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 |
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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. | ||
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| 490 | 0 | |a Springer finance | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Derivative securities |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1822663800881414144 |
|---|---|
| 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- |
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| author_sort | Kwok, Yue-Kuen 1957- |
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| building | Verbundindex |
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| callnumber-first | H - Social Science |
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| 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 | 2025-01-30T09:00:54Z |
| institution | BVB |
| isbn | 9783540422884 9783540686880 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013147060 |
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| publishDate | 2008 |
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| 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 Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Finanzinnovation (DE-588)4124975-6 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 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 Optionspreistheorie (DE-588)4135346-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Finanzinnovation (DE-588)4124975-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4135346-8 (DE-588)4381572-8 (DE-588)4124975-6 (DE-588)4114528-8 |
| 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 Optionspreistheorie (DE-588)4135346-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Finanzinnovation (DE-588)4124975-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Mathematisches Modell Derivative securities Mathematical models Optionspreistheorie Derivat Wertpapier Finanzinnovation |
| 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 |