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The new and updated material includes a critical examination of the 'perfect-replication' approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options.
The book is split into four parts. Part I deals with a Black world without smiles, sets out the author's 'philosophical' approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface.
Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes.
Praise for the First Edition:
"In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed."
--Professor Ian Cooper, London Business School
"Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense."
--Anthony Neuberger, London Business School
The new and updated material includes a critical examination of the 'perfect-replication' approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options.
The book is split into four parts. Part I deals with a Black world without smiles, sets out the author's 'philosophical' approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface.
Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes.
Praise for the First Edition:
"In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed."
--Professor Ian Cooper, London Business School
"Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense."
--Anthony Neuberger, London Business School
Prior to joining the Royal Bank of Scotland, he was Head of Complex Derivatives Trading Europe and Head of Derivatives Research at Barclays Capital (BZW), where he worked for nine years.
Before that he was a Research Fellow in Physics at Corpus Christi College, Oxford, UK. He is the author of three books, Modern Pricing of Interest-Rate Derivatives, Volatility and Correlation in Option Pricing and Interest-Rate Option Models. He has published several papers on finance in academic journals, and is on the editorial board of several journals. He is a regular speaker at conferences worldwide.
Preface xxi
0.1 Why a Second Edition? xxi
0.2 What This Book Is Not About xxiii
0.3 Structure of the Book xxiv
0.4 The New Subtitle xxiv
Acknowledgements xxvii
I Foundations 1
1 Theory and Practice of Option Modelling 3
1.1 The Role of Models in Derivatives Pricing 3
1.2 The Efficient Market Hypothesis and Why It Matters for Option Pricing 9
1.3 Market Practice 14
1.4 The Calibration Debate 17
1.5 Across-Markets Comparison of Pricing and Modelling Practices 27
1.6 Using Models 30
2 Option Replication 31
2.1 The Bedrock of Option Pricing 31
2.2 The Analytic (PDE) Approach 32
2.3 Binomial Replication 38
2.4 Justifying the Two-State Branching Procedure 65
2.5 The Nature of the Transformation between Measures: Girsanov's Theorem 69
2.6 Switching Between the PDE, the Expectation and the Binomial Replication Approaches 73
3 The Building Blocks 75
3.1 Introduction and Plan of the Chapter 75
3.2 Definition of Market Terms 75
3.3 Hedging Forward Contracts Using Spot Quantities 77
3.4 Hedging Options: Volatility of Spot and Forward Processes 80
3.5 The Link Between Root-Mean-Squared Volatilities and the Time-Dependence of Volatility 84
3.6 Admissibility of a Series of Root-Mean-Squared Volatilities 85
3.7 Summary of the Definitions So Far 87
3.8 Hedging an Option with a Forward-Setting Strike 89
3.9 Quadratic Variation: First Approach 95
4 Variance and Mean Reversion in the Real and the Risk-Adjusted Worlds 101
4.1 Introduction and Plan of the Chapter 101
4.2 Hedging a Plain-Vanilla Option: General Framework 102
4.3 Hedging Plain-Vanilla Options: Constant Volatility 106
4.4 Hedging Plain-Vanilla Options: Time-Dependent Volatility 116
4.5 Hedging Behaviour In Practice 121
4.6 Robustness of the Black-and-Scholes Model 127
4.7 Is the Total Variance All That Matters? 130
4.8 Hedging Plain-Vanilla Options: Mean-Reverting Real-World Drift 131
4.9 Hedging Plain-Vanilla Options: Finite Re-Hedging Intervals Again 135
5 Instantaneous and Terminal Correlation 141
5.1 Correlation, Co-Integration and Multi-Factor Models 141
5.2 The Stochastic Evolution of Imperfectly Correlated Variables 146
5.3 The Role of Terminal Correlation in the Joint Evolution of Stochastic Variables 151
5.4 Generalizing the Results 162
5.5 Moving Ahead 164
II Smiles - Equity and FX 165
6 Pricing Options in the Presence of Smiles 167
6.1 Plan of the Chapter 167
6.2 Background and Definition of the Smile 168
6.3 Hedging with a Compensated Process: Plain-Vanilla and Binary Options 169
6.4 Hedge Ratios for Plain-Vanilla Options in the Presence of Smiles 173
6.5 Smile Tale 1: 'Sticky' Smiles 180
6.6 Smile Tale 2: 'Floating' Smiles 182
6.7 When Does Risk Aversion Make a Difference? 184
7 Empirical Facts About Smiles 201
7.1 What is this Chapter About? 201
7.2 Market Information About Smiles 203
7.3 Equities 206
7.4 Interest Rates 222
7.5 FX Rates 227
7.6 Conclusions 235
8 General Features of Smile-Modelling Approaches 237
8.1 Fully-Stochastic-Volatility Models 237
8.2 Local-Volatility (Restricted-Stochastic-Volatility) Models 239
8.3 Jump-Diffusion Models 241
8.4 Variance-Gamma Models 243
8.5 Mixing Processes 243
8.6 Other Approaches 245
8.7 The Importance of the Quadratic Variation (Take 2) 246
9 The Input Data: Fitting an Exogenous Smile Surface 249
9.1 What is This Chapter About? 249
9.2 Analytic Expressions for Calls vs Process Specification 249
9.3 Direct Use of Market Prices: Pros and Cons 250
9.4 Statement of the Problem 251
9.5 Fitting Prices 252
9.6 Fitting Transformed Prices 254
9.7 Fitting the Implied Volatilities 255
9.8 Fitting the Risk-Neutral Density Function - General 256
9.9 Fitting the Risk-Neutral Density Function: Mixture of Normals 259
9.10 Numerical Results 265
9.11 Is the Term ¿C/¿S Really a Delta? 275
9.12 Fitting the Risk-Neutral Density Function: The Generalized-Beta Approach 277
10 Quadratic Variation and Smiles 293
10.1 Why This Approach Is Interesting 293
10.2 The BJN Framework for Bounding Option Prices 293
10.3 The BJN Approach - Theoretical Development 294
10.4 The BJN Approach: Numerical Implementation 300
10.5 Discussion of the Results 312
10.6 Conclusions (or, Limitations of Quadratic Variation) 316
11 Local-Volatility Models: the Derman-and-Kani Approach 319
11.1 General Considerations on Stochastic-Volatility Models 319
11.2 Special Cases of Restricted-Stochastic-Volatility Models 321
11.3 The Dupire, Rubinstein and Derman-and-Kani Approaches 321
11.4 Green's Functions (Arrow-Debreu Prices) in the DK Construction 322
11.5 The Derman-and-Kani Tree Construction 326
11.6 Numerical Aspects of the Implementation of the DK Construction 331
11.7 Implementation Results 334
11.8 Estimating Instantaneous Volatilities from Prices as an Inverse Problem 343
12 Extracting the Local Volatility from Option Prices 345
12.1 Introduction 345
12.2 The Modelling Framework 347
12.3 A Computational Method 349
12.4 Computational Results 355
12.5 The Link Between Implied and Local-Volatility Surfaces 357
12.6 Gaining an Intuitive Understanding 368
12.7 What Local-Volatility Models Imply about Sticky and Floating Smiles 373
12.8 No-Arbitrage Conditions on the Current Implied Volatility Smile Surface 375
12.9 Empirical Performance 385
12.10 Appendix I: Proof that ¿2Call(St, K, T, t)/¿k2 = ¿(ST)|K 386
13 Stochastic-Volatility Processes 389
13.1 Plan of the Chapter 389
13.2 Portfolio Replication in the Presence of Stochastic Volatility 389
13.3 Mean-Reverting Stochastic Volatility 401
13.4 Qualitative Features of Stochastic-Volatility Smiles 405
13.5 The Relation Between Future Smiles and Future Stock Price Levels 416
13.6 Portfolio Replication in Practice: The Stochastic-Volatility Case 418
13.7 Actual Fitting to Market Data 427
13.8 Conclusions 436
14 Jump-Diffusion Processes 439
14.1 Introduction 439
14.2 The Financial Model: Smile Tale 2 Revisited 441
14.3 Hedging and Replicability in the Presence of Jumps: First Considerations 444
14.4 Analytic Description of Jump-Diffusions 449
14.5 Hedging with Jump-Diffusion Processes 455
14.6 The Pricing Formula for Log-Normal Amplitude Ratios 470
14.7 The Pricing Formula in the Finite-Amplitude-Ratio Case 472
14.8 The Link Between the Price Density and the Smile Shape 485
14.9 Qualitative Features of Jump-Diffusion Smiles 494
14.10 Jump-Diffusion Processes and Market Completeness Revisited 500
14.11 Portfolio Replication in Practice: The Jump-Diffusion Case 502
15 Variance-Gamma 511
15.1 Who Can Make Best Use of the Variance-Gamma Approach? 511
15.2 The Variance-Gamma Process 513
15.3 Statistical Properties of the Price Distribution 522
15.4 Features of the Smile 523
15.5 Conclusions 527
16 Displaced Diffusions and Generalizations 529
16.1 Introduction 529
16.2 Gaining Intuition 530
16.3 Evolving the Underlying with Displaced Diffusions 531
16.4 Option Prices with Displaced Diffusions 532
16.5 Matching At-The-Money Prices with Displaced Diffusions 533
16.6 The Smile Produced by Displaced Diffusions 553
16.7 Extension to Other Processes 560
17 No-Arbitrage Restrictions on the Dynamics of Smile Surfaces 563
17.1 A Worked-Out Example: Pricing Continuous Double Barriers 564
17.2 Analysis of the Cost of Unwinding 571
17.3 The Trader's Dream 575
17.4 Plan of the Remainder of the Chapter 581
17.5 Conditions of No-Arbitrage for the Stochastic Evolution of Future Smile Surfaces 582
17.6 Deterministic Smile Surfaces 585
17.7 Stochastic Smiles 593
17.8 The Strength of the Assumptions 597
17.9 Limitations and Conclusions 598
III Interest Rates - Deterministic Volatilities 601
18 Mean Reversion in Interest-Rate Models 603
18.1 Introduction and Plan of the Chapter 603
18.2 Why Mean Reversion Matters in the Case of Interest-Rate Models 604
18.3 A Common Fallacy Regarding Mean Reversion 608
18.4 The BDT Mean-Reversion Paradox 610
18.5 The Unconditional Variance of the Short Rate in BDT - the Discrete Case 612
18.6 The Unconditional Variance of the Short Rate in BDT-the Continuous-Time Equivalent 616
18.7 Mean Reversion in Short-Rate Lattices: Recombining vs Bushy Trees 617
18.8 Extension to More General Interest-Rate Models 620
18.9 Appendix I: Evaluation of the Variance of the Logarithm of the Instantaneous Short Rate 622
19 Volatility and Correlation in the LIBOR Market Model 625
19.1 Introduction 625
19.2 Specifying the Forward-Rate Dynamics in the LIBOR Market Model 626
19.3 Link with the Principal Component Analysis 631
19.4 Worked-Out Example 1: Caplets and a Two-Period Swaption 632
19.5 Worked-Out Example 2: Serial Options 635
19.6 Plan of the Work Ahead 636
20 Calibration Strategies for the LIBOR Market...
| Erscheinungsjahr: | 2004 |
|---|---|
| Fachbereich: | Betriebswirtschaft |
| Genre: | Importe, Wirtschaft |
| Rubrik: | Recht & Wirtschaft |
| Medium: | Buch |
| Inhalt: | 864 S. |
| ISBN-13: | 9780470091395 |
| ISBN-10: | 0470091398 |
| Sprache: | Englisch |
| Herstellernummer: | 14509139000 |
| Einband: | Gebunden |
| Autor: | Rebonato, Riccardo |
| Auflage: | 2nd edition |
| Hersteller: |
Wiley
John Wiley & Sons |
| Verantwortliche Person für die EU: | Wiley-VCH GmbH, Boschstr. 12, D-69469 Weinheim, product-safety@wiley.com |
| Maße: | 250 x 175 x 50 mm |
| Von/Mit: | Riccardo Rebonato |
| Erscheinungsdatum: | 01.09.2004 |
| Gewicht: | 1,645 kg |
Prior to joining the Royal Bank of Scotland, he was Head of Complex Derivatives Trading Europe and Head of Derivatives Research at Barclays Capital (BZW), where he worked for nine years.
Before that he was a Research Fellow in Physics at Corpus Christi College, Oxford, UK. He is the author of three books, Modern Pricing of Interest-Rate Derivatives, Volatility and Correlation in Option Pricing and Interest-Rate Option Models. He has published several papers on finance in academic journals, and is on the editorial board of several journals. He is a regular speaker at conferences worldwide.
Preface xxi
0.1 Why a Second Edition? xxi
0.2 What This Book Is Not About xxiii
0.3 Structure of the Book xxiv
0.4 The New Subtitle xxiv
Acknowledgements xxvii
I Foundations 1
1 Theory and Practice of Option Modelling 3
1.1 The Role of Models in Derivatives Pricing 3
1.2 The Efficient Market Hypothesis and Why It Matters for Option Pricing 9
1.3 Market Practice 14
1.4 The Calibration Debate 17
1.5 Across-Markets Comparison of Pricing and Modelling Practices 27
1.6 Using Models 30
2 Option Replication 31
2.1 The Bedrock of Option Pricing 31
2.2 The Analytic (PDE) Approach 32
2.3 Binomial Replication 38
2.4 Justifying the Two-State Branching Procedure 65
2.5 The Nature of the Transformation between Measures: Girsanov's Theorem 69
2.6 Switching Between the PDE, the Expectation and the Binomial Replication Approaches 73
3 The Building Blocks 75
3.1 Introduction and Plan of the Chapter 75
3.2 Definition of Market Terms 75
3.3 Hedging Forward Contracts Using Spot Quantities 77
3.4 Hedging Options: Volatility of Spot and Forward Processes 80
3.5 The Link Between Root-Mean-Squared Volatilities and the Time-Dependence of Volatility 84
3.6 Admissibility of a Series of Root-Mean-Squared Volatilities 85
3.7 Summary of the Definitions So Far 87
3.8 Hedging an Option with a Forward-Setting Strike 89
3.9 Quadratic Variation: First Approach 95
4 Variance and Mean Reversion in the Real and the Risk-Adjusted Worlds 101
4.1 Introduction and Plan of the Chapter 101
4.2 Hedging a Plain-Vanilla Option: General Framework 102
4.3 Hedging Plain-Vanilla Options: Constant Volatility 106
4.4 Hedging Plain-Vanilla Options: Time-Dependent Volatility 116
4.5 Hedging Behaviour In Practice 121
4.6 Robustness of the Black-and-Scholes Model 127
4.7 Is the Total Variance All That Matters? 130
4.8 Hedging Plain-Vanilla Options: Mean-Reverting Real-World Drift 131
4.9 Hedging Plain-Vanilla Options: Finite Re-Hedging Intervals Again 135
5 Instantaneous and Terminal Correlation 141
5.1 Correlation, Co-Integration and Multi-Factor Models 141
5.2 The Stochastic Evolution of Imperfectly Correlated Variables 146
5.3 The Role of Terminal Correlation in the Joint Evolution of Stochastic Variables 151
5.4 Generalizing the Results 162
5.5 Moving Ahead 164
II Smiles - Equity and FX 165
6 Pricing Options in the Presence of Smiles 167
6.1 Plan of the Chapter 167
6.2 Background and Definition of the Smile 168
6.3 Hedging with a Compensated Process: Plain-Vanilla and Binary Options 169
6.4 Hedge Ratios for Plain-Vanilla Options in the Presence of Smiles 173
6.5 Smile Tale 1: 'Sticky' Smiles 180
6.6 Smile Tale 2: 'Floating' Smiles 182
6.7 When Does Risk Aversion Make a Difference? 184
7 Empirical Facts About Smiles 201
7.1 What is this Chapter About? 201
7.2 Market Information About Smiles 203
7.3 Equities 206
7.4 Interest Rates 222
7.5 FX Rates 227
7.6 Conclusions 235
8 General Features of Smile-Modelling Approaches 237
8.1 Fully-Stochastic-Volatility Models 237
8.2 Local-Volatility (Restricted-Stochastic-Volatility) Models 239
8.3 Jump-Diffusion Models 241
8.4 Variance-Gamma Models 243
8.5 Mixing Processes 243
8.6 Other Approaches 245
8.7 The Importance of the Quadratic Variation (Take 2) 246
9 The Input Data: Fitting an Exogenous Smile Surface 249
9.1 What is This Chapter About? 249
9.2 Analytic Expressions for Calls vs Process Specification 249
9.3 Direct Use of Market Prices: Pros and Cons 250
9.4 Statement of the Problem 251
9.5 Fitting Prices 252
9.6 Fitting Transformed Prices 254
9.7 Fitting the Implied Volatilities 255
9.8 Fitting the Risk-Neutral Density Function - General 256
9.9 Fitting the Risk-Neutral Density Function: Mixture of Normals 259
9.10 Numerical Results 265
9.11 Is the Term ¿C/¿S Really a Delta? 275
9.12 Fitting the Risk-Neutral Density Function: The Generalized-Beta Approach 277
10 Quadratic Variation and Smiles 293
10.1 Why This Approach Is Interesting 293
10.2 The BJN Framework for Bounding Option Prices 293
10.3 The BJN Approach - Theoretical Development 294
10.4 The BJN Approach: Numerical Implementation 300
10.5 Discussion of the Results 312
10.6 Conclusions (or, Limitations of Quadratic Variation) 316
11 Local-Volatility Models: the Derman-and-Kani Approach 319
11.1 General Considerations on Stochastic-Volatility Models 319
11.2 Special Cases of Restricted-Stochastic-Volatility Models 321
11.3 The Dupire, Rubinstein and Derman-and-Kani Approaches 321
11.4 Green's Functions (Arrow-Debreu Prices) in the DK Construction 322
11.5 The Derman-and-Kani Tree Construction 326
11.6 Numerical Aspects of the Implementation of the DK Construction 331
11.7 Implementation Results 334
11.8 Estimating Instantaneous Volatilities from Prices as an Inverse Problem 343
12 Extracting the Local Volatility from Option Prices 345
12.1 Introduction 345
12.2 The Modelling Framework 347
12.3 A Computational Method 349
12.4 Computational Results 355
12.5 The Link Between Implied and Local-Volatility Surfaces 357
12.6 Gaining an Intuitive Understanding 368
12.7 What Local-Volatility Models Imply about Sticky and Floating Smiles 373
12.8 No-Arbitrage Conditions on the Current Implied Volatility Smile Surface 375
12.9 Empirical Performance 385
12.10 Appendix I: Proof that ¿2Call(St, K, T, t)/¿k2 = ¿(ST)|K 386
13 Stochastic-Volatility Processes 389
13.1 Plan of the Chapter 389
13.2 Portfolio Replication in the Presence of Stochastic Volatility 389
13.3 Mean-Reverting Stochastic Volatility 401
13.4 Qualitative Features of Stochastic-Volatility Smiles 405
13.5 The Relation Between Future Smiles and Future Stock Price Levels 416
13.6 Portfolio Replication in Practice: The Stochastic-Volatility Case 418
13.7 Actual Fitting to Market Data 427
13.8 Conclusions 436
14 Jump-Diffusion Processes 439
14.1 Introduction 439
14.2 The Financial Model: Smile Tale 2 Revisited 441
14.3 Hedging and Replicability in the Presence of Jumps: First Considerations 444
14.4 Analytic Description of Jump-Diffusions 449
14.5 Hedging with Jump-Diffusion Processes 455
14.6 The Pricing Formula for Log-Normal Amplitude Ratios 470
14.7 The Pricing Formula in the Finite-Amplitude-Ratio Case 472
14.8 The Link Between the Price Density and the Smile Shape 485
14.9 Qualitative Features of Jump-Diffusion Smiles 494
14.10 Jump-Diffusion Processes and Market Completeness Revisited 500
14.11 Portfolio Replication in Practice: The Jump-Diffusion Case 502
15 Variance-Gamma 511
15.1 Who Can Make Best Use of the Variance-Gamma Approach? 511
15.2 The Variance-Gamma Process 513
15.3 Statistical Properties of the Price Distribution 522
15.4 Features of the Smile 523
15.5 Conclusions 527
16 Displaced Diffusions and Generalizations 529
16.1 Introduction 529
16.2 Gaining Intuition 530
16.3 Evolving the Underlying with Displaced Diffusions 531
16.4 Option Prices with Displaced Diffusions 532
16.5 Matching At-The-Money Prices with Displaced Diffusions 533
16.6 The Smile Produced by Displaced Diffusions 553
16.7 Extension to Other Processes 560
17 No-Arbitrage Restrictions on the Dynamics of Smile Surfaces 563
17.1 A Worked-Out Example: Pricing Continuous Double Barriers 564
17.2 Analysis of the Cost of Unwinding 571
17.3 The Trader's Dream 575
17.4 Plan of the Remainder of the Chapter 581
17.5 Conditions of No-Arbitrage for the Stochastic Evolution of Future Smile Surfaces 582
17.6 Deterministic Smile Surfaces 585
17.7 Stochastic Smiles 593
17.8 The Strength of the Assumptions 597
17.9 Limitations and Conclusions 598
III Interest Rates - Deterministic Volatilities 601
18 Mean Reversion in Interest-Rate Models 603
18.1 Introduction and Plan of the Chapter 603
18.2 Why Mean Reversion Matters in the Case of Interest-Rate Models 604
18.3 A Common Fallacy Regarding Mean Reversion 608
18.4 The BDT Mean-Reversion Paradox 610
18.5 The Unconditional Variance of the Short Rate in BDT - the Discrete Case 612
18.6 The Unconditional Variance of the Short Rate in BDT-the Continuous-Time Equivalent 616
18.7 Mean Reversion in Short-Rate Lattices: Recombining vs Bushy Trees 617
18.8 Extension to More General Interest-Rate Models 620
18.9 Appendix I: Evaluation of the Variance of the Logarithm of the Instantaneous Short Rate 622
19 Volatility and Correlation in the LIBOR Market Model 625
19.1 Introduction 625
19.2 Specifying the Forward-Rate Dynamics in the LIBOR Market Model 626
19.3 Link with the Principal Component Analysis 631
19.4 Worked-Out Example 1: Caplets and a Two-Period Swaption 632
19.5 Worked-Out Example 2: Serial Options 635
19.6 Plan of the Work Ahead 636
20 Calibration Strategies for the LIBOR Market...
| Erscheinungsjahr: | 2004 |
|---|---|
| Fachbereich: | Betriebswirtschaft |
| Genre: | Importe, Wirtschaft |
| Rubrik: | Recht & Wirtschaft |
| Medium: | Buch |
| Inhalt: | 864 S. |
| ISBN-13: | 9780470091395 |
| ISBN-10: | 0470091398 |
| Sprache: | Englisch |
| Herstellernummer: | 14509139000 |
| Einband: | Gebunden |
| Autor: | Rebonato, Riccardo |
| Auflage: | 2nd edition |
| Hersteller: |
Wiley
John Wiley & Sons |
| Verantwortliche Person für die EU: | Wiley-VCH GmbH, Boschstr. 12, D-69469 Weinheim, product-safety@wiley.com |
| Maße: | 250 x 175 x 50 mm |
| Von/Mit: | Riccardo Rebonato |
| Erscheinungsdatum: | 01.09.2004 |
| Gewicht: | 1,645 kg |
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