Multiscale stochastic volatility for equity, interest rate, and credit derivatives:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | Undetermined |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 441 S. graph. Darst. |
| ISBN: | 0521843588 9780521843584 |
Internformat
MARC
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| 245 | 1 | 0 | |a Multiscale stochastic volatility for equity, interest rate, and credit derivatives |c Jean-Pierre Fouque ... |
| 250 | |a 1. publ. | ||
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| 300 | |a XIII, 441 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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| adam_text |
Titel: Multiscale stochastic volatility for equity, interest rate, and credit derivatives
Autor: Fouque, Jean-Pierre
Jahr: 2011
Contents
Introduction page xi
The Black-Scholes Theory of Derivative Pricing 1
1.1 Market Model 1
1.2 Derivative Contracts 10
1.3 Replicating Strategies 13
1.4 Risk-Neutral Pricing 21
1.5 Risk-Neutral Expectations and Partial Differential
Equations 27
1.6 American Options and Free Boundary Problems 32
1.7 Path-Dependent Derivatives 36
1.8 First-Passage Structural Approach to Default 43
1.9 Multidimensional Stochastic Calculus 46
1.10 Complete Market 49
Introduction to Stochastic Volatility Models 51
2.1 Implied Volatility Surface 52
2.2 Local Volatility 57
2.3 Stochastic Volatility Models 62
2.4 Derivative Pricing 65
2.5 General Results on Stochastic Volatility Models 74
2.6 Summary and Conclusions 83
Volatility Time Scales 86
3.1 A Simple Picture of Fast and Slow
Time Scales 86
3.2 Ergodicity and Mean-Reversion 88
3.3 Examples of Mean-Reverting Processes 95
3.4 Time Scales in Synthetic Returns Data 110
3.5 Time Scales in Market Data 114
3.6 Multiscale Models 118
4 First-Order Perturbation Theory 121
4.1 Option Pricing under Multiscale Stochastic Volatility 121
4.2 Formal Regular and Singular Perturbation Analysis 125
4.3 Parameter Reduction 135
4.4 First-Order Approximation: Summary and Discussion 137
4.5 Accuracy of First-Order Approximation 138
5 Implied Volatility Formulas and Calibration 148
5.1 Approximate Call Prices and Implied Volatilities 149
5.2 Calibration Procedure 154
5.3 Illustration with S P 500 Data 155
5.4 Maturity Cycles 163
5.5 Higher-Order Corrections 174
6 Application to Exotic Derivatives 179
6.1 European Binary Options 179
6.2 B arrier Options 181
6.3 Asian Options 185
7 Application to American Derivatives 189
7.1 American Options Valuation under Stochastic
Volatility 189
7.2 Stochastic Volatility Correction for American Put 190
7.3 Parameter Reduction 196
7.4 Summary 197
8 Hedging Strategies 199
8.1 Black-Scholes Delta Hedging 200
8.2 The Strategy and its Cost 200
8.3 Mean Self-Financing Hedging Strategy 206
8.4 A Strategy with Frozen Parameters 209
8.5 Strategies Based on Implied Volatilities 217
8.6 Martingale Approach to Pricing 220
8.7 Non-Markovian Models of Volatility 226
9 Extensions 232
9.1 Dividends and Varying Interest Rates 232
9.2 Probabilistic Representation of the Approximate Prices 237
9.3 Second-Order Correction from Fast Scale 238
9.4 Second-Order Corrections from Slow and Fast Scales 247
9.5 Periodic Day Effect 249
9.6 Markovian Jump Volatility Models 251
9.7 Multidimensional Models 254
10 Around the Heston Model 259
10.1 The Heston Model 260
10.2 Approximations to the Heston Model 265
10.3 A Fast Mean-Reverting Correction to the Heston Model 271
10.4 Large Deviations and Short Maturity Asymptotics 276
11 Other Applications 283
11.1 Application to Variance Reduction in Monte Carlo
Computations 283
11.2 Portfolio Optimization under Stochastic Volatility 287
11.3 Application to CAPM Forward-Looking Beta Estimation 296
12 Interest Rate Models 307
12.1 The Vasicek Model 307
12.2 The Bond Price and its Expansion 315
12.3 The Quadratic Model 327
12.4 The CIR Model 330
12.5 Options on Bonds 335
13 Credit Risk I: Structural Models with Stochastic Volatility 342
13.1 Single-Name Credit Derivatives 342
13.2 Multiname Credit Derivatives 353
14 Credit Risk II: Multiscale Intensity-Based Models 377
14.1 Background on Stochastic Intensity Models 377
14.2 Multiname Credit Derivatives 385
14.3 Symmetric Vasicek Model 388
14.4 Homogeneous Group Structure 402
15 Epilogue 424
References 430
Index 439 |
| adam_txt |
Titel: Multiscale stochastic volatility for equity, interest rate, and credit derivatives
Autor: Fouque, Jean-Pierre
Jahr: 2011
Contents
Introduction page xi
The Black-Scholes Theory of Derivative Pricing 1
1.1 Market Model 1
1.2 Derivative Contracts 10
1.3 Replicating Strategies 13
1.4 Risk-Neutral Pricing 21
1.5 Risk-Neutral Expectations and Partial Differential
Equations 27
1.6 American Options and Free Boundary Problems 32
1.7 Path-Dependent Derivatives 36
1.8 First-Passage Structural Approach to Default 43
1.9 Multidimensional Stochastic Calculus 46
1.10 Complete Market 49
Introduction to Stochastic Volatility Models 51
2.1 Implied Volatility Surface 52
2.2 Local Volatility 57
2.3 Stochastic Volatility Models 62
2.4 Derivative Pricing 65
2.5 General Results on Stochastic Volatility Models 74
2.6 Summary and Conclusions 83
Volatility Time Scales 86
3.1 A Simple Picture of Fast and Slow
Time Scales 86
3.2 Ergodicity and Mean-Reversion 88
3.3 Examples of Mean-Reverting Processes 95
3.4 Time Scales in Synthetic Returns Data 110
3.5 Time Scales in Market Data 114
3.6 Multiscale Models 118
4 First-Order Perturbation Theory 121
4.1 Option Pricing under Multiscale Stochastic Volatility 121
4.2 Formal Regular and Singular Perturbation Analysis 125
4.3 Parameter Reduction 135
4.4 First-Order Approximation: Summary and Discussion 137
4.5 Accuracy of First-Order Approximation 138
5 Implied Volatility Formulas and Calibration 148
5.1 Approximate Call Prices and Implied Volatilities 149
5.2 Calibration Procedure 154
5.3 Illustration with S P 500 Data 155
5.4 Maturity Cycles 163
5.5 Higher-Order Corrections 174
6 Application to Exotic Derivatives 179
6.1 European Binary Options 179
6.2 B arrier Options 181
6.3 Asian Options 185
7 Application to American Derivatives 189
7.1 American Options Valuation under Stochastic
Volatility 189
7.2 Stochastic Volatility Correction for American Put 190
7.3 Parameter Reduction 196
7.4 Summary 197
8 Hedging Strategies 199
8.1 Black-Scholes Delta Hedging 200
8.2 The Strategy and its Cost 200
8.3 Mean Self-Financing Hedging Strategy 206
8.4 A Strategy with Frozen Parameters 209
8.5 Strategies Based on Implied Volatilities 217
8.6 Martingale Approach to Pricing 220
8.7 Non-Markovian Models of Volatility 226
9 Extensions 232
9.1 Dividends and Varying Interest Rates 232
9.2 Probabilistic Representation of the Approximate Prices 237
9.3 Second-Order Correction from Fast Scale 238
9.4 Second-Order Corrections from Slow and Fast Scales 247
9.5 Periodic Day Effect 249
9.6 Markovian Jump Volatility Models 251
9.7 Multidimensional Models 254
10 Around the Heston Model 259
10.1 The Heston Model 260
10.2 Approximations to the Heston Model 265
10.3 A Fast Mean-Reverting Correction to the Heston Model 271
10.4 Large Deviations and Short Maturity Asymptotics 276
11 Other Applications 283
11.1 Application to Variance Reduction in Monte Carlo
Computations 283
11.2 Portfolio Optimization under Stochastic Volatility 287
11.3 Application to CAPM Forward-Looking Beta Estimation 296
12 Interest Rate Models 307
12.1 The Vasicek Model 307
12.2 The Bond Price and its Expansion 315
12.3 The Quadratic Model 327
12.4 The CIR Model 330
12.5 Options on Bonds 335
13 Credit Risk I: Structural Models with Stochastic Volatility 342
13.1 Single-Name Credit Derivatives 342
13.2 Multiname Credit Derivatives 353
14 Credit Risk II: Multiscale Intensity-Based Models 377
14.1 Background on Stochastic Intensity Models 377
14.2 Multiname Credit Derivatives 385
14.3 Symmetric Vasicek Model 388
14.4 Homogeneous Group Structure 402
15 Epilogue 424
References 430
Index 439 |
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| spelling | Multiscale stochastic volatility for equity, interest rate, and credit derivatives Jean-Pierre Fouque ... 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2011 XIII, 441 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mehrskalenmodell (DE-588)7600619-0 gnd rswk-swf Volatilität (DE-588)4268390-7 gnd rswk-swf Kreditderivat (DE-588)7660453-6 gnd rswk-swf Mehrskalenmodell (DE-588)7600619-0 s Volatilität (DE-588)4268390-7 s Kreditderivat (DE-588)7660453-6 s DE-604 Fouque, Jean-Pierre 1934- Sonstige (DE-588)134219457 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014278908&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Multiscale stochastic volatility for equity, interest rate, and credit derivatives Mehrskalenmodell (DE-588)7600619-0 gnd Volatilität (DE-588)4268390-7 gnd Kreditderivat (DE-588)7660453-6 gnd |
| subject_GND | (DE-588)7600619-0 (DE-588)4268390-7 (DE-588)7660453-6 |
| title | Multiscale stochastic volatility for equity, interest rate, and credit derivatives |
| title_auth | Multiscale stochastic volatility for equity, interest rate, and credit derivatives |
| title_exact_search | Multiscale stochastic volatility for equity, interest rate, and credit derivatives |
| title_exact_search_txtP | Multiscale stochastic volatility for equity, interest rate, and credit derivatives |
| title_full | Multiscale stochastic volatility for equity, interest rate, and credit derivatives Jean-Pierre Fouque ... |
| title_fullStr | Multiscale stochastic volatility for equity, interest rate, and credit derivatives Jean-Pierre Fouque ... |
| title_full_unstemmed | Multiscale stochastic volatility for equity, interest rate, and credit derivatives Jean-Pierre Fouque ... |
| title_short | Multiscale stochastic volatility for equity, interest rate, and credit derivatives |
| title_sort | multiscale stochastic volatility for equity interest rate and credit derivatives |
| topic | Mehrskalenmodell (DE-588)7600619-0 gnd Volatilität (DE-588)4268390-7 gnd Kreditderivat (DE-588)7660453-6 gnd |
| topic_facet | Mehrskalenmodell Volatilität Kreditderivat |
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