Interest rates and coupon bonds in quantum finance:
"The economic crisis of 2008 has shown that the capital markets need new theoretical and mathematical concepts to describe and price financial instruments. Focusing almost exclusively on interest rates and coupon bonds, this book does not employ stochastic calculus - the bedrock of the present...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Pr.
2010
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Cover image Contributor biographical information Publisher description Inhaltsverzeichnis Inhaltsverzeichnis Inhaltsverzeichnis |
| Zusammenfassung: | "The economic crisis of 2008 has shown that the capital markets need new theoretical and mathematical concepts to describe and price financial instruments. Focusing almost exclusively on interest rates and coupon bonds, this book does not employ stochastic calculus - the bedrock of the present day mathematical finance - for any of the derivations. Instead, it analyzes interest rates and coupon bonds using quantum finance. The Heath-Jarrow-Morton and the Libor Market Model are generalized by realizing the forward and Libor interest rates as an imperfectly correlated quantum field. Theoretical models have been calibrated and tested using bond and interest rates market data. Building on the principles formulated in the author's previous book (Quantum Finance, Cambridge University Press, 2004) this ground-breaking book brings together a diverse collection of theoretical and mathematical interest rate models. It will interest physicists and mathematicians researching in finance, and professionals working in the finance industry"--Provided by publisher. |
| Beschreibung: | XVIII, 490 S. graph. Darst. |
| ISBN: | 9780521889285 |
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| 520 | 3 | |a "The economic crisis of 2008 has shown that the capital markets need new theoretical and mathematical concepts to describe and price financial instruments. Focusing almost exclusively on interest rates and coupon bonds, this book does not employ stochastic calculus - the bedrock of the present day mathematical finance - for any of the derivations. Instead, it analyzes interest rates and coupon bonds using quantum finance. The Heath-Jarrow-Morton and the Libor Market Model are generalized by realizing the forward and Libor interest rates as an imperfectly correlated quantum field. Theoretical models have been calibrated and tested using bond and interest rates market data. Building on the principles formulated in the author's previous book (Quantum Finance, Cambridge University Press, 2004) this ground-breaking book brings together a diverse collection of theoretical and mathematical interest rate models. It will interest physicists and mathematicians researching in finance, and professionals working in the finance industry"--Provided by publisher. | |
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Datensatz im Suchindex
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| adam_text | Titel: Interest rates and coupon bonds in quantum finance
Autor: Baaquie, Belal E.
Jahr: 2010
Contents
Prologue page xv
Acknowledgements xviii
1 Synopsis 1
2 Interest rates and coupon bonds 3
2.1 Introduction 3
2.2 Expanding global money capital 4
2.3 New centers of global finance 8
2.4 Interest rates 9
2.5 Three definitions of interest rates 10
2.6 Coupon and zero coupon bonds 12
2.7 Continuous compounding: forward interest rates 14
2.8 Instantaneous forward interest rates 16
2.9 Libor and Euribor 18
2.10 Simple interest rate 20
2.11 Discrete discounting: zero coupon yield curve 22
2.12 Zero coupon yield curve and interest rates 26
2.13 Summary 28
2.14 Appendix: De-noising financial data 29
3 Options and option theory 32
3.1 Introduction 32
3.2 Options 34
3.3 Vanilla options 36
3.4 Exotic options 37
3.5 Option pricing: arbitrage 39
3.6 Martingales and option pricing 40
Vll
viii Contents
3.7 Choice of numeraire 42
3.8 Hedging 42
3.9 Delta-hedging 44
3.10 Black-Scholes equation 46
3.11 Black-Scholes path integral 48
3.12 Path integration and option price 52
3.13 Path integration: European call option 54
3.14 Option price: volatility expansion 56
3.15 Derivatives and the real economy 59
3.16 Summary 62
4 Interest rate and coupon bond options 63
4.1 Introduction 63
4.2 Interest rate swaps 65
4.3 Interest rate caps and floors 70
4.4 Put-call parity for caplets and floorlets 73
4.5 Put-call: empirical Libor caplet and floorlet 75
4.6 Coupon bond options 76
4.7 Put-call parity for European bond option 77
4.8 American coupon bond option put-call
inequalities 78
4.9 Interest rate swaptions 79
4.10 Interest rate caps and swaptions 82
4.11 Heath-Jarrow-Morton path integral 83
4.12 HJM coupon bond European option price 85
4.13 Summary 89
5 Quantum field theory of bond forward interest rates 91
5.1 Introduction 91
5.2 Bond forward interest rates: a quantum field 92
5.3 Forward interest rates: Lagrangian and action 94
5.4 Velocity quantum field A(t, x) 98
5.5 Generating functional for Ait, x) propagator 100
5.6 Future market time 101
5.7 Stiff propagator 102
5.8 Integral condition for interest rates martingale 103
5.9 Pricing kernel and path integration 105
5.10 Wilson expansion of quantum field A{t, x) 108
5.11 Time evolution of a bond 110
5.12 Differential martingale condition for bonds 112
Contents ix
5.13 HJM limit of forward interest rates 114
5.14 Summary 115
6 Libor Market Model of interest rates 117
6.1 Introduction 117
6.2 Libor and zero coupon bonds 119
6.3 Libor Market Model and quantum finance 121
6.4 Libor Martingale: forward bond numeraire 123
6.5 Time evolution of Libor 125
6.6 Volatility y (t, x) for positive Libor 126
6.7 Forward bond numeraire: Libor drift £(£, Tn) 127
6.8 Libor dynamics and correlations 132
6.9 Logarithmic Libor rates (p(t,x) 134
6.10 Lagrangian and path integral for (pit, x) 139
6.11 Libor forward interest rates fi(t,x) 141
6.12 Summary 144
6.13 Appendix: Limits of the Libor Market Model 146
6.14 Appendix: Jacobian of Aiit,x) - p(t,x) 148
7 Empirical analysis of forward interest rates 150
7.1 Introduction 151
7.2 Interest rate correlation functions 152
7.3 Interest rate volatility 153
7.4 Empirical normalized propagators 155
7.5 Empirical stiff propagator 157
7.6 Empirical stiff propagator: future market time 159
7.7 Empirical analysis of the Libor Market Model 163
7.8 Stochastic volatility v(t,x) 166
7.9 Zero coupon yield curve and covariance 169
7.10 Summary 173
8 Libor Market Model of interest rate options 176
8.1 Introduction 176
8.2 Quantum Libor Market Model: Black caplet 178
8.3 Volatility expansion for Libor drift 180
8.4 Zero coupon bond option 182
8.5 Libor Market Model coupon bond option price 185
8.6 Libor Market Model European swaption price 189
8.7 Libor Asian swaption price 192
x Contents
8.8 BGM-Jamshidian swaption price 197
8.9 Summary 202
9 Numeraires for bond forward interest rates 204
9.1 Introduction 205
9.2 Money market numeraire 206
9.3 Forward bond numeraire 206
9.4 Change of numeraire 207
9.5 Forward numeraire 208
9.6 Common Libor numeraire 210
9.7 Linear pricing a mid-curve caplet 213
9.8 Forward numeraire and caplet price 214
9.9 Common Libor measure and caplet price 215
9.10 Money market numeraire and caplet price 216
9.11 Numeraire invariance: numerical example 218
9.12 Put-call parity for numeraires 219
9.13 Summary 222
10 Empirical analysis of interest rate caps 223
10.1 Introduction 223
10.2 Linear and Black caplet prices 225
10.3 Linear caplet price: parameters 227
10.4 Linear caplet price: market correlator 231
10.5 Effective volatility: parametric fit 233
10.6 Pricing an interest rate cap 235
10.7 Summary 236
11 Coupon bond European and Asian options 239
11.1 Introduction 239
11.2 Payoff function s volatility expansion 240
11.3 Coupon bond option: Feynman expansion 243
11.4 Cumulant coefficients 247
11.5 Coupon bond option: approximate price 249
11.6 Zero coupon bond option price 252
11.7 Coupon bond Asian option price 254
11.8 Coupon bond European option: HJM limit 258
11.9 Coupon bond option: BGM-Jamshidian limit 260
11.10 Coupon bond Asian option: HJM limit 262
11.11 Summary 263
Contents xi
11.12 Appendix: Coupon bond option price 264
11.13 Appendix: Zero coupon bond option price 266
12 Empirical analysis of interest rate swaptions 268
12.1 Introduction 268
12.2 Swaption price 269
12.3 Swaption price at the money 271
12.4 Volatility and correlation of swaptions 272
12.5 Data from swaption market 274
12.6 Zero coupon yield curve 275
12.7 Evaluating X: the forward bond correlator 276
12.8 Empirical results 279
12.9 Swaption pricing and HJM model 281
12.10 Summary 281
13 Correlation of coupon bond options 283
13.1 Introduction 283
13.2 Correlation function of coupon bond options 284
13.3 Perturbation expansion for correlator 285
13.4 Coefficients for martingale drift 288
13.5 Coefficients for market drift 293
13.6 Empirical study 295
13.7 Summary 300
13.8 Appendix: Bond option auto-correlation 300
14 Hedging interest rate options 304
14.1 Introduction 305
14.2 Portfolio for hedging a caplet 306
14.3 Delta-hedging interest rate caplet 307
14.4 Stochastic hedging 308
14.5 Residual variance 312
14.6 Empirical analysis of stochastic hedging 314
14.7 Hedging caplet with two futures for interest rate 317
14.8 Empirical results on residual variance 319
14.9 Summary 320
14.10 Appendix: Residual variance 321
14.11 Appendix: Conditional probability for interest rate 322
14.12 Appendix: Conditional probability - two interest rates 325
14.13 Appendix: HJM limit of hedging functions 327
xii Contents
15 Interest rate Hamiltonian and option theory 329
15.1 Introduction 329
15.2 Hamiltonian and equity option pricing 330
15.3 Equity Hamiltonian and martingale condition 332
15.4 Pricing kernel and Hamiltonian 333
15.5 Hamiltonian for Black-Scholes equation 335
15.6 Interest rate state space Vt 337
15.7 Interest rate Hamiltonian 339
15.8 Interest rate Hamiltonian: martingale condition 343
15.9 Numeraire and Hamiltonian 346
15.10 Hamiltonian and Libor Market Model drift 347
15.11 Interest rate Hamiltonian and option pricing 353
15.12 Bond evolution operator 356
15.13 Libor evolution operator 360
15.14 Summary 363
16 American options for coupon bonds and interest rates 365
16.1 Introduction 366
16.2 American equity option 367
16.3 American caplet and coupon bond options 372
16.4 Forward interest rates: lattice theory 375
16.5 American option: recursion equation 378
16.6 Forward interest rates: tree structure 382
16.7 American option: numerical algorithm 383
16.8 American caplet: numerical results 388
16.9 Numerical results: American coupon bond option 390
16.10 Put-call for American coupon bond option 394
16.11 Summary 397
17 Hamiltonian derivation of coupon bond options 399
17.1 Introduction 400
17.2 Coupon bond European option price 400
17.3 Coupon bond barrier eigenfunctions 406
17.4 Zero coupon bond barrier option price 407
17.5 Barrier function 410
17.6 Barrier linearization 413
17.7 Overcomplete barrier eigenfunctions 416
17.8 Coupon bond barrier option price 420
17.9 Barrier option: limiting cases 424
Contents xiii
17.10 Summary 427
17.11 Appendix: Barrier option coefficients 428
Epilogue 433
A Mathematical background 436
A.I Dirac-delta function 436
A.2 Martingale 439
A.3 Gaussian integration 441
A.4 White noise 446
A. 5 Functional differentiation 449
A.6 State space V 450
A.7 Quantum field 454
A. 8 Quantum mathematics 457
B US debt markets 460
B. 1 Growth of US debt market 460
B.2 2008 Financial meltdown: US subprime loans 462
Glossary of physics terms 468
Glossary of finance terms 470
List of symbols 473
References 481
Index 486
|
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| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| spelling | Baaquie, Belal E. Verfasser aut Interest rates and coupon bonds in quantum finance Belal E. Baaquie 1. publ. Cambridge [u.a.] Cambridge Univ. Pr. 2010 XVIII, 490 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier "The economic crisis of 2008 has shown that the capital markets need new theoretical and mathematical concepts to describe and price financial instruments. Focusing almost exclusively on interest rates and coupon bonds, this book does not employ stochastic calculus - the bedrock of the present day mathematical finance - for any of the derivations. Instead, it analyzes interest rates and coupon bonds using quantum finance. The Heath-Jarrow-Morton and the Libor Market Model are generalized by realizing the forward and Libor interest rates as an imperfectly correlated quantum field. Theoretical models have been calibrated and tested using bond and interest rates market data. Building on the principles formulated in the author's previous book (Quantum Finance, Cambridge University Press, 2004) this ground-breaking book brings together a diverse collection of theoretical and mathematical interest rate models. It will interest physicists and mathematicians researching in finance, and professionals working in the finance industry"--Provided by publisher. Finance Interest rates Zero coupon securities Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf HJM-Modell (DE-588)4642940-2 gnd rswk-swf Zinsstrukturtheorie (DE-588)4117720-4 gnd rswk-swf Zinsstrukturtheorie (DE-588)4117720-4 s Stochastisches Modell (DE-588)4057633-4 s HJM-Modell (DE-588)4642940-2 s DE-604 http://assets.cambridge.org/97805218/89285/cover/9780521889285.jpg Cover image http://www.loc.gov/catdir/enhancements/fy0913/2009024540-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0913/2009024540-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0913/2009024540-t.html Inhaltsverzeichnis DE-601 pdf/application http://www.gbv.de/dms/bowker/toc/9780521889285.pdf Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018721493&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baaquie, Belal E. Interest rates and coupon bonds in quantum finance Finance Interest rates Zero coupon securities Stochastisches Modell (DE-588)4057633-4 gnd HJM-Modell (DE-588)4642940-2 gnd Zinsstrukturtheorie (DE-588)4117720-4 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4642940-2 (DE-588)4117720-4 |
| title | Interest rates and coupon bonds in quantum finance |
| title_auth | Interest rates and coupon bonds in quantum finance |
| title_exact_search | Interest rates and coupon bonds in quantum finance |
| title_full | Interest rates and coupon bonds in quantum finance Belal E. Baaquie |
| title_fullStr | Interest rates and coupon bonds in quantum finance Belal E. Baaquie |
| title_full_unstemmed | Interest rates and coupon bonds in quantum finance Belal E. Baaquie |
| title_short | Interest rates and coupon bonds in quantum finance |
| title_sort | interest rates and coupon bonds in quantum finance |
| topic | Finance Interest rates Zero coupon securities Stochastisches Modell (DE-588)4057633-4 gnd HJM-Modell (DE-588)4642940-2 gnd Zinsstrukturtheorie (DE-588)4117720-4 gnd |
| topic_facet | Finance Interest rates Zero coupon securities Stochastisches Modell HJM-Modell Zinsstrukturtheorie |
| url | http://assets.cambridge.org/97805218/89285/cover/9780521889285.jpg http://www.loc.gov/catdir/enhancements/fy0913/2009024540-b.html http://www.loc.gov/catdir/enhancements/fy0913/2009024540-d.html http://www.loc.gov/catdir/enhancements/fy0913/2009024540-t.html http://www.gbv.de/dms/bowker/toc/9780521889285.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018721493&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT baaquiebelale interestratesandcouponbondsinquantumfinance |
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Inhaltsverzeichnis
Inhaltsverzeichnis