Pricing interest-rate derivatives: a Fourier-transform based approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Series: | Lecture notes in economics and mathematical systems
607 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Zugl.: Tübingen, Univ., Diss., 2007 u.d.T.: Pricing interest-rate derivatives with Fourier transform techniques |
| Physical Description: | XXII, 193 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783540770657 9783540770664 3540770658 |
Staff View
MARC
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| 245 | 1 | 0 | |a Pricing interest-rate derivatives |b a Fourier-transform based approach |c Markus Bouziane |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
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Record in the Search Index
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| adam_text | Contents
List of Abbreviations and Symbols
.............................
XV
List of Tables
.................................................XIX
List of Figures
................................................XXI
1
Introduction
............................................... 1
1.1
Motivation and Objectives
................................ 1
1.2
Structure of the Thesis
................................... 4
2
A General Multi-Factor Model of the Term Structure
of Interest Rates and the Principles of Characteristic
Functions
.................................................. 7
2.1
An Extended Jump-Diffusion Term-Structure Model
......... 7
2.2
Technical Preliminaries
................................... 11
2.3
The Risk-Neutral Pricing Approach
........................ 13
2.3.1
Arbitrage and the Equivalent Martingale Measure
..... 15
2.3.2
Derivation of the Risk-Neutral Coefficients
............ 16
2.4
The Characteristic Function
.............................. 21
3
Theoretical Prices of European Interest-Rate Derivatives
. . 31
3.1
Overview
............................................... 31
3.2
Derivatives with Unconditional Payoff Functions
............. 32
3.3
Derivatives with Conditional Payoff Functions
............... 38
XII Contents
4
Three Fourier Transform-Based Pricing Approaches
....... 45
4.1
Overview
............................................... 45
4.2
Heston Approach
........................................ 49
4.3
Carr-Madan Approach
................................... 55
4.4
Lewis Approach
......................................... 60
5
Payoff Transformations and the Pricing of European
Interest-Rate Derivatives
.................................. 69
5.1
Overview
............................................... 69
5.2
Unconditional Payoff Functions
........................... 70
5.2.1
General Results
................................... 70
5.2.2
Pricing Unconditional Interest-Rate Contracts
........ 79
5.3
Conditional Payoff Functions
.............................. 81
5.3.1
General Results
................................... 82
5.3.2
Pricing of Zero-Bond Options and Interest-Rate Caps
and Floors
........................................ 87
5.3.3
Pricing of Coupon-Bond Options and Yield-Based
Swaptions
........................................ 90
6
Numerical Computation of Model Prices
.................. 95
6.1
Overview
............................................... 95
6.2
Contracts with Unconditional Exercise Rights
............... 96
6.3
Contracts with Conditional Exercise Rights
................. 97
6.3.1
Calculating Option Prices with the IFFT
............. 97
6.3.2
Refinement of the IFFT Pricing Algorithm
...........101
6.3.3
Determination of the Optimal Parameters for the
Numerical Scheme
.................................103
7
Jump Specifications for
Affine
Term-Structure Models
.....
Ill
7.1
Overview
...............................................
Ill
7.2
Exponentially Distributed Jumps
..........................115
7.3
Normally Distributed Jumps
..............................117
7.4
Gamma Distributed Jumps
...............................120
8
Jump-Enhanced One-Factor Interest-Rate Models
.........125
8.1
Overview
...............................................125
8.2
The Ornstein-Uhlenbeck Model
...........................126
Contents XIII
8.2.1
Derivation of the Characteristic Function
.............126
8.2.2
Numerical Results
.................................128
8.3
The Square-Root Model
..................................136
8.3.1
Derivation of the Characteristic Function
.............136
8.3.2
Numerical Results
.................................138
9
Jump-Enhanced Two-Factor Interest-Rate Models
.........145
9.1
Overview
...............................................145
9.2
The Additive OU-SR Model
..............................146
9.2.1
Derivation of the Characteristic Function
.............146
9.2.2
Numerical Results
.................................148
9.3
The Fong-Vasicek Model
.................................159
9.3.1
Derivation of the Characteristic Function
.............159
9.3.2
Numerical Results
.................................163
10
Non-Afflne Term-Structure Models and Short-Rate
Models with Stochastic Jump Intensity
....................171
10.1
Overview
...............................................171
10.2
Quadratic Gaussian Models
...............................171
10.3
Stochastic Jump Intensity
................................174
11
Conclusion
................................................175
A Derivation of the Complex-Valued Coefficients for the
Characteristic Function in the Square-Root Model
.........179
В
Derivation of the Complex-Valued Coefficients for the
Characteristic Function in the Fong-Vasicek Model
........183
References
.....................................................187
Markus Bouziane
Pricing Interest-Rate Derivatives
This book provides a modular pricing framework which allows the
valuation of interest-rate derivatives in a general jump-diffusion setup.
Starting with a comparison of three Fourier-style pricing methodo¬
logies, the book covers the derivation of Fourier-transform based
solutions for different interest-rate derivatives by using contour
integration principles, the development of a IFFT-based pricing algo¬
rithm, and a detailed analysis of different jump-diffusion short-rate
models.
|
| adam_txt |
Contents
List of Abbreviations and Symbols
.
XV
List of Tables
.XIX
List of Figures
.XXI
1
Introduction
. 1
1.1
Motivation and Objectives
. 1
1.2
Structure of the Thesis
. 4
2
A General Multi-Factor Model of the Term Structure
of Interest Rates and the Principles of Characteristic
Functions
. 7
2.1
An Extended Jump-Diffusion Term-Structure Model
. 7
2.2
Technical Preliminaries
. 11
2.3
The Risk-Neutral Pricing Approach
. 13
2.3.1
Arbitrage and the Equivalent Martingale Measure
. 15
2.3.2
Derivation of the Risk-Neutral Coefficients
. 16
2.4
The Characteristic Function
. 21
3
Theoretical Prices of European Interest-Rate Derivatives
. . 31
3.1
Overview
. 31
3.2
Derivatives with Unconditional Payoff Functions
. 32
3.3
Derivatives with Conditional Payoff Functions
. 38
XII Contents
4
Three Fourier Transform-Based Pricing Approaches
. 45
4.1
Overview
. 45
4.2
Heston Approach
. 49
4.3
Carr-Madan Approach
. 55
4.4
Lewis Approach
. 60
5
Payoff Transformations and the Pricing of European
Interest-Rate Derivatives
. 69
5.1
Overview
. 69
5.2
Unconditional Payoff Functions
. 70
5.2.1
General Results
. 70
5.2.2
Pricing Unconditional Interest-Rate Contracts
. 79
5.3
Conditional Payoff Functions
. 81
5.3.1
General Results
. 82
5.3.2
Pricing of Zero-Bond Options and Interest-Rate Caps
and Floors
. 87
5.3.3
Pricing of Coupon-Bond Options and Yield-Based
Swaptions
. 90
6
Numerical Computation of Model Prices
. 95
6.1
Overview
. 95
6.2
Contracts with Unconditional Exercise Rights
. 96
6.3
Contracts with Conditional Exercise Rights
. 97
6.3.1
Calculating Option Prices with the IFFT
. 97
6.3.2
Refinement of the IFFT Pricing Algorithm
.101
6.3.3
Determination of the Optimal Parameters for the
Numerical Scheme
.103
7
Jump Specifications for
Affine
Term-Structure Models
.
Ill
7.1
Overview
.
Ill
7.2
Exponentially Distributed Jumps
.115
7.3
Normally Distributed Jumps
.117
7.4
Gamma Distributed Jumps
.120
8
Jump-Enhanced One-Factor Interest-Rate Models
.125
8.1
Overview
.125
8.2
The Ornstein-Uhlenbeck Model
.126
Contents XIII
8.2.1
Derivation of the Characteristic Function
.126
8.2.2
Numerical Results
.128
8.3
The Square-Root Model
.136
8.3.1
Derivation of the Characteristic Function
.136
8.3.2
Numerical Results
.138
9
Jump-Enhanced Two-Factor Interest-Rate Models
.145
9.1
Overview
.145
9.2
The Additive OU-SR Model
.146
9.2.1
Derivation of the Characteristic Function
.146
9.2.2
Numerical Results
.148
9.3
The Fong-Vasicek Model
.159
9.3.1
Derivation of the Characteristic Function
.159
9.3.2
Numerical Results
.163
10
Non-Afflne Term-Structure Models and Short-Rate
Models with Stochastic Jump Intensity
.171
10.1
Overview
.171
10.2
Quadratic Gaussian Models
.171
10.3
Stochastic Jump Intensity
.174
11
Conclusion
.175
A Derivation of the Complex-Valued Coefficients for the
Characteristic Function in the Square-Root Model
.179
В
Derivation of the Complex-Valued Coefficients for the
Characteristic Function in the Fong-Vasicek Model
.183
References
.187
Markus Bouziane
Pricing Interest-Rate Derivatives
This book provides a modular pricing framework which allows the
valuation of interest-rate derivatives in a general jump-diffusion setup.
Starting with a comparison of three Fourier-style pricing methodo¬
logies, the book covers the derivation of Fourier-transform based
solutions for different interest-rate derivatives by using contour
integration principles, the development of a IFFT-based pricing algo¬
rithm, and a detailed analysis of different jump-diffusion short-rate
models. |
| any_adam_object | 1 |
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| author | Bouziane, Markus |
| author_facet | Bouziane, Markus |
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| id | DE-604.BV023116473 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:50:12Z |
| indexdate | 2024-07-09T21:11:24Z |
| institution | BVB |
| isbn | 9783540770657 9783540770664 3540770658 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016318991 |
| oclc_num | 191760121 |
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| owner | DE-355 DE-BY-UBR DE-384 DE-703 DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-703 DE-83 |
| physical | XXII, 193 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in economics and mathematical systems |
| series2 | Lecture notes in economics and mathematical systems |
| spelling | Bouziane, Markus Verfasser aut Pricing interest-rate derivatives a Fourier-transform based approach Markus Bouziane Berlin [u.a.] Springer 2008 XXII, 193 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 607 Zugl.: Tübingen, Univ., Diss., 2007 u.d.T.: Pricing interest-rate derivatives with Fourier transform techniques Mathematisches Modell Derivative securities Prices Mathematical models Interest rates Mathematical models Zins (DE-588)4067845-3 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Preisbildung (DE-588)4047103-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zins (DE-588)4067845-3 s Derivat Wertpapier (DE-588)4381572-8 s Preisbildung (DE-588)4047103-2 s Fourier-Transformation (DE-588)4018014-1 s DE-604 Lecture notes in economics and mathematical systems 607 (DE-604)BV000000036 607 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016318991&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016318991&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Bouziane, Markus Pricing interest-rate derivatives a Fourier-transform based approach Lecture notes in economics and mathematical systems Mathematisches Modell Derivative securities Prices Mathematical models Interest rates Mathematical models Zins (DE-588)4067845-3 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Fourier-Transformation (DE-588)4018014-1 gnd Preisbildung (DE-588)4047103-2 gnd |
| subject_GND | (DE-588)4067845-3 (DE-588)4381572-8 (DE-588)4018014-1 (DE-588)4047103-2 (DE-588)4113937-9 |
| title | Pricing interest-rate derivatives a Fourier-transform based approach |
| title_auth | Pricing interest-rate derivatives a Fourier-transform based approach |
| title_exact_search | Pricing interest-rate derivatives a Fourier-transform based approach |
| title_exact_search_txtP | Pricing interest-rate derivatives a Fourier-transform based approach |
| title_full | Pricing interest-rate derivatives a Fourier-transform based approach Markus Bouziane |
| title_fullStr | Pricing interest-rate derivatives a Fourier-transform based approach Markus Bouziane |
| title_full_unstemmed | Pricing interest-rate derivatives a Fourier-transform based approach Markus Bouziane |
| title_short | Pricing interest-rate derivatives |
| title_sort | pricing interest rate derivatives a fourier transform based approach |
| title_sub | a Fourier-transform based approach |
| topic | Mathematisches Modell Derivative securities Prices Mathematical models Interest rates Mathematical models Zins (DE-588)4067845-3 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Fourier-Transformation (DE-588)4018014-1 gnd Preisbildung (DE-588)4047103-2 gnd |
| topic_facet | Mathematisches Modell Derivative securities Prices Mathematical models Interest rates Mathematical models Zins Derivat Wertpapier Fourier-Transformation Preisbildung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016318991&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016318991&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000036 |
| work_keys_str_mv | AT bouzianemarkus pricinginterestratederivativesafouriertransformbasedapproach |