Mathematical models of financial derivatives:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Ausgabe: | 2. ed., rev. and enl. |
| Schriftenreihe: | Springer finance
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 530 S. graph. Darst. |
| ISBN: | 9783540422884 9783540686880 |
Internformat
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| 100 | 1 | |a Kwok, Yue-Kuen |d 1957- |e Verfasser |0 (DE-588)136047629 |4 aut | |
| 245 | 1 | 0 | |a Mathematical models of financial derivatives |c Yue-Kuen Kwok |
| 250 | |a 2. ed., rev. and enl. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XV, 530 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Mathematisches Modell | |
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Datensatz im Suchindex
| _version_ | 1804133324696846336 |
|---|---|
| adam_text | Contents
Preface
............................................................
vii
1
Introduction
to Derivative Instruments
........................... 1
1.1
Financial Options and Their Trading Strategies
.................. 2
1.1.1
Trading Strategies Involving Options
.................... 5
1.2
Rational Boundaries for Option Values
......................... 10
1.2.1
Effects of Dividend Payments
.......................... 16
1.2.2
Put-Call Parity Relations
.............................. 18
1.2.3
Foreign Currency Options
............................. 19
1.3
Forward and Futures Contracts
............................... 21
1.3.1
Values and Prices of Forward Contracts
.................. 21
1.3.2
Relation between Forward and Futures Prices
............ 24
1.4
Swap Contracts
............................................ 25
1.4.1
Interest Rate Swaps
.................................. 26
1.4.2
Currency Swaps
..................................... 28
1.5
Problems
................................................. 29
2
Financial Economics and Stochastic Calculus
..................... 35
2.1
Single Period Securities Models
.............................. 36
2.1.1
Dominant Trading Strategies and Linear Pricing Measures
.. 37
2.1.2
Arbitrage Opportunities and Risk Neutral Probability
Measures
........................................... 43
2.1.3
Valuation of Contingent Claims
........................ 48
2.1.4
Principles of Binomial Option Pricing Model
............. 52
2.2
Filtrations, Martingales and Multiperiod Models
................. 55
2.2.1
Information Structures and Filtrations
................... 56
2.2.2
Conditional Expectations and Martingales
............... 58
2.2.3
Stopping Times and Stopped Processes
.................. 62
2.2.4
Multiperiod Securities Models
......................... 64
2.2.5
Multiperiod Binomial Models
.......................... 69
xii Contents
2.3
Asset Price Dynamics and Stochastic Processes
................. 72
2.3.1
Random Walk Models
................................ 73
2.3.2
Brownian Processes
.................................. 76
2.4
Stochastic Calculus: Ito s Lemma and Girsanov s Theorem
........ 79
2.4.1
Stochastic Integrals
.................................. 79
2.4.2
Ito s Lemma and Stochastic Differentials
................ 82
2.4.3
Ito s Processes and Feynman-Kac Representation
Formula
............................................ 85
2.4.4
Change of Measure: Radon-Nikodym Derivative and
Girsanov s Theorem
.................................. 87
2.5
Problems
................................................. 89
3
Option Pricing Models: Black-Scholes-Merton Formulation
........ 99
3.1
Black-Scholes-Merton Formulation
........................... 101
3.1.1
Riskless Hedging Principle
............................ 101
3.1.2
Dynamic Replication Strategy
......................... 104
3.1.3
Risk Neutrality Argument
............................. 106
3.2
Martingale Pricing Theory
................................... 108
3.2.1
Equivalent Martingale Measure and Risk Neutral
Valuation
........................................... 109
3.2.2
Black-Scholes Model Revisited
........................ 112
3.3
Black-Scholes Pricing Formulas and Their Properties
............ 114
3.3.1
Pricing Formulas for European Options
.................. 115
3.3.2
Comparative Statics
.................................. 121
3.4
Extended Option Pricing Models
.............................. 127
3.4.1
Options on a Dividend-Paying Asset
.................... 127
3.4.2
Futures Options
..................................... 132
3.4.3
Chooser Options
..................................... 135
3.4.4
Compound Options
.................................. 136
3.4.5
Merton s Model of Risky Debts
........................ 139
3.4.6
Exchange Options
................................... 142
3.4.7
Equity Options with Exchange Rate Risk Exposure
........ 144
3.5
Beyond the Black-Scholes Pricing Framework
.................. 147
3.5.1
Transaction Costs Models
............................. 149
3.5.2
Jump-Diffusion Models
............................... 151
3.5.3
Implied and Local Volatilities
.......................... 153
3.5.4
Stochastic Volatility Models
........................... 159
3.6
Problems
................................................. 164
4
Path Dependent Options
........................................ 181
4.1
Barrier Options
............................................ 182
4.1.1
European Down-and-Out Call Options
.................. 183
4.1.2
Transition Density Function and First Passage Time
Density
............................................ 188
4.1.3
Options with Double Barriers
.......................... 195
4.1.4
Discretely Monitored Barrier Options
................... 201
Contents xiii
4.2
Lookback Options
.......................................... 201
4.2.1
European
Fixed Strike
Lookback
Options
................ 203
4.2.2
European Floating Strike
Lookback
Options
.............. 205
4.2.3
More Exotic Forms of European
Lookback
Options
....... 207
4.2.4
Differential Equation Formulation
...................... 209
4.2.5
Discretely Monitored
Lookback
Options
................. 211
4.3
Asian Options
............................................. 212
4.3.1
Partial Differential Equation Formulation
................ 213
4.3.2
Continuously Monitored Geometric Averaging Options
___ 214
4.3.3
Continuously Monitored Arithmetic Averaging Options
___ 217
4.3.4
Put-Call Parity and Fixed-Floating Symmetry Relations
___ 219
4.3.5
Fixed Strike Options with Discrete Geometric Averaging
... 222
4.3.6
Fixed Strike Options with Discrete Arithmetic Averaging
... 225
4.4
Problems
................................................. 230
American Options
.............................................. 251
5.1
Characterization of the Optimal Exercise Boundaries
............. 253
5.1.1
American Options on an Asset Paying Dividend Yield
..... 253
5.1.2
Smooth Pasting Condition
............................. 255
5.1.3
Optimal Exercise Boundary for an American Call
......... 256
5.1.4
Put-Call Symmetry Relations
.......................... 260
5.1.5
American Call Options on an Asset Paying Single
Dividend
........................................... 263
5.1.6
One-Dividend and Multidividend American Put Options
... 267
5.2
Pricing Formulations of American Option Pricing Models
........ 270
5.2.1
Linear Complementarity Formulation
................... 270
5.2.2
Optimal Stopping Problem
............................ 272
5.2.3
Integral Representation of the Early Exercise Premium
..... 274
5.2.4
American Barrier Options
............................. 278
5.2.5
American
Lookback
Options
.......................... 280
5.3
Analytic Approximation Methods
............................. 282
5.3.1
Compound Option Approximation Method
............... 283
5.3.2
Numerical Solution of the Integral Equation
.............. 284
5.3.3
Quadratic Approximation Method
...................... 287
5.4
Options with Voluntary Reset Rights
.......................... 289
5.4.1
Valuation of the ShoutFloor
........................... 290
5.4.2
Reset-Strike Put Options
.............................. 292
5.5
Problems
................................................. 297
Numerical Schemes for Pricing Options
.......................... 313
6.1
Lattice Tree Methods
....................................... 315
6.1.1
Binomial Model Revisited
............................. 315
6.1.2
Continuous Limits of the Binomial Model
............... 316
6.1.3
Discrete Dividend Models
............................. 320
6.1.4
Early Exercise Feature and Callable Feature
.............. 322
Contents
6.1.5
Trinomial Schemes
................................... 323
6.1.6
Forward Shooting Grid Methods
....................... 327
6.2
Finite Difference Algorithms
................................. 332
6.2.1
Construction of Explicit Schemes
....................... 333
6.2.2
Implicit Schemes and Their Implementation Issues
........ 337
6.2.3
Front Fixing Method and Point Relaxation Technique
...... 340
6.2.4
Truncation Errors and Order of Convergence
............. 344
6.2.5
Numerical Stability and Oscillation Phenomena
........... 346
6.2.6
Numerical Approximation of Auxiliary Conditions
........ 349
6.3
Monte Carlo Simulation
..................................... 352
6.3.1
Variance Reduction Techniques
........................ 355
6.3.2
Low Discrepancy Sequences
........................... 358
6.3.3
Valuation of American Options
......................... 359
6.4
Problems
................................................. 369
Interest Rate Models and Bond Pricing
........................... 381
7.1
Bond Prices and Interest Rates
................................ 382
7.1.1
BondPrices and Yield Curves
.......................... 383
7.1.2
Forward Rate Agreement, Bond Forward and Vanilla
Swap
.............................................. 384
7.1.3
Forward Rates and Short Rates
......................... 387
7.1.4
Bond Prices under Deterministic Interest Rates
........... 389
7.2
One-Factor Short Rate Models
............................... 390
7.2.1
Short Rate Models and Bond Prices
..................... 391
7.2.2
Vasicek Mean Reversion Model
........................ 396
7.2.3
Cox-Ingersoll-Ross Square Root Diffusion Model
........ 397
7.2.4
Generalized One-Factor Short Rate Models
.............. 399
7.2.5
Calibration to Current Term Structures of Bond Prices
..... 400
7.3
Multifactor Interest Rate Models
.............................. 403
7.3.1
Short Rate/Long Rate Models
.......................... 404
7.3.2
Stochastic Volatility Models
........................... 407
7.3.3 Affine
Term Structure Models
.......................... 408
7.4
Heath-Jarrow-Morton Framework
............................ 411
7.4.1
Forward Rate Drift Condition
.......................... 413
7.4.2
Short Rate Processes and Their Markovian
Characterization
..................................... 414
7.4.3
Forward
LIBOR
Processes under Gaussian HJM
Framework
......................................... 418
7.5
Problems
................................................. 420
Interest Rate Derivatives: Bond Options,
LIBOR
and Swap Products
441
8.1
Forward Measure and Dynamics of Forward Prices
.............. 443
8.1.1
Forward Measure
.................................... 443
8.1.2
Pricing of Equity Options under Stochastic Interest Rates
... 446
8.1.3
Futures Process and Futures-Forward Price Spread
........ 448
Contents xv
8.2
Bond Options and Range Notes
............................... 450
8.2.1
Options on Discount Bonds and Coupon-Bearing Bonds
... 450
8.2.2
Range Notes
........................................ 457
8.3
Caps and
LIBOR
Market Models
............................. 460
8.3.1
Pricing of Caps under Gaussian HJM Framework
.........461
8.3.2
Black Formulas and
LIBOR
Market Models
.............. 462
8.4
Swap Products and Swaptions
................................ 468
8.4.1
Forward Swap Rates and Swap Measure
................. 469
8.4.2
Approximate Pricing of Swaption under
Lognormal
LIBOR
Market Model
................................ 473
8.4.3
Cross-Currency Swaps
................................ 477
8.5
Problems
................................................. 485
References
......................................................... 507
Author Index
...................................................... 517
Subject Index
...................................................... 521
|
| any_adam_object | 1 |
| author | Kwok, Yue-Kuen 1957- |
| author_GND | (DE-588)136047629 |
| author_facet | Kwok, Yue-Kuen 1957- |
| author_role | aut |
| author_sort | Kwok, Yue-Kuen 1957- |
| author_variant | y k k ykk |
| building | Verbundindex |
| bvnumber | BV019821801 |
| callnumber-first | H - Social Science |
| callnumber-label | HG6024 |
| callnumber-raw | HG6024.A3 |
| callnumber-search | HG6024.A3 |
| callnumber-sort | HG 46024 A3 |
| callnumber-subject | HG - Finance |
| classification_rvk | QK 620 QK 660 SK 980 |
| classification_tum | MAT 902f WIR 170f |
| ctrlnum | (OCoLC)81453636 (DE-599)BVBBV019821801 |
| dewey-full | 332.645 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.645 |
| dewey-search | 332.645 |
| dewey-sort | 3332.645 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed., rev. and enl. |
| format | Book |
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| id | DE-604.BV019821801 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:06:55Z |
| institution | BVB |
| isbn | 9783540422884 9783540686880 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013147060 |
| oclc_num | 81453636 |
| open_access_boolean | |
| owner | DE-824 DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-N2 DE-703 DE-1051 DE-945 DE-11 DE-634 DE-188 DE-20 |
| owner_facet | DE-824 DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-N2 DE-703 DE-1051 DE-945 DE-11 DE-634 DE-188 DE-20 |
| physical | XV, 530 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer finance |
| spelling | Kwok, Yue-Kuen 1957- Verfasser (DE-588)136047629 aut Mathematical models of financial derivatives Yue-Kuen Kwok 2. ed., rev. and enl. Berlin [u.a.] Springer 2008 XV, 530 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer finance Mathematisches Modell Derivative securities Mathematical models Finanzinnovation (DE-588)4124975-6 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Finanzinnovation (DE-588)4124975-6 s Optionspreistheorie (DE-588)4135346-8 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013147060&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kwok, Yue-Kuen 1957- Mathematical models of financial derivatives Mathematisches Modell Derivative securities Mathematical models Finanzinnovation (DE-588)4124975-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Optionspreistheorie (DE-588)4135346-8 gnd |
| subject_GND | (DE-588)4124975-6 (DE-588)4114528-8 (DE-588)4381572-8 (DE-588)4135346-8 |
| title | Mathematical models of financial derivatives |
| title_auth | Mathematical models of financial derivatives |
| title_exact_search | Mathematical models of financial derivatives |
| title_full | Mathematical models of financial derivatives Yue-Kuen Kwok |
| title_fullStr | Mathematical models of financial derivatives Yue-Kuen Kwok |
| title_full_unstemmed | Mathematical models of financial derivatives Yue-Kuen Kwok |
| title_short | Mathematical models of financial derivatives |
| title_sort | mathematical models of financial derivatives |
| topic | Mathematisches Modell Derivative securities Mathematical models Finanzinnovation (DE-588)4124975-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Optionspreistheorie (DE-588)4135346-8 gnd |
| topic_facet | Mathematisches Modell Derivative securities Mathematical models Finanzinnovation Derivat Wertpapier Optionspreistheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013147060&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kwokyuekuen mathematicalmodelsoffinancialderivatives |