810
28.3.3;22.3.3 The Central Limit Effect;813
28.4;22.4 Default Correlation and Trading;814
28.5;22.5 Delta Hedging and Correlation Trading;815
28.5.1;22.5.1 How to Calculate Deltas;816
28.5.2;22.5.2 Gamma Sensitivity;817
28.5.3;22.5.3 Correlation Trade and Gamma Gains;817
28.6;22.6 Real-World Complications;818
28.6.1;22.6.1 Base Correlations;819
28.6.2;22.6.2 The Dispersion Effect;819
28.6.3;22.6.3 The Time Effect;820
28.6.4;22.6.4 Do Deltas Add Up to One?;820
28.7;22.7 Default Correlation Case Study: May 2005;820
28.8;22.8 Conclusions;823
28.9;Suggested Reading;823
28.10;Appendix 22.1: Some Basic Statistical Concepts;824
28.11;Exercises;825
28.11.1;MATLAB Exercises;827
29;23 Principal Protection Techniques;828
29.1;23.1 Introduction;828
29.2;23.2 The Classical Case;829
29.3;23.3 The CPPI;830
29.4;23.4 Modeling the CPPI Dynamics;832
29.4.1;23.4.1 Interpretation;833
29.4.2;23.4.2 How to Pick .;834
29.5;23.5 An Application: CPPI and Equity Tranches;834
29.5.1;23.5.1 A Numerical Example;835
29.5.1.1;23.5.1.1 The initial position;836
29.5.1.2;23.5.1.2 Dynamic adjustments;837
29.5.1.3;23.5.1.3 Default and switching out of CPPI into zero-coupon bond;839
29.6;23.6 Differences Between CPDO and CPPI;839
29.7;23.7 A Variant: The DPPI;840
29.8;23.8 Application of CPPI in the Insurance Sector: ICPPI;841
29.9;23.9 Real-World Complications;843
29.9.1;23.9.1 The Gap Risk;843
29.9.2;23.9.2 The Issue of Liquidity;843
29.9.3;23.9.3 Which Principal Protection Technique is Best in Practice?;844
29.10;23.10 Conclusions;844
29.11;Suggested Reading;845
29.12;Exercises;845
30;24 Counterparty Risk, Multiple Curves, CVA, DVA, and FVA;846
30.1;24.1 Introduction;846
30.2;24.2 Counterparty Risk;848
30.3;24.3 Credit Valuation Adjustment;850
30.3.1;24.3.1 Counterparty Risk Example and CVA;850
30.3.2;24.3.2 CVA as an Option;852
30.3.2.1;24.3.2.1 Close-out proceedings;853
30.3.3;24.3.3 Counterparty Risk and Unilateral CVA in a Single IRS;855
30.3.4;24.3.4 Numerical CVA Example for IRS Portfolio;856
30.4;24.4 Debit Valuation Adjustment;861
30.5;24.5 Bilateral Counterparty Risk;862
30.6;24.6 Hedging Counterparty Risk;862
30.6.1;24.6.1 CVA and DVA Hedging in Practice;863
30.6.2;24.6.2 Contingent CDS;864
30.7;24.7 Funding Valuation Adjustment;864
30.8;24.8 CVA Desk;865
30.9;24.9 Choice of the Discount Rate and Multiple Curves;866
30.10;24.10 Conclusions;868
30.11;Suggested Reading;868
30.12;Exercises;869
30.12.1;MATLAB Exercise;869
31;References;870
32;Index;876

Leseproben

Chapter 1 Introduction
This chapter provides an overview of some of the concepts and applications discussed in the book. We introduce the concept of replication and apply it to forwards, interest rate swaps, credit default swaps, and total returns swaps. We highlight the importance of funding, regulatory, balance sheet, and tax considerations in financial engineering. Keywords
Forwards; money market; swaps; trading volatility Chapter Outline 1.1 A Unique Instrument 2 1.1.1 Buying a Default-Free Bond 3 1.1.2 Buying Stocks 5 1.1.3 Buying a Defaultable Bond 7 1.1.4 First Conclusions 10 1.2 A Money Market Problem 10 1.2.1 The Problem 11 1.2.2 Solution 11 1.2.3 Some Implications 13 1.3 A Taxation Example 13 1.3.1 The Problem 14 1.3.1.1 Another strategy 15 1.3.2 Implications 16 1.4 Some Caveats for What Is to Follow 17 1.5 Trading Volatility 18 1.5.1 A Volatility Trade 20 1.5.2 Recap 21 1.6 Conclusions 22 Suggested Reading 22 Exercises 22 Market professionals and investors take long and short positions on elementary assets such as stocks, default-free bonds, and debt instruments that carry a default risk. There is also a great deal of interest in trading currencies, commodities, and, recently, inflation, volatility, and correlation. Looking from the outside, an observer may think that these trades are done overwhelmingly by buying and selling the asset in question outright, for example, by paying “cash” and buying a US Treasury bond. This is wrong. It turns out that most of the financial objectives can be reached in a much more convenient fashion by going through a proper swap. There is an important logic behind this and we choose this as the first principle to illustrate in this introductory chapter. 1.1 A Unique Instrument
First, we would like to introduce the equivalent of the integer zero, in finance. Remember the property of zero in algebra. Adding (subtracting) zero to any other real number leaves this number the same. There is a unique financial instrument that has the same property with respect to market and credit risk. Consider the cash flow diagram in Figure 1.1. Here, the time is continuous and the t0, t1, t2 represent some specific dates. Initially we place ourselves at time t0. The following deal is struck with a bank. At time t1 we borrow 100 US dollars (USD100), at the going interest rate of time t1, called the LIBOR and denoted by the symbol t1.1 We pay the interest and the principal back at time t2. The loan has no default risk and is for a period of d units of time.2 Note that the contract is written at time t0, but starts at the future date t1. Hence this is an example of forward contracts. The actual value of t1 will also be determined at the future date t1.
Figure 1.1 A forward loan. Now, consider the time interval from t0 to t1, expressed as t?[t0, t1]. At any time during this interval, what can we say about the value of this forward contract initiated at t0? It turns out that this contract will have a value identically equal to zero for all t?[t0, t1] regardless of what happens in world financial markets. Perceptions of future interest rate movements may go from zero to infinity, but the value of the contract will still remain zero. In order to prove this assertion, we calculate the value of the contract at time t0. Actually, the value is obvious in one sense. Look at Figure 1.1. No cash changes hands at time t0. So, the value of the contract at time t0 must be zero. This may be obvious but let us show it formally. To value the cash flows in Figure 1.1, we will calculate the time t1 value of the cash flows that will be exchanged at time t2. This can be done by discounting them with the proper discount factor. The best discounting is done using the t1 itself, although at time t0 the value of this LIBOR rate is not known. Still, the time t1 value of the future cash flows are Vt1=Lt1d100(1+Lt1d)+100(1+Lt1d) (1.1) (1.1) At first sight, it seems we would need an estimate of the random variable t1 to obtain a numerical answer from this formula. In fact, some market practitioners may suggest using the corresponding forward rate that is observed at time t0 in lieu of t1, for example. But a closer look suggests a much better alternative. Collecting the terms in the numerator Vt1=(1+Lt1d)100(1+Lt1d) (1.2) (1.2) the unknown terms cancel out and we obtain: Vt1=100 (1.3) (1.3) This looks like a trivial result, but consider what it means. In order to calculate the value of the cash flows shown in Figure 1.1, we don’t need to know t1. Regardless of what happens to interest rate expectations and regardless of market volatility, the value of these cash flows, and hence the value of this contract, is always equal to zero for any t?[t0, t1]. In other words, the price volatility of this instrument is identically equal to zero. This means that given any instrument at time t, we can add (or subtract) the LIBOR loan to it, and the value of the original instrument will not change for all t?[t0, t1]. We now apply this simple idea to a number of basic operations in financial markets. 1.1.1 Buying a Default-Free Bond
For many of the operations they need, market practitioners do not “buy” or “sell” bonds. There is a much more convenient way of doing business. The cash flows of buying a default-free coupon bond with par value 100 forward are shown in Figure 1.2. The coupon rate, set at time t0, is t0. The price is USD100, hence this is a par bond and the maturity date is t2. Note that this implies the following equality: =rt0d100(1+rt0d)+100(1+rt0d) (1.4) (1.4) which is true, because at t0, the buyer is paying USD100 for the cash flows shown in Figure 1.2.
Figure 1.2 Buying default-free bond. Buying (selling) such a bond is inconvenient in many respects. First, one needs cash to do this. Practitioners call this funding, in case the bond is purchased.3 When the bond is sold short it will generate new cash and this must be managed.4 Hence, such outright sales and purchases require inconvenient and costly cash management. Second, the security in question may be a registered bond, instead of being a bearer bond, whereas the buyer may prefer to stay anonymous. Third, buying (selling) the bond will affect balance sheets, called books in the industry. Suppose the practitioner borrows USD100 and buys the bond. Both the asset and the liability sides of the balance sheet are now larger. This may have regulatory implications.5 Finally, by securing the funding, the practitioner is getting a loan. Loans involve credit risk. The loan counterparty may want to factor a default risk premium into the interest rate.6 Now consider the following operation. The bond in question is a contract. To this contract “add” the forward LIBOR loan that we discussed in the previous section. This is shown in Figure 1.3a. As we already proved, for all t?[t0, t1], the value of the LIBOR loan is identically equal to zero. Hence, this operation is similar to adding zero to a risky contract. This addition does not change the market risk characteristics of the original position in any way. On the other hand, as Figures 1.3a and b show, the resulting cash flows are significantly more convenient than the original bond.
Figure 1.3 Engineering a simple IRS. The cash flows require no upfront cash, they do not involve buying a registered security, and the balance sheet is not affected in any way.7 Yet, the cash flows shown in Figure 1.3 have exactly the same market risk characteristics as the original bond. Since the cash flows generated by the bond and the LIBOR loan in Figure 1.3 accomplish the same market risk objectives as the original bond transaction, then why not package them as a...