Interest Rate Modeling: Post-Crisis challenges and approaches
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham
Springer
[2015]
|
| Series: | Springer Briefs in Quantitative Finance
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 140 Seiten Illustrationen |
| ISBN: | 9783319253831 |
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MARC
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Record in the Search Index
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| adam_text | Contents
1 Post-Crisis Fixed-Income Markets......................................... 1
1.1 Types of Interest Rates and Market Conventions..................... 5
1.1.1 Basic Interest Rates: Libor/Euribor, Eonia/FF
and OIS Rates. .............................................. 5
1.2 Implications of the Crisis . ........ *.......................... 8
1.2.1 Spreads and Their Interpretation: Credit
and Liquidity Risk....................................... 8
1.2.2 From Unsecured to Secured Transactions...................... 11
1.2.3 Clean Prices Versus Global Prices........................... 12
1.3 The New Paradigm: Multiple Curves at All Levels.................. 13
1.3.1 Choice of the Discount Curve. .............................. 16
1.3.2 Standard Martingale Measure and Forward
Measures Related to OIS Bonds.......................... 17
1.4 Interest Rate Derivatives.......................................... 18
1.4.1 Forward Rate Agreements..................................... 18
1.4.2 Fixed and Floating Rate Bonds............................... 21
1.43 Interest Rate Swaps......................................... 22
1.4.4 Overnight Indexed Swaps (OIS)............................... 23
1.4.5 Basis Swaps................................................. 27
1.4.6 Caps and Floors............................................. 29
1.4.7 Swaptions................................................... 30
2 Short-Rate and Rational Pricing Kernel Models
for Multiple Curves............................................... 35
2.1 Exponentially Affine Factor Models............................... 37
2.LI The Factor Model and Properties............................. 37
2.1.2 Technical Preliminaries................ .................. 39
2.1.3 Explicit Representation of the Libor Rate .................. 45
2.2 Gaussian. Exponentially Quadratic Models................... 48
XI
çji Contents
2.3 Pricing of FRAs and Other Linear Derivatives................. 49
2.3.1 Computation of FRA Prices and FRA Rates................ 50
2.3.2 Adjustment Factors for FRAs............................ 51
2.3.2.1 Comments on Calibration to the Initial
Term Structure................................ 55
2.4 Pricing of Caps and Floors................................... 55
2.5 Pricing of Swaptions........................................... 61
2.6 Relationship with Models from the Literature................. 69
2.6.1 The Models of Kenyon (2010)
and Kijima et al. (2009)................................ 69
2.6.2 The Model of Filipovič and Trolle (2013)............. . 69
2.7 Multiple Curve Rational Pricing Kernel Models................ 72
3 Multiple Curve Heath-Jarrow-Morton (HJM) Framework................. 77
3.1 Adapting the Classical HJM Approach ......................... 80
3.2 Hybrid HJM-LMM Models...................................... 82
3.2.1 HJM-LMM Model for the Forward Rates................. 82
3.2.1.1 Model and No-Arbitrage Conditions............... 82
3.2.1.2 Markovianity and Induced Short Rates
(Vasicek-Type Volatility Structure)............. 84
3.2.2 HJM-LMM Model for the Fictitious Bond Prices............. 87
3.2.2.1 Model and No-Arbitrage Condition
for the pA (tj T)-Bonds......................... 88
3.2.2.2 Markovianity and Induced Short Rates
(Vasiček-Type Volatility Structure)............. 89
3.3 Foreign Exchange and Credit Risk Analogy..................... 91
3.3.1 Models and No-Arbitrage Conditions....................... 91
3.3.1.1 No-Arbitrage Condition
for the Pit, T)-Bonds........................... 93
3.3.1.2 No-Arbitrage Condition
for the pf (i, F)-Bonds......................... 93
3.4 Pricing of Interest Rate Derivatives........................... 96
3.4.1 Linear Derivatives: Interest Rate Swaps................. 99
3.4.2 Linear Derivatives: Specific Swaps and Ensuing Spreads ... 100
3.4.2.1 FRA Rates...................................... 100
3.4.2.2 OIS Swaps and Spreads.......................... 101
3.4.2.3 Basis Swaps and Spreads..................... 101
3.4.3 Caps and Floors........................................ 101
3.4.3.1 Black-Scholes-Type Approach.................... 102
3.4.3.2 Fourier Transform-Based Approach.............. 105
3.4.3.3 Exponentially Affine Structure............... 106
3.4.4 Swaptions........................................... 107
Contents xiii
3.5 Adjustment Factors.............................................. Ill
3.5.1 Adjustment Factor for the Instantaneous
Forward Rate Models...................................... Ill
3.5.1.1 Vasiôek-Type Volatility Structure............... 112
3.5.2 Adjustment Factor for the HJM-LMM
Forward Rate Model..................................... 113
4 Multiple Curve Extensions of Libor Market Models (LMM)............... 115
4.1 Multi-curve Extended LMM........................................ 116
4.1.1 Description of the Model............................... 117
4.1.2 Model Specifications..................................... 119
4.2 Affine Libor Models with Multiple Curves........................ 121
4.2.1 The Driving Process and Its Properties.................. 121
4.2.2 The Model................................................ 123
4.2.3 Pricing in the Multiple Curve Affine Libor Model......... 128
4.3 Multiplicative Spread Models.................................... 132
References............................................................... 137
|
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| indexdate | 2024-07-10T07:25:08Z |
| institution | BVB |
| isbn | 9783319253831 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028825459 |
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| physical | xiii, 140 Seiten Illustrationen |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Springer |
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| spelling | Grbac, Zorana (DE-588)1084345218 aut Interest Rate Modeling Post-Crisis challenges and approaches Zorana Grbac, Wolfgang J. Runggaldier Cham Springer [2015] © 2015 xiii, 140 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer Briefs in Quantitative Finance Mathematics Game theory Economics, Mathematical Quantitative Finance Game Theory, Economics, Social and Behav. Sciences Mathematik Runggaldier, Wolfgang J. (DE-588)171302184 aut Erscheint auch als Online-Ausgabe 978-3-319-25385-5 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028825459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grbac, Zorana Runggaldier, Wolfgang J. Interest Rate Modeling Post-Crisis challenges and approaches Mathematics Game theory Economics, Mathematical Quantitative Finance Game Theory, Economics, Social and Behav. Sciences Mathematik |
| title | Interest Rate Modeling Post-Crisis challenges and approaches |
| title_auth | Interest Rate Modeling Post-Crisis challenges and approaches |
| title_exact_search | Interest Rate Modeling Post-Crisis challenges and approaches |
| title_full | Interest Rate Modeling Post-Crisis challenges and approaches Zorana Grbac, Wolfgang J. Runggaldier |
| title_fullStr | Interest Rate Modeling Post-Crisis challenges and approaches Zorana Grbac, Wolfgang J. Runggaldier |
| title_full_unstemmed | Interest Rate Modeling Post-Crisis challenges and approaches Zorana Grbac, Wolfgang J. Runggaldier |
| title_short | Interest Rate Modeling |
| title_sort | interest rate modeling post crisis challenges and approaches |
| title_sub | Post-Crisis challenges and approaches |
| topic | Mathematics Game theory Economics, Mathematical Quantitative Finance Game Theory, Economics, Social and Behav. Sciences Mathematik |
| topic_facet | Mathematics Game theory Economics, Mathematical Quantitative Finance Game Theory, Economics, Social and Behav. Sciences Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028825459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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