Martingale methods in financial modelling:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
|
| Ausgabe: | Corr. 2. print. |
| Schriftenreihe: | Applications of mathematics
36 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [471] - 512 |
| Beschreibung: | XII, 518 S. |
| ISBN: | 354061477X |
Internformat
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| 245 | 1 | 0 | |a Martingale methods in financial modelling |c Marek Musiela ; Marek Rutkowski |
| 250 | |a Corr. 2. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1998 | |
| 300 | |a XII, 518 S. | ||
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| 490 | 1 | |a Applications of mathematics |v 36 | |
| 500 | |a Literaturverz. S. [471] - 512 | ||
| 650 | 4 | |a Finanzas - Modelos matemáticos | |
| 650 | 4 | |a Tasas de interés - Modelos matemáticos | |
| 650 | 4 | |a Valores - Modelos matemáticos | |
| 650 | 4 | |a Valores de rentas fijas - Modelos matemáticos | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Derivative securities |x Mathematical models | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Fixed-income securities |x Mathematical models | |
| 650 | 4 | |a Interest rates |x Mathematical models | |
| 650 | 4 | |a Options (Finance) |x Mathematical models | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Table of Contents
Preface V
Note on the Second Printing VI
Part I. Spot and Futures Markets
1. An Introduction to Financial Derivatives 3
1.1 Options 3
1.2 Futures Contracts and Options 6
1.3 Forward Contracts 7
1.4 Call and Put Spot Options 8
1.4.1 One period Spot Market 10
1.4.2 Replicating Portfolios 11
1.4.3 Martingale Measure for a Spot Market 12
1.4.4 Absence of Arbitrage 14
1.4.5 Optimality of Replication 15
1.4.6 Put Option 18
1.5 Futures Call and Put Options 19
1.5.1 Futures Contracts and Futures Prices 20
1.5.2 One period Futures Market 20
1.5.3 Martingale Measure for a Futures Market 22
1.5.4 Absence of Arbitrage 22
1.5.5 One period Spot/Futures Market 24
1.6 Forward Contracts 25
1.6.1 Forward Price 25
1.7 Options of American Style 27
2. The Cox Ross Rubinstein Model 33
2.1 The CRR Model of a Stock Price 33
2.1.1 The CRR Option Pricing Formula 34
2.1.2 The Black Scholes Option Pricing Formula 40
2.2 Probabilistic Approach 44
2.2.1 Martingale Measure 45
2.2.2 Risk neutral Valuation Formula 47
2.3 Valuation of American Options 48
VIII Table of Contents
2.3.1 American Call Options 48
2.3.2 American Put Options 50
2.4 Options on a Dividend paying Stock 53
2.5 Transaction Costs 55
2.5.1 Replication of Options 57
2.5.2 Perfect Hedging of Options 61
3. Finite Security Markets 69
3.1 Finite Spot Markets 70
3.1.1 Arbitrage Opportunities 72
3.1.2 Arbitrage Price 72
3.1.3 Risk neutral Valuation Formula 74
3.1.4 Price Systems 76
3.1.5 Completeness of a Finite Market 79
3.2 Finite Futures Markets 80
3.2.1 Self financing Futures Strategies 81
3.2.2 Martingale Measures for a Futures Market 83
3.2.3 Risk neutral Valuation Formula 84
3.3 Futures Prices Versus Forward Prices 85
4. Market Imperfections 87
4.1 Perfect Hedging 88
4.1.1 Incomplete Markets 88
4.1.2 Constraints on Short selling and Borrowing of Cash... 96
4.1.3 Different Lending and Borrowing Rates 97
4.2 Mean variance Hedging 99
4.2.1 Variance minimizing Hedging 99
4.2.2 Risk minimizing Hedging 102
5. The Black Scholes Model 109
5.1 Spot Market 110
5.1.1 Self financing Strategies 112
5.1.2 Martingale Measure for the Spot Market 113
5.1.3 The Black Scholes Option Valuation Formula 115
5.1.4 The Put Call Parity for Spot Options 123
5.1.5 The Black Scholes PDE 124
5.2 A Riskless Portfolio Method 127
5.3 Sensitivity Analysis 130
6. Modifications of the Black Scholes Model 135
6.1 Futures Market 135
6.1.1 Self financing Strategies 136
6.1.2 Martingale Measure for the Futures Market 136
6.1.3 The Black Futures Option Formula 137
6.1.4 Options on Forward Contracts 141
Table of Contents IX
6.2 Option on a Dividend paying Stock 144
6.2.1 Case of a Constant Dividend Yield 144
6.2.2 Case of Known Dividends 146
6.3 Stock Price Volatility 150
6.3.1 Historical Volatility 151
6.3.2 Implied Volatility 151
6.3.3 Volatility Misspecification 153
6.3.4 Stochastic Volatility Models 154
6.3.5 Numerical Methods 157
7. Foreign Market Derivatives 159
7.1 Cross currency Market Model 159
7.1.1 Domestic Martingale Measure 160
7.1.2 Foreign Martingale Measure 162
7.1.3 Foreign Stock Price Dynamics 164
7.2 Currency Forward Contracts and Options 164
7.2.1 Forward Exchange Rate 165
7.2.2 Currency Option Valuation Formula 166
7.3 Foreign Equity Forward Contracts 169
7.3.1 Forward Price of a Foreign Stock 169
7.3.2 Quanto Forward Contracts 171
7.4 Foreign Market Futures Contracts 172
7.5 Foreign Equity Options 176
7.5.1 Options Struck in a Foreign Currency 176
7.5.2 Options Struck in Domestic Currency 178
7.5.3 Quanto Options 179
7.5.4 Equity linked Foreign Exchange Options 181
8. American Options 183
8.1 Valuation of American Claims 184
8.2 American Call and Put Options 192
8.3 Early Exercise Representation of an American Put 194
8.4 Analytical Approach 197
8.5 Approximations of the American Put Price 200
8.6 Option on a Dividend paying Stock 203
9. Exotic Options 205
9.1 Packages 206
9.2 Forward start Options 207
9.3 Chooser Options ; 208
9.4 Compound Options 209
9.5 Digital Options 210
9.6 Barrier Options 211
9.7 Lookback Options 214
9.8 Asian Options 218
X Table of Contents
9.9 Basket Options 221
9.10 Quantile Options 225
9.11 Combined Options 228
9.12 Russian Option 228
10. Continuous time Security Markets 229
10.1 Standard Market Models 230
10.1.1 Standard Spot Market 230
10.1.2 Futures Market 239
10.1.3 Choice of a Numeraire 241
10.1.4 Existence of a Martingale Measure 245
10.1.5 Fundamental Theorem of Asset Pricing 246
10.2 Multidimensional Black Scholes Model 248
10.2.1 Market Completeness 250
10.2.2 Variance minimizing Hedging 252
10.2.3 Risk minimizing Hedging 253
10.2.4 Market Imperfections 260
Part II. Fixed income Markets
11. Interest Rates and Related Contracts 265
11.1 Zero coupon Bonds 265
11.1.1 Term Structure of Interest Rates 266
11.1.2 Forward Interest Rates 267
11.1.3 Short term Interest Rate 268
11.2 Coupon bearing Bonds 268
11.2.1 Yield to Maturity 269
11.2.2 Market Conventions 271
11.3 Interest Rate Futures 272
11.3.1 Treasury Bond Futures 272
11.3.2 Bond Options 274
11.3.3 Treasury Bill Futures 274
11.3.4 Eurodollar Futures 276
11.4 Interest Rate Swaps 277
11.4.1 Forward Rate Agreements 278
12. Models of the Short term Rate 281
12.1 Arbitrage free Family of Bond Prices 282
12.1.1 Expectations Hypotheses 283
12.2 Case of Ito Processes 284
12.3 Single factor Models 288
12.3.1 Time homogeneous Models 288
12.3.2 Time inhomogeneous Models 292
12.3.3 Model Choice 296
Table of Contents XI
12.3.4 American Bond Options 297
12.3.5 Options on Coupon bearing Bonds 298
12.4 Multi factor Models 299
12.4.1 Consol Yield Model 300
12.5 Defaultable Bonds 302
13. Models of Instantaneous Forward Rates 303
13.1 Heath Jarrow Morton Methodology 304
13.1.1 Ho Lee Model 304
13.1.2 Heath Jarrow Morton Model 305
13.1.3 Absence of Arbitrage 307
13.1.4 Short term Interest Rate 312
13.2 Forward Measure Approach 313
13.2.1 Forward Price 314
13.2.2 Forward Martingale Measure 316
13.3 Gaussian HJM Model 319
13.3.1 Markovian Case 321
14. Models of Bond Prices and LIBOR Rates 325
14.1 Bond Price Models 326
14.1.1 Family of Bond Prices 327
14.1.2 Spot and Forward Martingale Measures 329
14.1.3 Arbitrage free Properties 330
14.1.4 Implied Savings Account 331
14.1.5 Bond Price Volatility 336
14.2 Bbrward Processes 340
14.3 Models of Forward LIBOR Rates 344
14.3.1 Discrete tenor Case 345
14.3.2 Continuous tenor Case 348
14.3.3 Spot LIBOR Measure 351
14.4 Model of Forward Swap Rates 353
15. Option Valuation in Gaussian Models. 357
15.1 European Spot Options 358
15.1.1 Bond Options 359
15.1.2 Stock Options 362
15.1.3 Option on a Coupon bearing Bond 365
15.1.4 Pricing of General Contingent Claims 368
15.1.5 Replication of Options 370
15.2 Futures Prices .373
15.2.1 Futures Options 374
15.3 PDE Approach to Interest Rate Derivatives 378
15.3.1 PDEs for Spot Derivatives 379
15.3.2 PDEs for Futures Derivatives 383
XII Table of Contents
16. Swap Derivatives 387
16.1 Interest Rate Swaps 387
16.2 Gaussian Model 390
16.2.1 Forward Caps and Floors 390
16.2.2 Captions 394
16.2.3 Swaptions 394
16.2.4 Options on a Swap Rate Spread 399
16.2.5 Yield Curve Swaps 400
16.2.6 Exotic Caps 401
16.3 Model of Forward LIBOR Rates 403
16.3.1 Caps 403
16.3.2 Swaptions 406
16.4 Model of Forward Swap Rates 410
16.5 Flesaker Hughston Model 411
16.5.1 Absence of Arbitrage 411
16.5.2 Valuation of Caps and Swaptions 414
16.6 Empirical Studies 417
17. Cross currency Derivatives 419
17.1 Arbitrage free Cross currency Markets 420
17.1.1 Forward Price of a Foreign Asset 422
17.1.2 Valuation of Foreign Contingent Claims 426
17.1.3 Cross currency Rates 427
17.2 Gaussian HJM Model 427
17.2.1 Currency Options 428
17.2.2 Foreign Equity Options 429
17.2.3 Cross currency Swaps 434
17.2.4 Cross currency Swaptions 445
17.2.5 Basket Caps 448
17.3 Model of Forward LIBOR Rates 449
Part III. APPENDICES
A. Conditional Expectations 455
B. Ito Stochastic Calculus 459
B.I The Ito Integral 459
B.2 Girsanov s Theorem 466
B.3 Laws of Certain Functional of a Brownian Motion 468
References 471
Index 513
|
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| edition | Corr. 2. print. |
| format | Book |
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| id | DE-604.BV012287006 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:24:58Z |
| institution | BVB |
| isbn | 354061477X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008330432 |
| oclc_num | 39708865 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-573 DE-945 DE-29T DE-91G DE-BY-TUM DE-706 DE-523 DE-634 DE-11 DE-188 |
| owner_facet | DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-573 DE-945 DE-29T DE-91G DE-BY-TUM DE-706 DE-523 DE-634 DE-11 DE-188 |
| physical | XII, 518 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Musiela, Marek 1950- Verfasser (DE-588)124044719 aut Martingale methods in financial modelling Marek Musiela ; Marek Rutkowski Corr. 2. print. Berlin [u.a.] Springer 1998 XII, 518 S. txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 36 Literaturverz. S. [471] - 512 Finanzas - Modelos matemáticos Tasas de interés - Modelos matemáticos Valores - Modelos matemáticos Valores de rentas fijas - Modelos matemáticos Mathematisches Modell Derivative securities Mathematical models Finance Mathematical models Fixed-income securities Mathematical models Interest rates Mathematical models Options (Finance) Mathematical models Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Kapitalmarkttheorie (DE-588)4137411-3 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Modellierung (DE-588)4170297-9 gnd rswk-swf Martingaltheorie (DE-588)4168982-3 gnd rswk-swf Kapitalmarkttheorie (DE-588)4137411-3 s DE-604 Optionspreistheorie (DE-588)4135346-8 s DE-188 Finanzmathematik (DE-588)4017195-4 s Modellierung (DE-588)4170297-9 s Martingal (DE-588)4126466-6 s Martingaltheorie (DE-588)4168982-3 s 1\p DE-604 Rutkowski, Marek Verfasser (DE-588)171429893 aut Applications of mathematics 36 (DE-604)BV000895226 36 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008330432&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Musiela, Marek 1950- Rutkowski, Marek Martingale methods in financial modelling Applications of mathematics Finanzas - Modelos matemáticos Tasas de interés - Modelos matemáticos Valores - Modelos matemáticos Valores de rentas fijas - Modelos matemáticos Mathematisches Modell Derivative securities Mathematical models Finance Mathematical models Fixed-income securities Mathematical models Interest rates Mathematical models Options (Finance) Mathematical models Finanzmathematik (DE-588)4017195-4 gnd Optionspreistheorie (DE-588)4135346-8 gnd Kapitalmarkttheorie (DE-588)4137411-3 gnd Martingal (DE-588)4126466-6 gnd Modellierung (DE-588)4170297-9 gnd Martingaltheorie (DE-588)4168982-3 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4135346-8 (DE-588)4137411-3 (DE-588)4126466-6 (DE-588)4170297-9 (DE-588)4168982-3 |
| title | Martingale methods in financial modelling |
| title_auth | Martingale methods in financial modelling |
| title_exact_search | Martingale methods in financial modelling |
| title_full | Martingale methods in financial modelling Marek Musiela ; Marek Rutkowski |
| title_fullStr | Martingale methods in financial modelling Marek Musiela ; Marek Rutkowski |
| title_full_unstemmed | Martingale methods in financial modelling Marek Musiela ; Marek Rutkowski |
| title_short | Martingale methods in financial modelling |
| title_sort | martingale methods in financial modelling |
| topic | Finanzas - Modelos matemáticos Tasas de interés - Modelos matemáticos Valores - Modelos matemáticos Valores de rentas fijas - Modelos matemáticos Mathematisches Modell Derivative securities Mathematical models Finance Mathematical models Fixed-income securities Mathematical models Interest rates Mathematical models Options (Finance) Mathematical models Finanzmathematik (DE-588)4017195-4 gnd Optionspreistheorie (DE-588)4135346-8 gnd Kapitalmarkttheorie (DE-588)4137411-3 gnd Martingal (DE-588)4126466-6 gnd Modellierung (DE-588)4170297-9 gnd Martingaltheorie (DE-588)4168982-3 gnd |
| topic_facet | Finanzas - Modelos matemáticos Tasas de interés - Modelos matemáticos Valores - Modelos matemáticos Valores de rentas fijas - Modelos matemáticos Mathematisches Modell Derivative securities Mathematical models Finance Mathematical models Fixed-income securities Mathematical models Interest rates Mathematical models Options (Finance) Mathematical models Finanzmathematik Optionspreistheorie Kapitalmarkttheorie Martingal Modellierung Martingaltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008330432&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT musielamarek martingalemethodsinfinancialmodelling AT rutkowskimarek martingalemethodsinfinancialmodelling |