Equity hybrid derivatives:
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| Main Authors: | , , , , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken ; New Jersey
John Wiley & Sons, Inc.
[2007]
|
| Series: | [Wiley finance]
|
| Subjects: | |
| Online Access: | Table of contents only Publisher description Contributor biographical information Inhaltsverzeichnis |
| Item Description: | Series from jacket Includes bibliographical references (p. 313-321) and index |
| Physical Description: | ix, 326 Seiten Illustrationen 26 cm |
| ISBN: | 9780471770589 0471770582 9781119201816 |
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| 100 | 1 | |a Overhaus, Marcus |d 1971- |0 (DE-588)122651294 |4 aut | |
| 245 | 1 | 0 | |a Equity hybrid derivatives |c Marcus Overhaus ; Ana Bermúdez ; Hans Bühler ; Andrew Ferraris ; Christopher Jordinson ; Aziz Jordinson |
| 264 | 1 | |a Hoboken ; New Jersey |b John Wiley & Sons, Inc. |c [2007] | |
| 264 | 4 | |c © 2007 | |
| 300 | |a ix, 326 Seiten |b Illustrationen |c 26 cm | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a [Wiley finance] | |
| 500 | |a Series from jacket | ||
| 500 | |a Includes bibliographical references (p. 313-321) and index | ||
| 650 | 4 | |a Derivative securities | |
| 650 | 4 | |a Convertible securities | |
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| 700 | 1 | |a Ferraris, Andrew |4 aut | |
| 700 | 1 | |a Jordinson, Christopher |4 aut | |
| 700 | 1 | |a Lamnouar, Aziz |4 aut | |
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| adam_text | Contents
Preface ix
PART ONE
Modeling Volatility
CHAPTER 1
Theory 3
1.1 Concepts of Equity Modeling 3
1.1.1 The Forward 5
1.1.2 The Shape of Dividends to Come 6
1.1.3 European Options on the Pure Stock Process 10
1.2 Implied Volatility 11
1.2.1 Sticky Volatilities 13
1.3 Fitting the Market 16
1.3.1 Arbitrage-Free Option Price Surfaces 16
1.3.2 Implied Local Volatility 17
1.3.3 European Payoffs 21
1.3.4 Fitting the Market with Discrete Martingales 23
1.4 Theory of Replication 27
1.4.1 Replication in Diffusion-Driven Markets 30
CHAPTER 2
Applications 35
2.1 Classic Equity Models 35
2.1.1 Heston 35
2.1.2 SABR 43
2.1.3 Scott s Exponential Ornstein-Uhlenbeck Model 45
2.1.4 Other Stochastic Volatility Models 45
2.1.5 Extensions of Heston s Model 46
2.1.6 Cliquets 49
2.1.7 Forward-Skew Propagation 52
2.2 Variance Swaps, Entropy Swaps, Gamma Swaps 56
2.2.1 Variance Swaps 58
2.2.2 Entropy Swaps 68
2.2.3 Gamma Swaps 69
2.3 Variance Swap Market Models 71
2.3.1 Finite Dimensional Parametrizations 76
2.3.2 Examples 79
2.3.3 Fitting to the Market 83
iy CONTENTS
PART TWO
Equity Interest Rate Hybrids
CHAPTER 3
Short-Rate Models 91
3.1 Introduction 91
3.2 Ornstein-Uhlenbeck Models 94
3.3 Calibrating to the Yield Curve 95
3.3.1 Hull-White Model 95
3.3.2 Generic Ornstein-Uhlenbeck Models 98
3.4 Calibrating the Volatility 100
3.4.1 Hull-White/Vasicek 101
3.4.2 Generic Ornstein-Uhlenbeck Models 104
3.5 Pricing Hybrids 105
3.5.1 Finite Differences 106
3.5.2 Monte Carlo 107
3.6 Appendix: Least-Squares Minimization 109
3.6.1 Newton-Raphson Method 110
3.6.2 Broyden s Method 110
CHAPTER 4
Hybrid Products 112
4.1 The Effects of Assuming Stochastic Rates 112
4.2 Conditional Trigger Swaps 115
4.3 Target Redemption Notes 118
4.3.1 Structure 118
4.3.2 Back-Testing 120
4.3.3 Valuation Approach 123
4.3.4 Hedging 127
4.4 Convertible Bonds 128
4.4.1 Introduction 128
4.4.2 The Governing Equation 131
4.4.3 Detailed Specification of the Model 134
4.4.4 Analytical Solutions for a Special CB 137
4.5 Exchangeable Bonds 138
4.5.1 The Valuation PDE 138
4.5.2 Coordinate Transformations for Numerical Solution 140
CHAPTER 5
Constant Proportion Portfolio Insurance 145
5.1 Introduction to Portfolio Insurance 145
5.2 Classical CPPI 146
5.3 Restricted CPPI 149
5.3.1 Constraints on the Investment Level 149
5.3.2 Constraints on the Floor 149
5.3.3 An Example Structure 151
Contents y
5.4 Options on CPPI 152
5.4.1 The Pricing 152
5.4.2 Delta, Gamma, and Vega Exposures 152
5.4.3 Hedging 152
5.5 Nonstandard CPPIs 153
5.5.1 Complex Fee Structures 153
5.5.2 Dynamic Gearing 154
5.5.3 Perpetual CPPI 154
5.5.4 Flexi-Portfolio CPPI 155
5.5.5 Off-Balance-Sheet CPPI 156
5.6 CPPI as an Underlying 158
5.7 Other Issues Related to the CPPI 158
5.7.1 Liquidity Issues (Hedge Funds) 158
5.7.2 Assets Suitable for CPPIs 158
5.8 Appendixes 159
5.8.1 Appendix A 159
5.8.2 Appendix B 160
5.8.3 Appendix C 161
PART THREE
Equity Credit Hybrids
CHAPTER B
Credit Modeling 167
6.1 Introduction 167
6.2 Background on Credit Modeling 167
6.2.1 Structural Approach 168
6.2.2 Reduced-Form Approach 171
6.3 Modeling Equity Credit Hybrids 175
6.3.1 Dynamics of the Hazard Rate 175
6.3.2 Model Choice 176
6.4 Pricing 180
6.4.1 Credit Default Swap 180
6.4.2 Credit Default Swaption 181
6.4.3 European Call 184
6.5 Calibration 186
6.5.1 Stripping of Hazard Rate 186
6.5.2 Calibration of the Hazard Rate Process 187
6.5.3 Calibration of the Equity Volatility 188
6.5.4 Discussion 188
6.6 Introduction of Discontinuities 188
6.6.1 The New Framework 189
6.6.2 Dynamics of the Survival Probability 189
6.6.3 Pricing of European Options 190
6.6.4 Fourier Pricing 194
6.7 Equity Default Swaps 196
6.7.1 Modeling Equity Default Swaps 198
Vj CONTENTS
6.7.2 Single-Name EDSs in a Deterministic Hazard Rate Model 198
6.8 Conclusion 203
PART FOUR
Advanced Pricing Techniques
CHAPTER 7
Copulas Applied to Derivatives Pricing 207
7.1 Introduction 207
7.2 Theoretical Background of Copulas 207
7.2.1 Definitions 207
7.2.2 Measures of Dependence 209
7.2.3 Copulas and Stochastic Processes 211
7.2.4 Some Popular Copulas 213
7.3 Factor Copula Framework 217
7.4 Applications to Derivatives Pricing 218
7.4.1 Equity Derivatives: The Altiplano 218
7.4.2 Credit Derivatives: Basket and Tranche Pricing 223
7.5 Conclusion 228
CHAPTER 8
Forward PDEs and Local Volatility Calibration 229
8.1 Introduction 229
8.1.1 Local and Implied Volatilities 229
8.1.2 Dupire s Formula and Its Problems 231
8.1.3 Dupire-like Formula in Multifactor Models 232
8.2 Forward PDEs 233
8.3 Pure Equity Case 235
8.4 Local Volatility with Stochastic Interest Rates 238
8.5 Calibrating the Local Volatility 242
8.6 Special Case: Vasicek Plus a Term Structure of Equity Volatilities 244
CHAPTER 9
Numerical Solution of Multifactor Pricing Problems Using
Lagrange-Galerkln with Duality Methods 248
9.1 Introduction 248
9.2 The Modeling Framework: A General D-factor Model 250
9.2.1 Strong Formulation of the Linear Problem:
Partial Differential Equations 251
9.2.2 Truncation of the Domain and Boundary Conditions 253
9.2.3 Strong Formulation of the Nonlinear Problem: Partial
Differential Inequalities 254
9.2.4 Weak Formulation of the Nonlinear Problem:
Variational Inequalities 256
Contents VN
9.3 Numerical Solution of Partial Differential Inequalities
(Variational Inequalities) 259
9.3.1 A Duality (or Lagrange Multiplier) Method 260
9.4 Numerical Solution of Partial Differential Equations (Variational
Equalities): Classical Lagrange-Galerkin Method 262
9.4.1 Semi-Lagrangian Time Discretization: Method
of Characteristics 262
9.4.2 Space Discretization: Galerkin Finite Element Method 265
9.4.3 Order of Classical Lagrange-Galerkin Method 270
9.5 Higher-Order Lagrange-Galerkin Methods 271
9.5.1 Crank-Nicolson Characteristics/Finite Elements 272
9.6 Application to Pricing of Convertible Bonds 279
9.6.1 Numerical Solution 280
9.6.2 Numerical Results 280
9.7 Appendix: Lagrange Triangular Finite Elements 285
9.7.1 Lagrange Triangular Finite Elements 285
9.7.2 Coefficients Matrix and Independent Term in Two
Dimensions 287
CHAPTER 10
American Monte Carlo 297
10.1 Introduction 297
10.2 Broadie and Glasserman 299
10.3 Regularly Spaced Restarts 299
10.4 The Longstaff and Schwartz Algorithm 301
10.4.1 The Algorithm 301
10.4.2 Example: A Call Option with Monthly
Bermudan Exercise 303
10.5 Accuracy and Bias 305
10.5.1 Extension: Regressing on In-the-Money Paths 306
10.5.2 Linear Regression 308
10.5.3 Other Regression Schemes 310
10.5.4 Upper Bounds 310
10.6 Parameterizing the Exercise Boundary 311
Bibliography 313
Index 323
|
| adam_txt |
Contents
Preface ix
PART ONE
Modeling Volatility
CHAPTER 1
Theory 3
1.1 Concepts of Equity Modeling 3
1.1.1 The Forward 5
1.1.2 The Shape of Dividends to Come 6
1.1.3 European Options on the Pure Stock Process 10
1.2 Implied Volatility 11
1.2.1 Sticky Volatilities 13
1.3 Fitting the Market 16
1.3.1 Arbitrage-Free Option Price Surfaces 16
1.3.2 Implied Local Volatility 17
1.3.3 European Payoffs 21
1.3.4 Fitting the Market with Discrete Martingales 23
1.4 Theory of Replication 27
1.4.1 Replication in Diffusion-Driven Markets 30
CHAPTER 2
Applications 35
2.1 Classic Equity Models 35
2.1.1 Heston 35
2.1.2 SABR 43
2.1.3 Scott's Exponential Ornstein-Uhlenbeck Model 45
2.1.4 Other Stochastic Volatility Models 45
2.1.5 Extensions of Heston's Model 46
2.1.6 Cliquets 49
2.1.7 Forward-Skew Propagation 52
2.2 Variance Swaps, Entropy Swaps, Gamma Swaps 56
2.2.1 Variance Swaps 58
2.2.2 Entropy Swaps 68
2.2.3 Gamma Swaps 69
2.3 Variance Swap Market Models 71
2.3.1 Finite Dimensional Parametrizations 76
2.3.2 Examples 79
2.3.3 Fitting to the Market 83
iy CONTENTS
PART TWO
Equity Interest Rate Hybrids
CHAPTER 3
Short-Rate Models 91
3.1 Introduction 91
3.2 Ornstein-Uhlenbeck Models 94
3.3 Calibrating to the Yield Curve 95
3.3.1 Hull-White Model 95
3.3.2 Generic Ornstein-Uhlenbeck Models 98
3.4 Calibrating the Volatility 100
3.4.1 Hull-White/Vasicek 101
3.4.2 Generic Ornstein-Uhlenbeck Models 104
3.5 Pricing Hybrids 105
3.5.1 Finite Differences 106
3.5.2 Monte Carlo 107
3.6 Appendix: Least-Squares Minimization 109
3.6.1 Newton-Raphson Method 110
3.6.2 Broyden's Method 110
CHAPTER 4
Hybrid Products 112
4.1 The Effects of Assuming Stochastic Rates 112
4.2 Conditional Trigger Swaps 115
4.3 Target Redemption Notes 118
4.3.1 Structure 118
4.3.2 Back-Testing 120
4.3.3 Valuation Approach 123
4.3.4 Hedging 127
4.4 Convertible Bonds 128
4.4.1 Introduction 128
4.4.2 The Governing Equation 131
4.4.3 Detailed Specification of the Model 134
4.4.4 Analytical Solutions for a Special CB 137
4.5 Exchangeable Bonds 138
4.5.1 The Valuation PDE 138
4.5.2 Coordinate Transformations for Numerical Solution 140
CHAPTER 5
Constant Proportion Portfolio Insurance 145
5.1 Introduction to Portfolio Insurance 145
5.2 Classical CPPI 146
5.3 Restricted CPPI 149
5.3.1 Constraints on the Investment Level 149
5.3.2 Constraints on the Floor 149
5.3.3 An Example Structure 151
Contents y
5.4 Options on CPPI 152
5.4.1 The Pricing 152
5.4.2 Delta, Gamma, and Vega Exposures 152
5.4.3 Hedging 152
5.5 Nonstandard CPPIs 153
5.5.1 Complex Fee Structures 153
5.5.2 Dynamic Gearing 154
5.5.3 Perpetual CPPI 154
5.5.4 Flexi-Portfolio CPPI 155
5.5.5 Off-Balance-Sheet CPPI 156
5.6 CPPI as an Underlying 158
5.7 Other Issues Related to the CPPI 158
5.7.1 Liquidity Issues (Hedge Funds) 158
5.7.2 Assets Suitable for CPPIs 158
5.8 Appendixes 159
5.8.1 Appendix A 159
5.8.2 Appendix B 160
5.8.3 Appendix C 161
PART THREE
Equity Credit Hybrids
CHAPTER B
Credit Modeling 167
6.1 Introduction 167
6.2 Background on Credit Modeling 167
6.2.1 Structural Approach 168
6.2.2 Reduced-Form Approach 171
6.3 Modeling Equity Credit Hybrids 175
6.3.1 Dynamics of the Hazard Rate 175
6.3.2 Model Choice 176
6.4 Pricing 180
6.4.1 Credit Default Swap 180
6.4.2 Credit Default Swaption 181
6.4.3 European Call 184
6.5 Calibration 186
6.5.1 Stripping of Hazard Rate 186
6.5.2 Calibration of the Hazard Rate Process 187
6.5.3 Calibration of the Equity Volatility 188
6.5.4 Discussion 188
6.6 Introduction of Discontinuities 188
6.6.1 The New Framework 189
6.6.2 Dynamics of the Survival Probability 189
6.6.3 Pricing of European Options 190
6.6.4 Fourier Pricing 194
6.7 Equity Default Swaps 196
6.7.1 Modeling Equity Default Swaps 198
Vj CONTENTS
6.7.2 Single-Name EDSs in a Deterministic Hazard Rate Model 198
6.8 Conclusion 203
PART FOUR
Advanced Pricing Techniques
CHAPTER 7
Copulas Applied to Derivatives Pricing 207
7.1 Introduction 207
7.2 Theoretical Background of Copulas 207
7.2.1 Definitions 207
7.2.2 Measures of Dependence 209
7.2.3 Copulas and Stochastic Processes 211
7.2.4 Some Popular Copulas 213
7.3 Factor Copula Framework 217
7.4 Applications to Derivatives Pricing 218
7.4.1 Equity Derivatives: The Altiplano 218
7.4.2 Credit Derivatives: Basket and Tranche Pricing 223
7.5 Conclusion 228
CHAPTER 8
Forward PDEs and Local Volatility Calibration 229
8.1 Introduction 229
8.1.1 Local and Implied Volatilities 229
8.1.2 Dupire's Formula and Its Problems 231
8.1.3 Dupire-like Formula in Multifactor Models 232
8.2 Forward PDEs 233
8.3 Pure Equity Case 235
8.4 Local Volatility with Stochastic Interest Rates 238
8.5 Calibrating the Local Volatility 242
8.6 Special Case: Vasicek Plus a Term Structure of Equity Volatilities 244
CHAPTER 9
Numerical Solution of Multifactor Pricing Problems Using
Lagrange-Galerkln with Duality Methods 248
9.1 Introduction 248
9.2 The Modeling Framework: A General D-factor Model 250
9.2.1 Strong Formulation of the Linear Problem:
Partial Differential Equations 251
9.2.2 Truncation of the Domain and Boundary Conditions 253
9.2.3 Strong Formulation of the Nonlinear Problem: Partial
Differential Inequalities 254
9.2.4 Weak Formulation of the Nonlinear Problem:
Variational Inequalities 256
Contents VN
9.3 Numerical Solution of Partial Differential Inequalities
(Variational Inequalities) 259
9.3.1 A Duality (or Lagrange Multiplier) Method 260
9.4 Numerical Solution of Partial Differential Equations (Variational
Equalities): Classical Lagrange-Galerkin Method 262
9.4.1 Semi-Lagrangian Time Discretization: Method
of Characteristics 262
9.4.2 Space Discretization: Galerkin Finite Element Method 265
9.4.3 Order of Classical Lagrange-Galerkin Method 270
9.5 Higher-Order Lagrange-Galerkin Methods 271
9.5.1 Crank-Nicolson Characteristics/Finite Elements 272
9.6 Application to Pricing of Convertible Bonds 279
9.6.1 Numerical Solution 280
9.6.2 Numerical Results 280
9.7 Appendix: Lagrange Triangular Finite Elements 285
9.7.1 Lagrange Triangular Finite Elements 285
9.7.2 Coefficients Matrix and Independent Term in Two
Dimensions 287
CHAPTER 10
American Monte Carlo 297
10.1 Introduction 297
10.2 Broadie and Glasserman 299
10.3 Regularly Spaced Restarts 299
10.4 The Longstaff and Schwartz Algorithm 301
10.4.1 The Algorithm 301
10.4.2 Example: A Call Option with Monthly
Bermudan Exercise 303
10.5 Accuracy and Bias 305
10.5.1 Extension: Regressing on In-the-Money Paths 306
10.5.2 Linear Regression 308
10.5.3 Other Regression Schemes 310
10.5.4 Upper Bounds 310
10.6 Parameterizing the Exercise Boundary 311
Bibliography 313
Index 323 |
| any_adam_object | 1 |
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| author | Overhaus, Marcus 1971- Bermúdez, Ana Bühler, Hans Ferraris, Andrew Jordinson, Christopher Lamnouar, Aziz |
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| author_facet | Overhaus, Marcus 1971- Bermúdez, Ana Bühler, Hans Ferraris, Andrew Jordinson, Christopher Lamnouar, Aziz |
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| callnumber-subject | HG - Finance |
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| ctrlnum | (OCoLC)602451082 (DE-599)BVBBV023402915 |
| dewey-full | 332.64/57 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.64/57 |
| dewey-search | 332.64/57 |
| dewey-sort | 3332.64 257 |
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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV023402915 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:24:26Z |
| indexdate | 2024-07-09T21:17:50Z |
| institution | BVB |
| isbn | 9780471770589 0471770582 9781119201816 |
| language | English |
| lccn | 2006005369 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016585671 |
| oclc_num | 602451082 |
| open_access_boolean | |
| owner | DE-29T DE-11 DE-83 |
| owner_facet | DE-29T DE-11 DE-83 |
| physical | ix, 326 Seiten Illustrationen 26 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | John Wiley & Sons, Inc. |
| record_format | marc |
| series2 | [Wiley finance] |
| spelling | Overhaus, Marcus 1971- (DE-588)122651294 aut Equity hybrid derivatives Marcus Overhaus ; Ana Bermúdez ; Hans Bühler ; Andrew Ferraris ; Christopher Jordinson ; Aziz Jordinson Hoboken ; New Jersey John Wiley & Sons, Inc. [2007] © 2007 ix, 326 Seiten Illustrationen 26 cm txt rdacontent n rdamedia nc rdacarrier [Wiley finance] Series from jacket Includes bibliographical references (p. 313-321) and index Derivative securities Convertible securities Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Gleichgewichtsmodell (DE-588)4125214-7 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 s Gleichgewichtsmodell (DE-588)4125214-7 s Finanzmathematik (DE-588)4017195-4 s DE-604 Bermúdez, Ana (DE-588)1321560451 aut Bühler, Hans (DE-588)1053071949 aut Ferraris, Andrew aut Jordinson, Christopher aut Lamnouar, Aziz aut Erscheint auch als Online-Ausgabe 978-1-119-20181-6 http://www.loc.gov/catdir/toc/ecip068/2006005369.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0714/2006005369-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0740/2006005369-b.html Contributor biographical information HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016585671&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Overhaus, Marcus 1971- Bermúdez, Ana Bühler, Hans Ferraris, Andrew Jordinson, Christopher Lamnouar, Aziz Equity hybrid derivatives Derivative securities Convertible securities Finanzmathematik (DE-588)4017195-4 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Gleichgewichtsmodell (DE-588)4125214-7 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4381572-8 (DE-588)4125214-7 |
| title | Equity hybrid derivatives |
| title_auth | Equity hybrid derivatives |
| title_exact_search | Equity hybrid derivatives |
| title_exact_search_txtP | Equity hybrid derivatives |
| title_full | Equity hybrid derivatives Marcus Overhaus ; Ana Bermúdez ; Hans Bühler ; Andrew Ferraris ; Christopher Jordinson ; Aziz Jordinson |
| title_fullStr | Equity hybrid derivatives Marcus Overhaus ; Ana Bermúdez ; Hans Bühler ; Andrew Ferraris ; Christopher Jordinson ; Aziz Jordinson |
| title_full_unstemmed | Equity hybrid derivatives Marcus Overhaus ; Ana Bermúdez ; Hans Bühler ; Andrew Ferraris ; Christopher Jordinson ; Aziz Jordinson |
| title_short | Equity hybrid derivatives |
| title_sort | equity hybrid derivatives |
| topic | Derivative securities Convertible securities Finanzmathematik (DE-588)4017195-4 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Gleichgewichtsmodell (DE-588)4125214-7 gnd |
| topic_facet | Derivative securities Convertible securities Finanzmathematik Derivat Wertpapier Gleichgewichtsmodell |
| url | http://www.loc.gov/catdir/toc/ecip068/2006005369.html http://www.loc.gov/catdir/enhancements/fy0714/2006005369-d.html http://www.loc.gov/catdir/enhancements/fy0740/2006005369-b.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016585671&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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