Implementing derivatives models:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2007
|
| Ausgabe: | Reprint. |
| Schriftenreihe: | Wiley series in financial engineering
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XX, 309 S. zahlr. graph. Darst. |
| ISBN: | 9780471966517 0471966517 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | As the market for new derivative instruments
continues to expand both ¡n volume and complexity,
traders and brokers everywhere are clamouring for
sound numerical techniques to model, price and
comfortably hedge complex, exotic options.
Implementing Derivatives Models is the single
comprehensive source of this application-oriented
guidance. Written in a highly accessible style, it is
of great assistance to practitioners and finance
academics who need to implement models, examine
their behaviour, compare with new models, and
perform empirical estimation of the models.
Les Clewlow and Chris
Strickland both hold
positions
at
the Financial Options Research Centre, Warwick
University, UK, at the School of Finance and
Economics, University of Technology Sydney,
Australia, and the
Instituto
de Estudios Superiores
de Administración, Caracas, Venezuela.
They are
also both principals of Lacima Consultants
specialising in derivatives pricing and risk
management education and software.
IMPLEMENTING DERIVATIVES MODELS
Les Clewlow
and Chris Strickland
Derivatives markets, particularly the over-the-counter market in complex or exotic options,
are continuing to expand rapidly on a global scale. However, the availability of information
regarding the theory and applications of the numerical techniques required to succeed in
these markets is limited. This lack of information is extremely damaging to all kinds of
financial institutions and consequently there is enormous demand for a source of sound
numerical methods for pricing and hedging.
Implementing Derivatives Models answers this demand, providing comprehensive
coverage of practical pricing and hedging techniques for complex options. Highly accessible
to practitioners seeking the latest methods and uses of models,including
The Binomial Method
Trinomial Trees and Finite Difference Methods
Monte Carlo Simulation
Implied Trees and Exotic Options
Option Pricing. Hedging and Numerical Techniques for Pricing Interest Rate
Derivatives
Term Structure Consistent Short Rate Models
The Heath, Jarrow and Morton Model
Implementing Derivatives Models is also a potent resource for financial academics who
need to implement, compare, and empirically estimate the behaviour of various option pricing
models.
Contents
PREFACE
ix
ACKNOWLEDGEMENTS xffi
NOTATION
xv
PART ONE: IMPLEMENTING MODELS IN
A GENERALISED BLACK-SCHOLES WORLD
CHAPTER
1:
THE BLACK-SCHOLES WORLD, OPTION PRICING
AND NUMERICAL TECHNIQUES
3
1.1
Introduction
3
1.2
A Model for Asset Prices
3
1.3
The Black-Scholes Partial Differential Equation
4
1.4
The Black-Scholes Formula
7
1.5
Hedging and the Black-Scholes Formula
7
1.6
The Need for Numerical Techniques
8
CHAPTER
2:
THE BINOMIAL METHOD
10
2.1
Introduction
10
2.2
A Binomial Model for a Non-Dividend Paying Asset
10
2.3
A General Formulation of the Binomial Model
17
2.4
Implementation of the General Binomial Model
19
2.5
Computing Hedge Sensitivities
29
2.6
The Binomial Model for Assets Paying a Continuous Dividend Yield
30
2.7
The Binomial Model with a Known Discrete Proportional Dividend
31
2.8
The Binomial Model
witìi a
Known Discrete Cash Dividend
34
2.9
Adapting the Binomial Model to Time Varying Volatility
37
2.10
Pricing Path-dependent Options
40
2.11
The Multidimensional Binomial Method
44
2.12
Summary
51
vi
Contents
CHAPTER
3:
TRINOMIAL TREES AND FINITE
DIFFERENCE METHODS
52
3.1
Introduction
52
3.2
A Trinomial Tree Model of the Asset Price
52
3.3
Extending the Tree into a Grid
56
3.4
The Explicit Finite Difference Method
57
3.5
Stability and Convergence
64
3.6
The Implicit Finite Difference Method
65
3.7
The Crank-Nicolson Finite Difference Method
72
3.8
Computing Hedge Sensitivities
76
3.9
Options on More Than One Asset
77
3.10
The Alternating Direction Implicit Method
77
3.11
Summary
80
CHAPTER
4:
MONTE CARLO SIMULATION
82
4.1
Introduction
82
4.2
Valuation by Simulation
82
4.3
Antithetic
Variâtes
and Variance Reduction
87
4.4
Control
Variâtes
and Hedging
91
4.5
Monte Carlo Simulation with Control
Variâtes
96
4.6
Computing Hedge Sensitivities
105
4.7
Multiple Stochastic Factors
108
4.8
Path Dependent Options
115
4.9
An Arithmetic Asian Option with a Geometric Asian Option Control
Variate
118
4.10
A Lookback
Call Option under Stochastic Volatility with Delta, Gamma
and
Vega
Control
Variâtes
123
4.11
Generating Standard Normal Random Numbers
127
4.12
Quasi-random Numbers
129
4.13
Summary
133
CHAPTER
5:
IMPLIED TREES AND EXOTIC OPTIONS
134
5.1
Introduction
134
5.2
Computing the Implied State Prices
135
5.3
Computing the Implied Transition Probabilities
140
5.4
Pricing Barrier Options in Trinomial Trees
145
5.5
Pricing
Lookback
Options in Trinomial Trees
152
5.6
Pricing Asian Options in Trinomial Trees
160
5.7
Pricing General Path-dependent Options in Trinomial Trees
167
5.8
Static Replication of Exotic Options
169
5.9
Summary
177
Contents
PART TWO: IMPLEMENTING INTEREST RATE MODELS
CHAPTER
6:
OPTION PRICING AND HEDGING AND NUMERICAL
TECHNIQUES FOR PRICING INTEREST RATE DERIVATIVES
181
6.1
Introduction
181
6.2
Government Debt Security Instruments
181
6.3
Money Market Instruments
182
6.4
The Term Structures of Interest Rates and Interest Rate Volatilities
183
6.5
Interest Rate Derivatives as Portfolios of Discount Bond Options
185
6.6
Valuation of Interest Rate Derivatives
188
6.7
Summary
206
6.A
F
and
G
Functions for Fong and Vasicek Model
206
CHAPTER
7:
TERM STRUCTURE CONSISTENT MODELS
208
7.1
Introduction
208
7.2
Ho and Lee
(1986) 208
7.3
Hull and White Model
215
7.4
Hull and White
—
Fitting Market Volatility Data and More General
Specifications for the Short-rate Volatility
219
7.5
Black, Derman and Toy
221
7.6
Black and Karasinski
222
7.7
A Note on the Behaviour of the Volatility Structure for Single-factor
Markovian Short-rate Models
222
7.8
Hull and White
—
Two-factor Model
225
7.9
Heath, Jarrow and Morton
(1992) 229
7.10
Summary
232
7.A A(t,
s)
Function for Hull and White
(1994)
Two-factor Model
232
CHAPTER
8:
CONSTRUCTING BINOMIAL TREES FOR THE SHORT
RATE
233
8.1
Introduction
—
Interest Rate Trees vs Stock Price Trees
233
8.2
Building Binomial Short Rate Trees for Black, Derman and Toy
(1990) 234
8.3
Determining the Time-dependent Functions U(i) and a(i)
236
8.4
Black-Derman-Toy Model Fitted to the Yield Curve Only
237
8.5
Black-Derman-Toy Model Fitted to Interest Rate Yield and Volatility
Data
240
8.6
Pricing Interest Rate Derivatives Within a Binomial Tree
246
8.7
Summary
254
CHAPTER
9:
CONSTRUCTING TRINOMIAL TREES FOR THE SHORT
RATE
255
9.1
Introduction
255
9.2
Building Short-rate Trees
255
viii Contents
9.3 Building
Trinomial Trees Consistent with the Process
dr
- [0(0 -
<xr]dt + adz
257
9.4
Building Trees Consistent with the Process dr
= [0(0 -
ar]dt
+ arßdz 262
9.5
A More Efficient Procedure for the Processor
= [0(0-
ar ]dt +
σ
dz 267
9.6
Building A Tree for the Process
d
In
r
= [0(0 -
a In r]dt + adz
273
9.7
Building Trees Consistent with Yield and Volatility Data
278
9.8
Building Trees Consistent with the Process dr
= [0(0 -
a(t)r]dt + adz
278
9.9
Pricing Interest Rate Derivatives in a Trinomial Tree
285
9.10
Summary
288
CHAPTER
10:
THE HEATH, JARROW AND MORTON MODEL
290
10.1
Introduction
290
10.2
Monte Carlo Simulation for Pure Discount Bond Options in General
HJM
292
10.3
Monte Carlo Simulation for Coupon Bond Options in General HJM
292
10.4
Pure Discount Bond Options in Gaussian HJM
293
10.5
Monte Carlo Simulation for European Swaptions in Gaussian HJM
294
10.6
Binomial Trees for Single-factor HJM
297
10.7
Trinomial Trees for Two-factor HJM
298
10.8
Summary
299
REFERENCES
300
INDEX
304
|
| adam_txt |
As the market for new derivative instruments
continues to expand both ¡n volume and complexity,
traders and brokers everywhere are clamouring for
sound numerical techniques to model, price and
comfortably hedge complex, exotic options.
Implementing Derivatives Models is the single
comprehensive source of this application-oriented
guidance. Written in a highly accessible style, it is
of great assistance to practitioners and finance
academics who need to implement models, examine
their behaviour, compare with new models, and
perform empirical estimation of the models.
Les Clewlow and Chris
Strickland both hold
positions
at
the Financial Options Research Centre, Warwick
University, UK, at the School of Finance and
Economics, University of Technology Sydney,
Australia, and the
Instituto
de Estudios Superiores
de Administración, Caracas, Venezuela.
They are
also both principals of Lacima Consultants
specialising in derivatives pricing and risk
management education and software.
IMPLEMENTING DERIVATIVES MODELS
Les Clewlow
and Chris Strickland
Derivatives markets, particularly the over-the-counter market in complex or exotic options,
are continuing to expand rapidly on a global scale. However, the availability of information
regarding the theory and applications of the numerical techniques required to succeed in
these markets is limited. This lack of information is extremely damaging to all kinds of
financial institutions and consequently there is enormous demand for a source of sound
numerical methods for pricing and hedging.
Implementing Derivatives Models answers this demand, providing comprehensive
coverage of practical pricing and hedging techniques for complex options. Highly accessible
to practitioners seeking the latest methods and uses of models,including
The Binomial Method
Trinomial Trees and Finite Difference Methods
Monte Carlo Simulation
Implied Trees and Exotic Options
Option Pricing. Hedging and Numerical Techniques for Pricing Interest Rate
Derivatives
Term Structure Consistent Short Rate Models
The Heath, Jarrow and Morton Model
Implementing Derivatives Models is also a potent resource for financial academics who
need to implement, compare, and empirically estimate the behaviour of various option pricing
models.
Contents
PREFACE
ix
ACKNOWLEDGEMENTS xffi
NOTATION
xv
PART ONE: IMPLEMENTING MODELS IN
A GENERALISED BLACK-SCHOLES WORLD
CHAPTER
1:
THE BLACK-SCHOLES WORLD, OPTION PRICING
AND NUMERICAL TECHNIQUES
3
1.1
Introduction
3
1.2
A Model for Asset Prices
3
1.3
The Black-Scholes Partial Differential Equation
4
1.4
The Black-Scholes Formula
7
1.5
Hedging and the Black-Scholes Formula
7
1.6
The Need for Numerical Techniques
8
CHAPTER
2:
THE BINOMIAL METHOD
10
2.1
Introduction
10
2.2
A Binomial Model for a Non-Dividend Paying Asset
10
2.3
A General Formulation of the Binomial Model
17
2.4
Implementation of the General Binomial Model
19
2.5
Computing Hedge Sensitivities
29
2.6
The Binomial Model for Assets Paying a Continuous Dividend Yield
30
2.7
The Binomial Model with a Known Discrete Proportional Dividend
31
2.8
The Binomial Model
witìi a
Known Discrete Cash Dividend
34
2.9
Adapting the Binomial Model to Time Varying Volatility
37
2.10
Pricing Path-dependent Options
40
2.11
The Multidimensional Binomial Method
44
2.12
Summary
51
vi
Contents
CHAPTER
3:
TRINOMIAL TREES AND FINITE
DIFFERENCE METHODS
52
3.1
Introduction
52
3.2
A Trinomial Tree Model of the Asset Price
52
3.3
Extending the Tree into a Grid
56
3.4
The Explicit Finite Difference Method
57
3.5
Stability and Convergence
64
3.6
The Implicit Finite Difference Method
65
3.7
The Crank-Nicolson Finite Difference Method
72
3.8
Computing Hedge Sensitivities
76
3.9
Options on More Than One Asset
77
3.10
The Alternating Direction Implicit Method
77
3.11
Summary
80
CHAPTER
4:
MONTE CARLO SIMULATION
82
4.1
Introduction
82
4.2
Valuation by Simulation
82
4.3
Antithetic
Variâtes
and Variance Reduction
87
4.4
Control
Variâtes
and Hedging
91
4.5
Monte Carlo Simulation with Control
Variâtes
96
4.6
Computing Hedge Sensitivities
105
4.7
Multiple Stochastic Factors
108
4.8
Path Dependent Options
115
4.9
An Arithmetic Asian Option with a Geometric Asian Option Control
Variate
118
4.10
A Lookback
Call Option under Stochastic Volatility with Delta, Gamma
and
Vega
Control
Variâtes
123
4.11
Generating Standard Normal Random Numbers
127
4.12
Quasi-random Numbers
129
4.13
Summary
133
CHAPTER
5:
IMPLIED TREES AND EXOTIC OPTIONS
134
5.1
Introduction
134
5.2
Computing the Implied State Prices
135
5.3
Computing the Implied Transition Probabilities
140
5.4
Pricing Barrier Options in Trinomial Trees
145
5.5
Pricing
Lookback
Options in Trinomial Trees
152
5.6
Pricing Asian Options in Trinomial Trees
160
5.7
Pricing General Path-dependent Options in Trinomial Trees
167
5.8
Static Replication of Exotic Options
169
5.9
Summary
177
Contents
PART TWO: IMPLEMENTING INTEREST RATE MODELS
CHAPTER
6:
OPTION PRICING AND HEDGING AND NUMERICAL
TECHNIQUES FOR PRICING INTEREST RATE DERIVATIVES
181
6.1
Introduction
181
6.2
Government Debt Security Instruments
181
6.3
Money Market Instruments
182
6.4
The Term Structures of Interest Rates and Interest Rate Volatilities
183
6.5
Interest Rate Derivatives as Portfolios of Discount Bond Options
185
6.6
Valuation of Interest Rate Derivatives
188
6.7
Summary
206
6.A
F
and
G
Functions for Fong and Vasicek Model
206
CHAPTER
7:
TERM STRUCTURE CONSISTENT MODELS
208
7.1
Introduction
208
7.2
Ho and Lee
(1986) 208
7.3
Hull and White Model
215
7.4
Hull and White
—
Fitting Market Volatility Data and More General
Specifications for the Short-rate Volatility
219
7.5
Black, Derman and Toy
221
7.6
Black and Karasinski
222
7.7
A Note on the Behaviour of the Volatility Structure for Single-factor
Markovian Short-rate Models
222
7.8
Hull and White
—
Two-factor Model
225
7.9
Heath, Jarrow and Morton
(1992) 229
7.10
Summary
232
7.A A(t,
s)
Function for Hull and White
(1994)
Two-factor Model
232
CHAPTER
8:
CONSTRUCTING BINOMIAL TREES FOR THE SHORT
RATE
233
8.1
Introduction
—
Interest Rate Trees vs Stock Price Trees
233
8.2
Building Binomial Short Rate Trees for Black, Derman and Toy
(1990) 234
8.3
Determining the Time-dependent Functions U(i) and a(i)
236
8.4
Black-Derman-Toy Model Fitted to the Yield Curve Only
237
8.5
Black-Derman-Toy Model Fitted to Interest Rate Yield and Volatility
Data
240
8.6
Pricing Interest Rate Derivatives Within a Binomial Tree
246
8.7
Summary
254
CHAPTER
9:
CONSTRUCTING TRINOMIAL TREES FOR THE SHORT
RATE
255
9.1
Introduction
255
9.2
Building Short-rate Trees
255
viii Contents
9.3 Building
Trinomial Trees Consistent with the Process
dr
- [0(0 -
<xr]dt + adz
257
9.4
Building Trees Consistent with the Process dr
= [0(0 -
ar]dt
+ arßdz 262
9.5
A More Efficient Procedure for the Processor
= [0(0-
ar ]dt +
σ
dz 267
9.6
Building A Tree for the Process
d
In
r
= [0(0 -
a In r]dt + adz
273
9.7
Building Trees Consistent with Yield and Volatility Data
278
9.8
Building Trees Consistent with the Process dr
= [0(0 -
a(t)r]dt + adz
278
9.9
Pricing Interest Rate Derivatives in a Trinomial Tree
285
9.10
Summary
288
CHAPTER
10:
THE HEATH, JARROW AND MORTON MODEL
290
10.1
Introduction
290
10.2
Monte Carlo Simulation for Pure Discount Bond Options in General
HJM
292
10.3
Monte Carlo Simulation for Coupon Bond Options in General HJM
292
10.4
Pure Discount Bond Options in Gaussian HJM
293
10.5
Monte Carlo Simulation for European Swaptions in Gaussian HJM
294
10.6
Binomial Trees for Single-factor HJM
297
10.7
Trinomial Trees for Two-factor HJM
298
10.8
Summary
299
REFERENCES
300
INDEX
304 |
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| any_adam_object_boolean | 1 |
| author | Clewlow, Les Strickland, Chris |
| author_facet | Clewlow, Les Strickland, Chris |
| author_role | aut aut |
| author_sort | Clewlow, Les |
| author_variant | l c lc c s cs |
| building | Verbundindex |
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| discipline_str_mv | Wirtschaftswissenschaften |
| edition | Reprint. |
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| geographic | Deutschland (DE-588)4011882-4 gnd |
| geographic_facet | Deutschland |
| id | DE-604.BV022874483 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:48:32Z |
| indexdate | 2024-07-09T21:07:28Z |
| institution | BVB |
| isbn | 9780471966517 0471966517 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016079541 |
| oclc_num | 254875392 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-11 |
| physical | XX, 309 S. zahlr. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in financial engineering |
| spelling | Clewlow, Les Verfasser aut Implementing derivatives models Les Clewlow and Chris Strickland Reprint. Chichester [u.a.] Wiley 2007 XX, 309 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in financial engineering Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Bewertung (DE-588)4006340-9 gnd rswk-swf Hedging (DE-588)4123357-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Deutschland (DE-588)4011882-4 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 s Bewertung (DE-588)4006340-9 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Deutschland (DE-588)4011882-4 g Hedging (DE-588)4123357-8 s Strickland, Chris Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016079541&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016079541&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Clewlow, Les Strickland, Chris Implementing derivatives models Mathematisches Modell (DE-588)4114528-8 gnd Bewertung (DE-588)4006340-9 gnd Hedging (DE-588)4123357-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4006340-9 (DE-588)4123357-8 (DE-588)4381572-8 (DE-588)4011882-4 |
| title | Implementing derivatives models |
| title_auth | Implementing derivatives models |
| title_exact_search | Implementing derivatives models |
| title_exact_search_txtP | Implementing derivatives models |
| title_full | Implementing derivatives models Les Clewlow and Chris Strickland |
| title_fullStr | Implementing derivatives models Les Clewlow and Chris Strickland |
| title_full_unstemmed | Implementing derivatives models Les Clewlow and Chris Strickland |
| title_short | Implementing derivatives models |
| title_sort | implementing derivatives models |
| topic | Mathematisches Modell (DE-588)4114528-8 gnd Bewertung (DE-588)4006340-9 gnd Hedging (DE-588)4123357-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd |
| topic_facet | Mathematisches Modell Bewertung Hedging Derivat Wertpapier Deutschland |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016079541&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016079541&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT clewlowles implementingderivativesmodels AT stricklandchris implementingderivativesmodels |