Pricing of bond options: unspanned stochastic volatility and random field models
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Abschlussarbeit Buch |
Sprache: | English |
Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
Schriftenreihe: | Lecture Notes in Economics and Mathematical Systems
615 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis Klappentext |
Beschreibung: | X, 137 S. graph. Darst. |
ISBN: | 9783540707219 |
Internformat
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245 | 1 | 0 | |a Pricing of bond options |b unspanned stochastic volatility and random field models |c Detlef Repplinger |
264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
300 | |a X, 137 S. |b graph. Darst. | ||
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490 | 1 | |a Lecture Notes in Economics and Mathematical Systems |v 615 | |
502 | |a Zugl.: Tübingen, Univ., Diss., 2008 | ||
650 | 4 | |a Mathematisches Modell | |
650 | 4 | |a Bonds |x Mathematical models | |
650 | 4 | |a Options (Finance) |x Mathematical models | |
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Datensatz im Suchindex
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---|---|
adam_text | Contents
1
Introduction
............................................. 1
2
The option pricing framework
............................. 7
2.1
Zero-coupon bond options
.............................. 8
2.2
Coupon bond options
.................................. 10
3
The Edgeworth Expansion
................................. 15
3.1
The generalized
ЕЕ
scheme
............................. 16
3.2
The approximation of a^-pdf
.......................... 21
3.3
The approximation of a lognormal-pdf
.................... 24
4
The Integrated Edgeworth Expansion
...................... 29
4.1
The generalized IEE scheme
............................ 30
4.2
An approximation of the J^-cdf
......................... 32
4.3
An approximation of the lognormal-cdf
................... 34
5
Multi-Factor
ЩМ
models
................................. 39
5.1
The change of measure
................................. 43
5.2
Pricing of zero-coupon bond options
..................... 44
5.2.1
The closed-form solution
....................,___ 45
5.2.2
The closed-form solution performing a FRFT
___..... 49
5.3
Pricing of coupon bond options
.......................... 53
5.3.1
A special closed-form solution
.................... 55
5.3.2
The special solution performing an IEE
............. 57
5.3.3
The one-factor solution performing an
ШЕ
.......... 62
5.3.4
The multi-factor solution performing an EEE
........ 65
6
Multiple-Random Fields term structure
modete
............. 71
6.1
RandomFíelds
....................................... 71
їх
x
Contents
6.2
Multiple-Random Field HJM-framework
.................. 75
6.3
Change of measure
.................................... 80
6.4
Pricing of zero bond options
............................ 81
6.4.1
A closed-form Random Field solution
.............. 81
6.5
Pricing of coupon bond options
.......................... 86
6.5.1
The single-Random Field solution performing an IEE
. 86
6.5.2
The multiple-Random Field solution running an IEE
.. 89
7
Multi-factor USV term structure model
.................... 93
7.1
The change of measure
................................. 97
7.2
Pricing of zero-coupon bond options
..................... 98
7.2.1
The independent solution performing a FRFT
........ 99
7.2.2
The dependent solution performing a FRFT
.........102
7.3
Pricing of coupon bond options
..........................106
7.3.1
The one-factor solution performing an IEE
..........107
7.3.2
The multi-factor solution performing an
ШЕ
.........110
8
Conclusions
..............................................113
9
Appendix
................................................117
9.1
Independent Brownian motions
..........................117
9.2
Dependent Brownian motions
...........................119
9.2.1
Case
1.........................................120
9.2.2
Case
2.........................................121
9.2.3
Case
3..........................................122
10
Matlab
codes for the
ЕЕ
and IEE
...........................125
10.1
Integer equation
......................................125
10.2
Computation of the
cumulants
given the moments
..........126
10.3
Computation of the Hermite polynomial
..................127
10.4
The
ЕЕ
..............................................128
10.5
The
ГЕЕ
.............................................129
References
...................................................131
List of figures
................................................135
List of tables
.................................................137
Detlef
Reppłinger
Pricing of Bond Options
A major theme of this book is the development of a consistent unified
model framework for the evaluation of bond options. In general op¬
tions on zero bonds (e.g. caps) and options on coupon bearing bonds
(e.g. swaptions) are linked by no-arbitrage relations through the
correlation structure of interest rates. Therefore, unspanned stochastic
volatility (USV) as well as Random Field (RF) models are used to
model the dynamics of entire yield curves. The USV models postulate
a correlation between the bond price dynamics and the subordinated
stochastic volatility process, whereas Random Field models allow
for a deterministic correlation structure between bond prices of
different terms. Then the pricing of bond options is done either by
running a Fractional Fourier Transform or by applying the Integrated
Edgeworth Expansion approach. The later is a new extension of
a generalized series expansion of the (log) characteristic function,
especially adapted for the computation of exercise probabilities.
|
adam_txt |
Contents
1
Introduction
. 1
2
The option pricing framework
. 7
2.1
Zero-coupon bond options
. 8
2.2
Coupon bond options
. 10
3
The Edgeworth Expansion
. 15
3.1
The generalized
ЕЕ
scheme
. 16
3.2
The approximation of a^-pdf
. 21
3.3
The approximation of a lognormal-pdf
. 24
4
The Integrated Edgeworth Expansion
. 29
4.1
The generalized IEE scheme
. 30
4.2
An approximation of the J^-cdf
. 32
4.3
An approximation of the lognormal-cdf
. 34
5
Multi-Factor
ЩМ
models
. 39
5.1
The change of measure
. 43
5.2
Pricing of zero-coupon bond options
. 44
5.2.1
The closed-form solution
.,_ 45
5.2.2
The closed-form solution performing a FRFT
_. 49
5.3
Pricing of coupon bond options
. 53
5.3.1
A special closed-form solution
. 55
5.3.2
The special solution performing an IEE
. 57
5.3.3
The one-factor solution performing an
ШЕ
. 62
5.3.4
The multi-factor solution performing an EEE
. 65
6
Multiple-Random Fields term structure
modete
. 71
6.1
RandomFíelds
. 71
їх
x
Contents
6.2
Multiple-Random Field HJM-framework
. 75
6.3
Change of measure
. 80
6.4
Pricing of zero bond options
. 81
6.4.1
A closed-form Random Field solution
. 81
6.5
Pricing of coupon bond options
. 86
6.5.1
The single-Random Field solution performing an IEE
. 86
6.5.2
The multiple-Random Field solution running an IEE
. 89
7
Multi-factor USV term structure model
. 93
7.1
The change of measure
. 97
7.2
Pricing of zero-coupon bond options
. 98
7.2.1
The independent solution performing a FRFT
. 99
7.2.2
The dependent solution performing a FRFT
.102
7.3
Pricing of coupon bond options
.106
7.3.1
The one-factor solution performing an IEE
.107
7.3.2
The multi-factor solution performing an
ШЕ
.110
8
Conclusions
.113
9
Appendix
.117
9.1
Independent Brownian motions
.117
9.2
Dependent Brownian motions
.119
9.2.1
Case
1.120
9.2.2
Case
2.121
9.2.3
Case
3.122
10
Matlab
codes for the
ЕЕ
and IEE
.125
10.1
Integer equation
.125
10.2
Computation of the
cumulants
given the moments
.126
10.3
Computation of the Hermite polynomial
.127
10.4
The
ЕЕ
.128
10.5
The
ГЕЕ
.129
References
.131
List of figures
.135
List of tables
.137
Detlef
Reppłinger
Pricing of Bond Options
A major theme of this book is the development of a consistent unified
model framework for the evaluation of bond options. In general op¬
tions on zero bonds (e.g. caps) and options on coupon bearing bonds
(e.g. swaptions) are linked by no-arbitrage relations through the
correlation structure of interest rates. Therefore, unspanned stochastic
volatility (USV) as well as Random Field (RF) models are used to
model the dynamics of entire yield curves. The USV models postulate
a correlation between the bond price dynamics and the subordinated
stochastic volatility process, whereas Random Field models allow
for a deterministic correlation structure between bond prices of
different terms. Then the pricing of bond options is done either by
running a Fractional Fourier Transform or by applying the Integrated
Edgeworth Expansion approach. The later is a new extension of
a generalized series expansion of the (log) characteristic function,
especially adapted for the computation of exercise probabilities. |
any_adam_object | 1 |
any_adam_object_boolean | 1 |
author | Repplinger, Detlef |
author_facet | Repplinger, Detlef |
author_role | aut |
author_sort | Repplinger, Detlef |
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ctrlnum | (OCoLC)232976383 (DE-599)DNB989198804 |
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dewey-ones | 332 - Financial economics |
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discipline_str_mv | Wirtschaftswissenschaften |
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genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
genre_facet | Hochschulschrift |
id | DE-604.BV023479437 |
illustrated | Illustrated |
index_date | 2024-07-02T21:37:24Z |
indexdate | 2024-07-09T21:19:43Z |
institution | BVB |
isbn | 9783540707219 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016661624 |
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owner | DE-355 DE-BY-UBR DE-83 DE-384 |
owner_facet | DE-355 DE-BY-UBR DE-83 DE-384 |
physical | X, 137 S. graph. Darst. |
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 | Repplinger, Detlef Verfasser aut Pricing of bond options unspanned stochastic volatility and random field models Detlef Repplinger Berlin [u.a.] Springer 2008 X, 137 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Economics and Mathematical Systems 615 Zugl.: Tübingen, Univ., Diss., 2008 Mathematisches Modell Bonds Mathematical models Options (Finance) Mathematical models Preisbildung (DE-588)4047103-2 gnd rswk-swf Optionspreis (DE-588)4115453-8 gnd rswk-swf Optionsanleihe (DE-588)4043668-8 gnd rswk-swf Volatilität (DE-588)4268390-7 gnd rswk-swf Anleihe (DE-588)4002107-5 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Anleihe (DE-588)4002107-5 s Optionspreis (DE-588)4115453-8 s Preisbildung (DE-588)4047103-2 s Volatilität (DE-588)4268390-7 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Optionsanleihe (DE-588)4043668-8 s 1\p DE-604 Erscheint auch als Online-Ausgabe 978-3-540-70729-5 Lecture Notes in Economics and Mathematical Systems 615 (DE-604)BV000000036 615 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016661624&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=016661624&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Repplinger, Detlef Pricing of bond options unspanned stochastic volatility and random field models Lecture Notes in Economics and Mathematical Systems Mathematisches Modell Bonds Mathematical models Options (Finance) Mathematical models Preisbildung (DE-588)4047103-2 gnd Optionspreis (DE-588)4115453-8 gnd Optionsanleihe (DE-588)4043668-8 gnd Volatilität (DE-588)4268390-7 gnd Anleihe (DE-588)4002107-5 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
subject_GND | (DE-588)4047103-2 (DE-588)4115453-8 (DE-588)4043668-8 (DE-588)4268390-7 (DE-588)4002107-5 (DE-588)4057633-4 (DE-588)4113937-9 |
title | Pricing of bond options unspanned stochastic volatility and random field models |
title_auth | Pricing of bond options unspanned stochastic volatility and random field models |
title_exact_search | Pricing of bond options unspanned stochastic volatility and random field models |
title_exact_search_txtP | Pricing of bond options unspanned stochastic volatility and random field models |
title_full | Pricing of bond options unspanned stochastic volatility and random field models Detlef Repplinger |
title_fullStr | Pricing of bond options unspanned stochastic volatility and random field models Detlef Repplinger |
title_full_unstemmed | Pricing of bond options unspanned stochastic volatility and random field models Detlef Repplinger |
title_short | Pricing of bond options |
title_sort | pricing of bond options unspanned stochastic volatility and random field models |
title_sub | unspanned stochastic volatility and random field models |
topic | Mathematisches Modell Bonds Mathematical models Options (Finance) Mathematical models Preisbildung (DE-588)4047103-2 gnd Optionspreis (DE-588)4115453-8 gnd Optionsanleihe (DE-588)4043668-8 gnd Volatilität (DE-588)4268390-7 gnd Anleihe (DE-588)4002107-5 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
topic_facet | Mathematisches Modell Bonds Mathematical models Options (Finance) Mathematical models Preisbildung Optionspreis Optionsanleihe Volatilität Anleihe Stochastisches Modell Hochschulschrift |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016661624&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=016661624&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV000000036 |
work_keys_str_mv | AT repplingerdetlef pricingofbondoptionsunspannedstochasticvolatilityandrandomfieldmodels |