Engineering BGM:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL
Chapman & Hall/CRC
c2008
|
| Series: | Chapman & Hall/CRC financial mathematics series
|
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 203-211) and index |
| Physical Description: | XV, 217 S. 25 cm |
| ISBN: | 9781584889687 1584889683 |
Staff View
MARC
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| 100 | 1 | |a Brace, Alan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Engineering BGM |c Alan Brace |
| 264 | 1 | |a Boca Raton, FL |b Chapman & Hall/CRC |c c2008 | |
| 300 | |a XV, 217 S. |c 25 cm | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Chapman & Hall/CRC financial mathematics series | |
| 500 | |a Includes bibliographical references (p. 203-211) and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Interest rates |x Mathematical models | |
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Record in the Search Index
| _version_ | 1804143680984973312 |
|---|---|
| adam_text | Contents
Preface xiii
1 Introduction 1
1.1 Background HJM ........................ 2
1.2 The first correct Black caplet ................. 6
1.3 Forward BGM construction................... 8
2 Bond and Swap Basics 11
2.1 Zero coupon bonds - drifts and volatilities .......... 11
2.2 Swaps and swap notation.................... 14
2.2.1 Forward over several periods .............. 18
2.2.2 Current time....................... 19
3 Shifted BGM 21
3.1 Definition of shifted model ................... 21
3.1.1 Several points worth noting............... 22
3.2 Backward construction ..................... 24
4 Swaprate Dynamics 27
4.1 Splitting the swaprate...................... 28
4.2 The shift part.......................... 29
4.3 The stochastic part ....................... 31
4.4 Swaption values......................... 34
4.4.1 Multi-period caplets................... 35
4.5 Swaprate models......................... 36
5 Properties of Measures 39
5.1 Changes among forward and swaprate measures ....... 40
5.2 Terminal measure........................ 41
5.3 Spot Libor measure ....................... 42
5.3.1 Jumping measure..................... 44
6 Historical Correlation and Volatility 45
6.1 Flat and shifted BGM off forwards............... 48
6.2 Gaussian HJM off yield-to-matuiity .............. 49
6.3 Flat and shifted BGM off swaprates.............. 50
Vlll
7 Calibration Techniques 55
7.1 Fitting the skew ......................... 57
7.2 Maturity only fit......................... 58
7.3 Homogeneous spines....................... 59
7.3.1 Piecewise linear...................... 59
7.3.2 Rebonato s function................... 60
7.3.3 Bi-exponential function................. 60
7.3.4 Sum of exponentials................... 60
7.4 Separable one-factor fit ..................... 61
7.5 Separable multi-factor fit .................... 63
7.5.1 Alternatively....................... 65
7.6 Pedersen s method........................ 66
7.7 Cascade fit ............................ 69
7.7.1 Extension......................... 71
7.8 Exact fit with semidefinite programming ........... 71
8 Interpolating Between Nodes 75
8.1 Interpolating forwards...................... 75
8.2 Dead forwards .......................... 76
8.3 Interpolation of discount factors ................ 77
8.4 Consistent volatility....................... 78
9 Simulation 79
9.1 Glasserman type simulation................... 79
9.1.1 Under the terminal measure Pn............. 80
9.1.2 Under the spot measure Po............... 80
9.2 Big-step simulation ....................... 81
9.2.1 Volatility approximation................. 81
9.2.2 Drift approximation................... 82
9.2.3 Big-stepping under the terminal measure Pn...... 84
9.2.4 Big-stepping under a tailored spot measure Po ¦ . • • 84
10 Timeslicers 87
10.1 Terminal measure timeslicer .................. 88
10.2 Intermediate measure timeslicer ................ 89
10.3 A spot measure timeslicer is problematical .......... 90
10.4 Some technical points ...................... 91
10.4.1 Node placement ..................... 91
10.4.2 Cubics against Gaussian density............ 92
10.4.3 Splining the integrand.................. 92
10.4.4 Alternative spline..................... 93
10.5 Two-dimensional timeslicer................... 93
11 Pathwise Deltas 95
11.1 Partial derivatives of forwards ................. 96
11.2 Partial derivatives of zeros and swaps ............. 97
11.3 Differentiating option payoffs.................. 98
11.4 Vanilla caplets and swaptions.................. 99
11.5 Barrier caps and floors ..................... 100
12 Bermudans 103
12.1 Backward recursion ....................... 104
12.1.1 Alternative backward recursion............. 106
12.2 The Longstaff-Schwartz lower bound technique........ 106
12.2.1 When to exercise..................... 107
12.2.2 Regression technique................... 108
12.2.3 Comments on the Longstaff-Schwartz technique .... 109
12.3 Upper bounds .......................... 110
12.4 Bermudan deltas......................... Ill
13 Vega and Shift Hedging 113
13.1 When calibrated to coterminal swaptions ........... 114
13.1.1 The shift part....................... 115
13.1.2 The volatility part.................... 116
13.2 When calibrated to liquid swaptions.............. 118
14 Cross-Economy BGM 121
14.1 Cross-economy HJM....................... 121
14.2 Forward FX contracts...................... 123
14.2.1 In the HJM framework.................. 124
14.2.2 In the BGM framework................. 125
14.3 Cross-economy models ..................... 127
14.4 Model with the spot volatility deterministic.......... 128
14.5 Cross-economy correlation ................... 131
14.6 Pedersen type cross-economy calibration ........... 135
15 Inflation 141
15.1 TIPS and the CPI........................ 141
15.2 Dynamics of the forward inflat ion curve............ 143
15.2.1 Futures contracts..................... 145
15.2.2 The CME futures contract................ 146
16 Stochastic Volatility BGM 149
16.1 Construction ........................... 149
16.2 Swaprate dynamics ....................... 153
16.3 Shifted Heston options ..................... 155
16.3.1 Characteristic function.................. 155
16.3.2 Option price as a Fourier integral............ 158
16.4 Simulation ............................ 160
16.4.1 Simulating V {t) ..................... 160
16.5 Interpolation, Greeks and calibration ............. 162
16.5.1 Interpolation....................... 162
16.5.2 Greeks........................... 162
16.5.3 Caplet calibration .................... 163
16.5.4 Swaption calibration................... 164
17 Options in Brazil 165
17.1 Overnight DI........................... 165
17.2 Pre-DI swaps and swaptions .................. 166
17.2.1 In the HJM framework.................. 168
17.2.2 In the BGM framework................. 168
17.3 DI index options......................... 169
17.3.1 In the HJM framework.................. 169
17.4 DI futures contracts....................... 170
17.4.1 Hedging with futures contracts............. 172
17.5 DI futures options ........................ 172
A Notation and Formulae 175
A.I Swap notation .......................... 175
A.2 Gaussian distributions...................... 176
A.2.1 Conditional expectations ................ 176
A.2.2 Density shift ....................... 176
A.2.3 Black formula....................... 178
A.2.4 Gaussian density derivatives............... 179
A.2.5 Gamma and vega connection.............. 181
A.2.6 Bivariate distribution .................. 182
A.2.7 Ratio of cumulative and density distributions..... 182
A.2.8 Expected values of normals............... 183
A.3 Stochastic calculus........................ 185
A.3.1 Multi-dimensional Ito.................. 185
A.3.2 Brownian bridge..................... 185
A.3.3 Product and quotient processes............. 185
A.3.4 Conditional change of measure............. 186
A.3.5 Girsanov theorem .................... 186
A.3.6 One-dimensional Ornstein Uhlenbeck process..... 188
A.3.7 Generalized multi-dimensional OU process....... 188
A.3.8 SDE of a discounted variable.............. 188
A.3.9 Ito-Venttsel formula................... 189
A.4 Linear Algebra.......................... 189
A.4.1 Cholesky decomposition................. 189
A.4.2 Singular value decomposition.............. 190
A.4.3 Semidefinite programming (SDP)............ 192
A.5 Some Fourier transform technicalities ............. 195
XI
A.6 The chi-squared distribution .................. 198
A.7 Miscellaneous .......................... 201
A.7.1 Futures contracts..................... 201
A.7.2 Random variables from an arbitrary distribution . . . 201
A.7.3 Copula methodology................... 201
References 203
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV036957357 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:51:31Z |
| institution | BVB |
| isbn | 9781584889687 1584889683 |
| language | English |
| lccn | 2008297063 |
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| owner | DE-11 |
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| physical | XV, 217 S. 25 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series2 | Chapman & Hall/CRC financial mathematics series |
| spelling | Brace, Alan Verfasser aut Engineering BGM Alan Brace Boca Raton, FL Chapman & Hall/CRC c2008 XV, 217 S. 25 cm txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series Includes bibliographical references (p. 203-211) and index Mathematisches Modell Interest rates Mathematical models http://www.loc.gov/catdir/enhancements/fy0829/2008297063-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020872303&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brace, Alan Engineering BGM Mathematisches Modell Interest rates Mathematical models |
| title | Engineering BGM |
| title_auth | Engineering BGM |
| title_exact_search | Engineering BGM |
| title_full | Engineering BGM Alan Brace |
| title_fullStr | Engineering BGM Alan Brace |
| title_full_unstemmed | Engineering BGM Alan Brace |
| title_short | Engineering BGM |
| title_sort | engineering bgm |
| topic | Mathematisches Modell Interest rates Mathematical models |
| topic_facet | Mathematisches Modell Interest rates Mathematical models |
| url | http://www.loc.gov/catdir/enhancements/fy0829/2008297063-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020872303&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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