Risk-neutral valuation: pricing and hedging of financial derivatives
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2004
|
| Edition: | 2. ed. |
| Series: | Springer finance
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 437 S. graph. Darst. |
| ISBN: | 1852334584 |
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| 100 | 1 | |a Bingham, Nicholas H. |d 1945- |e Verfasser |0 (DE-588)118095315 |4 aut | |
| 245 | 1 | 0 | |a Risk-neutral valuation |b pricing and hedging of financial derivatives |c N. H. Bingham and R. Kiesel |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a London [u.a.] |b Springer |c 2004 | |
| 300 | |a XVIII, 437 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer finance | |
| 650 | 4 | |a Derivat <Wertpapier> - Hedging - Zinsstruktur - Arbitrage | |
| 650 | 4 | |a Finanzderivat / Optionspreistheorie / Hedging / Risiko / Theorie | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Investments |x Mathematical models | |
| 650 | 4 | |a Finance |x Mathematical models | |
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| adam_text | Contents
Preface
to the Second Edition
................................
vii
Preface to the First Edition
.................................. ix
1.
Derivative Background
................................... 1
1.1
Financial Markets and Instruments
....................... 2
1.1.1
Derivative Instruments
............................ 2
1.1.2
Underlying Securities
............................. 4
1.1.3
Markets
......................................... 5
1.1.4
Types of Traders
................................. 6
1.1.5
Modeling Assumptions
............................ 6
1.2
Arbitrage
.............................................. 8
1.3
Arbitrage Relationships
................................. 11
1.3.1
Fundamental Determinants of Option Values
......... 11
1.3.2
Arbitrage Bounds
................................ 13
1.4
Single-period Market Models
............................. 15
1.4.1
A Fundamental Example
.......................... 15
1.4.2
A Single-period Model
............................ 18
1.4.3
A Few Financial-economic Considerations
........... 25
Exercises
.................................................. 26
2.
Probability Background
.................................. 29
2.1
Measure
............................................... 30
2.2
Integral
............................................... 34
2.3
Probability
............................................ 37
2.4
Equivalent Measures and
Radon-Nikodým
Derivatives
....... 42
2.5
Conditional Expectation
................................. 44
2.6
Modes of Convergence
.................................. 51
2.7
Convolution and Characteristic Functions
................. 53
2.8
The Central Limit Theorem
............................. 57
2.9
Asset Return Distributions
.............................. 61
2.10
Infinite Divisibility and the Levy-Khmtchine Formula
....... 63
2.11
Elliptically Contoured Distributions
....................... 65
2.12
Hyberbolic Distributions
................................ 67
xiv Contents
Exercises
.................................................. 71
3.
Stochastic Processes in Discrete Time
.................... 75
3.1
Information and Filtrations
.............................. 75
3.2
Discrete-parameter Stochastic Processes
................... 77
3.3
Definition and Basic Properties of Martingales
............. 78
3.4
Martingale Transforms
.................................. 80
3.5
Stopping Times and Optional Stopping
.................... 82
3.6
The Snell Envelope and Optimal Stopping
................. 88
3.7
Spaces of Martingales
................................... 94
3.8
Markov Chains
......................................... 96
Exercises
.................................................. 98
4.
Mathematical Finance in Discrete Time
..................101
4.1
The Model
............................................101
4.2
Existence of Equivalent Martingale Measures
...............105
4.2.1
The No-arbitrage Condition
.......................105
4.2.2
Risk-Neutral Pricing
..............................112
4.3
Complete Markets: Uniqueness of EMMs
..................116
4.4
The Fundamental Theorem of Asset Pricing: Risk-Neutral
Valuation
..............................................118
4.5
The Cox-Ross-Rubinstein Model
.........................121
4.5.1
Model Structure
.................................. 122
4.5.2
Risk-neutral Pricing
.............................. 124
4.5.3
Hedging
......................................... 126
4.6
Binomial Approximations
................................ 130
4.6.1
Model Structure
..................................130
4.6.2
The Black-Scholes Option Pricing Formula
..........131
4.6.3
Further Limiting Models
..........................136
4.7
American Options
......................................138
4.7.1
Theory
..........................................138
4.7.2
American Options in the CRR Model
...............141
4.8
Further Contingent Claim Valuation in Discrete Time
.......143
4.8.1
Barrier Options
..................................143
4.8.2
Lookback
Options
................................144
4.8.3
A Three-period Example
..........................145
4.9
Multifactor Models
.....................................147
4.9.1
Extended Binomial Model
.........................147
4.9.2
Multinomial Models
..............................148
Exercises
..................................................150
Contents xv
5. Stochastic
Processes
in Continuous Time
.................153
5.1
Filtrations; Finite-dimensional Distributions
...............153
5.2
Classes of Processes
.....................................155
5.2.1
Martingales
......................................155
5.2.2
Gaussian Processes
...............................158
5.2.3
Markov Processes
................................158
5.2.4
Diffusions
.......................................159
5.3
Brownian Motion
.......................................160
5.3.1
Definition and Existence
..........................160
5.3.2
Quadratic Variation of Brownian Motion
............167
5.3.3
Properties of Brownian Motion
.....................171
5.3.4
Brownian Motion in Stochastic Modeling
............173
5.4
Point Processes
........................................175
5.4.1
Exponential Distribution
..........................175
5.4.2
The
Poisson
Process
..............................176
5.4.3
Compound
Poisson
Processes
......................176
5.4.4
Renewal Processes
................................177
5.5
Levy Processes
.........................................179
5.5.1
Distributions
....................................179
5.5.2
Levy Processes
...................................181
5.5.3
Levy Processes and the
Lévy-Khintchine
Formula
.....183
5.6
Stochastic Integrals;
Ito
Calculus
.........................187
5.6.1
Stochastic Integration
.............................187
5.6.2
Itô s
Lemma
.....................................193
5.6.3
Geometric Brownian Motion
.......................196
5.7
Stochastic Calculus for Black-Scholes Models
...............198
5.8
Stochastic Differential Equations
.........................202
5.9
Likelihood Estimation for Diffusions
......................206
5.10
Martingales, Local Martingales and Semi-martingales
.......209
5.10.1
Definitions
......................................209
5.10.2
Semi-martingale Calculus
..........................211
5.10.3
Stochastic Exponentials
...........................215
5.10.4
Semi-martingale Characteristics
....................217
5.11
Weak Convergence of Stochastic Processes
.................219
5.11.1
The Spaces Cd and Dd
............................219
5.11.2
Definition and Motivation
.........................220
5.11.3
Basic Theorems of Weak Convergence
...............222
5.11.4
Weak Convergence Results for Stochastic Integrals
___223
Exercises
..................................................225
6.
Mathematical Finance in Continuous Time
...............229
6.1
Continuous-time Financial Market Models
.................229
6.1.1
The Financial Market Model
.......................229
6.1.2
Equivalent Martingale Measures
....................232
6.1.3
Risk-neutral Pricing
..............................235
xvi Contents
6.1.4
Changes
of
Numéraire
............................239
6.2
The Generalized Black-Scholes Model
.....................242
6.2.1
The Model
......................................242
6.2.2
Pricing and Hedging Contingent Claims
.............250
6.2.3
The Greeks
......................................254
6.2.4
Volatility
........................................255
6.3
Further Contingent Claim Valuation
......................258
6.3.1
American Options
................................258
6.3.2
Asian Options
...................................260
6.3.3
Barrier Options
..................................263
6.3.4
Lookback
Options
................................266
6.3.5
Binary Options
..................................269
6.4
Discrete- versus Continuous-time Market Models
...........270
6.4.1
Discrete- to Continuous-time
Convergence Reconsidered
.........................270
6.4.2
Finite Market Approximations
.....................271
6.4.3
Examples of Finite Market Approximations
..........274
6.4.4
Contiguity
.......................................280
6.5
Further Applications of the Risk-neutral
Valuation Principle
.....................................281
6.5.1
Futures Markets
..................................281
6.5.2
Currency Markets
................................285
Exercises
..................................................287
7.
Incomplete Markets
......................................289
7.1
Pricing in Incomplete Markets
...........................289
7.1.1
A General Option-Pricing Formula
.................289
7.1.2
The Esscher Measure
.............................292
7.2
Hedging in Incomplete Markets
..........................295
7.2.1
Quadratic Principles
..............................296
7.2.2
The Financial Market Model
.......................297
7.2.3
Equivalent Martingale Measures
....................299
7.2.4
Hedging Contingent Claims
........................300
7.2.5
Mean-variance Hedging and the Minimal ELMM
.....305
7.2.6
Explicit Example
.................................307
7.2.7
Quadratic Principles in Insurance
..................312
7.3
Stochastic Volatility Models
.............................314
7.4
Models Driven by Levy Processes
.........................318
7.4.1
Introduction
.....................................318
7.4.2
General
Lévy-process
Based Financial
Market Model
....................................319
7.4.3
Existence of Equivalent Martingale Measures
........321
7.4.4
Hyperbolic Models: The Hyperbolic Levy Process
.... 323
Contents xvii
8.
Interest
Rate
Theory
.....................................327
8.1
The Bond Market
......................................328
8.1.1
The Term Structure of Interest Rates
...............328
8.1.2
Mathematical Modelling
...........................330
8.1.3
Bond Pricing,
....................................334
8.2
Short-rate Models
......................................336
8.2.1
The Term-structure Equation
......................337
8.2.2
Martingale Modelling
.............................338
8.2.3
Extensions: Multi-Factor Models
...................342
8.3
Heath-Jarrow-Morton Methodology
.......................343
8.3.1
The Heath-Jarrow-Morton Model Class
.............343
8.3.2
Forward Risk-neutral Martingale Measures
..........346
8.3.3
Completeness
....................................348
8.4
Pricing and Hedging Contingent Claims
...................350
8.4.1
Short-rate Models
................................350
8.4.2
Gaussian HJM Framework
.........................351
8.4.3
Swaps
..........................................353
8.4.4
Caps
............................................354
8.5
Market Models of
LIBOR-
and Swap-rates
.................356
8.5.1
Description of the Economy
.......................356
8.5.2
LIBOR
Dynamics Under the Forward
LIBOR
Measure
..................................357
8.5.3
The Spot
LIBOR
Measure
.........................361
8.5.4
Valuation of Caplets and Floorlets in the LMM
......362
8.5.5
The Swap Market Model
..........................363
8.5.6
The Relation Between
LIBOR-
and
Swap-market Models
..............................367
8.6
Potential Models and the Flesaker-Hughston Framework
.....368
8.6.1
Pricing Kernels and Potentials
.....................368
8.6.2
The Flesaker-Hughston Framework
.................370
Exercises
..................................................372
9.
Credit Risk
...............................................375
9.1
Aspects of Credit Risk
..................................376
9.1.1
The Market
......................................376
9.1.2
What Is Credit Risk?
.............................376
9.1.3
Portfolio Risk Models
.............................377
9.2
Basic Credit Risk Modeling
...............................378
9.3
Structural Models
......................................379
9.3.1
Merton s Model
..................................379
9.3.2
A Jump-diffusion Model
...........................382
9.3.3
Structural Model with Premature Default
...........384
9.3.4
Structural Model with Stochastic Interest Rates
......388
9.3.5
Optimal Capital Structure
-
Leland s Approach
......389
9.4
Reduced Form Models
..................................390
xviii Contents
9.5
Credit
Derivatives......................................399
9.6
Portfolio Credit
Risk Models
.............................400
9.7
CoUateralized Debt Obligations (CDOs)
...................404
9.7.1
Introduction
.....................................404
9.7.2
Review of Modelling Methods
......................405
A. Hilbert Space
.............................................409
B. Projections and Conditional Expectations
................411
C. The Separating
Hyperplane
Theorem
.....................415
Bibliography
..................................................417
Index
.........................................................433
|
| any_adam_object | 1 |
| author | Bingham, Nicholas H. 1945- Kiesel, Rüdiger 1962- |
| author_GND | (DE-588)118095315 (DE-588)172185262 |
| author_facet | Bingham, Nicholas H. 1945- Kiesel, Rüdiger 1962- |
| author_role | aut aut |
| author_sort | Bingham, Nicholas H. 1945- |
| author_variant | n h b nh nhb r k rk |
| building | Verbundindex |
| bvnumber | BV017185540 |
| callnumber-first | H - Social Science |
| callnumber-label | HG4515 |
| callnumber-raw | HG4515.2.B56 2004 |
| callnumber-search | HG4515.2.B56 2004 |
| callnumber-sort | HG 44515.2 B56 42004 |
| callnumber-subject | HG - Finance |
| classification_rvk | QK 620 QK 660 SK 980 |
| classification_tum | MAT 902f WIR 160f |
| ctrlnum | (OCoLC)249076370 (DE-599)BVBBV017185540 |
| dewey-full | 332.6457 332.64/5722 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.6457 332.64/57 22 |
| dewey-search | 332.6457 332.64/57 22 |
| dewey-sort | 3332.6457 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV017185540 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:14:43Z |
| institution | BVB |
| isbn | 1852334584 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010356812 |
| oclc_num | 249076370 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-703 DE-824 DE-355 DE-BY-UBR DE-20 DE-384 DE-521 DE-706 DE-29T DE-83 DE-11 DE-N2 DE-188 |
| owner_facet | DE-473 DE-BY-UBG DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-703 DE-824 DE-355 DE-BY-UBR DE-20 DE-384 DE-521 DE-706 DE-29T DE-83 DE-11 DE-N2 DE-188 |
| physical | XVIII, 437 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer finance |
| spelling | Bingham, Nicholas H. 1945- Verfasser (DE-588)118095315 aut Risk-neutral valuation pricing and hedging of financial derivatives N. H. Bingham and R. Kiesel 2. ed. London [u.a.] Springer 2004 XVIII, 437 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer finance Derivat <Wertpapier> - Hedging - Zinsstruktur - Arbitrage Finanzderivat / Optionspreistheorie / Hedging / Risiko / Theorie Mathematisches Modell Investments Mathematical models Finance Mathematical models Hedging (DE-588)4123357-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Arbitrage (DE-588)4002820-3 gnd rswk-swf Bewertung (DE-588)4006340-9 gnd rswk-swf Zinsstruktur (DE-588)4067855-6 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 s Hedging (DE-588)4123357-8 s Zinsstruktur (DE-588)4067855-6 s Arbitrage (DE-588)4002820-3 s DE-604 Bewertung (DE-588)4006340-9 s 1\p DE-604 Kiesel, Rüdiger 1962- Verfasser (DE-588)172185262 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010356812&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 | Bingham, Nicholas H. 1945- Kiesel, Rüdiger 1962- Risk-neutral valuation pricing and hedging of financial derivatives Derivat <Wertpapier> - Hedging - Zinsstruktur - Arbitrage Finanzderivat / Optionspreistheorie / Hedging / Risiko / Theorie Mathematisches Modell Investments Mathematical models Finance Mathematical models Hedging (DE-588)4123357-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Arbitrage (DE-588)4002820-3 gnd Bewertung (DE-588)4006340-9 gnd Zinsstruktur (DE-588)4067855-6 gnd |
| subject_GND | (DE-588)4123357-8 (DE-588)4381572-8 (DE-588)4002820-3 (DE-588)4006340-9 (DE-588)4067855-6 |
| title | Risk-neutral valuation pricing and hedging of financial derivatives |
| title_auth | Risk-neutral valuation pricing and hedging of financial derivatives |
| title_exact_search | Risk-neutral valuation pricing and hedging of financial derivatives |
| title_full | Risk-neutral valuation pricing and hedging of financial derivatives N. H. Bingham and R. Kiesel |
| title_fullStr | Risk-neutral valuation pricing and hedging of financial derivatives N. H. Bingham and R. Kiesel |
| title_full_unstemmed | Risk-neutral valuation pricing and hedging of financial derivatives N. H. Bingham and R. Kiesel |
| title_short | Risk-neutral valuation |
| title_sort | risk neutral valuation pricing and hedging of financial derivatives |
| title_sub | pricing and hedging of financial derivatives |
| topic | Derivat <Wertpapier> - Hedging - Zinsstruktur - Arbitrage Finanzderivat / Optionspreistheorie / Hedging / Risiko / Theorie Mathematisches Modell Investments Mathematical models Finance Mathematical models Hedging (DE-588)4123357-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Arbitrage (DE-588)4002820-3 gnd Bewertung (DE-588)4006340-9 gnd Zinsstruktur (DE-588)4067855-6 gnd |
| topic_facet | Derivat <Wertpapier> - Hedging - Zinsstruktur - Arbitrage Finanzderivat / Optionspreistheorie / Hedging / Risiko / Theorie Mathematisches Modell Investments Mathematical models Finance Mathematical models Hedging Derivat Wertpapier Arbitrage Bewertung Zinsstruktur |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010356812&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT binghamnicholash riskneutralvaluationpricingandhedgingoffinancialderivatives AT kieselrudiger riskneutralvaluationpricingandhedgingoffinancialderivatives |