Foreign exchange option pricing: a practitioner's guide
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2011
|
| Edition: | 1. ed. |
| Series: | Wiley finance series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 280 S. Ill., graph. Darst. |
| ISBN: | 9780470683682 0470683686 |
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MARC
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| 100 | 1 | |a Clark, Iain J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Foreign exchange option pricing |b a practitioner's guide |c Iain J. Clark |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2011 | |
| 300 | |a XVIII, 280 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley finance series | |
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Record in the Search Index
| _version_ | 1804151654101024768 |
|---|---|
| adam_text | Contents
Acknowledgements
xiii
List of Tables
xv
List of Figures
xvii
1
Introduction
1
1.1
A Gentle Introduction to FX Markets
1
1.2
Quotation Styles
2
1.3
Risk Considerations
5
1.4
Spot Settlement Rules
5
1.5
Expiry and Delivery Rules
8
1.5.1
Expiry and delivery rules-days or weeks
8
1.5.2
Expiry and delivery rules
-
months or years
9
1.6
Cutoff
Ti
mes
10
2
Mathematical Preliminaries
13
2.1
The Black-Scholes Model
13
2.1.1
Assumptions of the Black-Scholes model
13
2.2
Risk Neutrality
13
2.3
Derivation of the Black-Scholes equation
14
2.3.1
Equity derivatives (without dividends)
14
2.3.2
FX derivatives
15
2.3.3
Terminal conditions and present value
17
2.4
Integrating the SDE for ST
17
2.5
Black-Scholes PDEs Expressed in
Logspot 18
2.6
Feynman-Kac and Risk-Neutral Expectation
18
2.7
Risk Neutrality and the Presumption of Drift
20
2.7.1
Equity derivatives (without dividends)
20
2.7.2
FX derivatives
-
domestic risk-neutral measure
21
2.7.3
FX derivatives
-
foreign risk-neutral measure
22
2.8
Valuation of European Options
23
2.8.1
Forward
26
viii
Contents
2.9
The Law
oi
One Price
27
2.10
The Black Scholes
lenn
Structure
Minici
28
2.11
В
rocile
M I i t
/en berger
Analysis
3í)
2.1 2
European Digitals
31
2.12.1
Slalic replication lor
bid/oľľer
digital pricing
32
2.13
Settlement Adjustments
32
2.14
Delayed Delivery Adjustments ^^
2.14.1
Delayed delivery adjustments
-
digitals ^^
2.14.2
Delayed delivery adjustments Europeans
34
2.15
Pricing
usine
Ічнпіег
Methods
35
2.15.1
European option pricing involving one numerical integral
37
2.16
Leptokurtosis
-
More than l;at Fails
W
3
Deltas and Market Conventions
41
3.1
Quote Style Conversions
41
3.2
The Law of Many Deltas
43
3.2.1
Pips spot delta
44
3.2.2
Percentage spot delta (premium adjusted)
45
3.2.3
Pips forward delta
45
3.2.4
Percentage forward delta (premium adjusted)
45
3.2.5
Simple delta
45
3.2.6
Equivalence between pips and percentage deltas
46
3.2.7
Premium adjustment
46
3.2.8
Summary
47
3.3
FX Delta Conventions
47
3.3.1
To premium adjust or not?
47
3.3.2
Spot delta or forward delta?
48
3.3.3
Notation
49
3.4
Market Volatility Surfaces
49
3.4.1
Sample market volatility surfaces
50
3.5
At-the-Money
50
3.5.1
At-the-money
-
ATMF
51
3.5.2
At-the-money
-
DNS
51
3.5.3
At-the-money strikes
-
summary
52
3.5.4
Example
-
EURUSD
1
Y
52
3.5.5
Example
-
USDJPY
1
Y
53
3.6
Market Strangle
53
3.6.1
Example
-
EURUSD
1
Y
55
3.7
Smile Strangle and Risk Reversal
55
3.7.1
Smile strangle from market strangle
-
algorithm
56
3.8
Visualisation of Strangles
57
3.9
Smile Interpolation
-
Polynomial in Delta
59
3.9.1
Example
-
EURUSD
1
Y
-
polynomial in delta
59
3.10
Smile Interpolation
-
SABR
60
3.10.1
Example
-
EURUSD 1Y-SABR
61
3.11
Concluding Remarks
62
Contents
ix
4
Volatility Surface Construction
63
4.1
Volatility Backbone
-
Flat Forward Interpolation
65
4.2
Volatility Surface Temporal Interpolation
67
4.2.1
Volatility smile extrapolation
67
4.2.2
Volatility smile interpolation
68
4.2.3
Flat forward
vol
interpolation in smile strikes
69
4.2.4
Example
-
ĽUKUSD
І Ш
from
1
Y
and 2Y tenors
-
SABR
70
4.3
Volatility Surface Temporal Interpolation Holidays and Weekends
70
4.4
Volatility Surface Temporal Interpolation
-
Intraday Effects
73
5
Local Volatility and Implied Volatility
77
5.1
Introduction
77
5.2
The Fokker-Planck Equation
78
5.2.1
Derivation of the one-dimensional Fokker-Planck equation
79
5.2.2
The multidimensional Fokker-Planck equation
82
5.3
Dupire s Construction of Local Volatility
83
5.3.1
Dupire s local volatility
-
the rd
=
rA
= 0
case
84
5.3.2
Dupire s local volatility
-
with nonzero but constant interest
rates
85
5.4
Implied Volatility and Relationship to Local Volatility
86
5.5
Local Volatility as Conditional Expectation
87
5.6
Local Volatility for FX Markets
88
5.7
Diffusion and PDE for Local Volatility
89
5.8
The
CE
V Model
90
5.8.1
Asymptotic expansion
91
6
Stochastic Volatility
95
6.1
Introduction
95
6.2
Uncertain Volatility
95
6.3
Stochastic Volatility Models
96
6.3.1
The Heston model
98
6.3.2
The Stein and Stein model
104
6.3.3
LongstafTs double square root model
105
6.3.4
Scott s exponential Ornstein-Uhlenbeck model
105
6.3.5
The SABR model
106
6.4
Uncorrelated Stochastic Volatility
107
6.5
Stochastic Volatility Correlated with Spot
108
6.6
The Fokker-Planck PDE Approach
1 1 1
6.7
The Feynman-Kac PDE Approach
113
6.7.1
Heston model
-
example
116
6.7.2
Heston model
-
logspot coordinates
117
6.8
Local Stochastic Volatility (LSV) Models
117
6.8.1
Calibration of local volatility in LSV models
118
6.8.2
Fokker-Planck equation for the LSV model
119
6.8.3
Forward induction for local volatility calibration on LSV
120
6.8.4
Calibrating stochastic and local volatilities
124
6.8.5
The pricing PDE for LSV models
127
CniitenlN
7
Numerical Methods for Pricing and Calibration
129
7.1
One-Dimensional Root Finding
-
Implied Volatility Calculation
129
7.2
Nonlinear Least Squares Minimisation
130
7.3
Monte Carlo Simulation
131
7.3.1
Handling large timesteps with local volatility
134
7.3.2
Monte Carlo convergence goes as
ì/ /N
135
7.3.3
Finding a balance between simulations and limesteps
138
7.3.4
Quasi Monte Carlo convergence can be as good as
Ι/Λ/
142
7.3.5
Variance reduction
143
7.4
Convection-Diffusion
PDĽs
in Finance
147
7.4.1
Visualising diffusion
149
7.4.2
Visualising convection
151
7.5
Numerical Methods tor PDHs
153
7.6
Explicit Finite Difference Scheme
155
7.6.1
Boundary conditions
157
7.6.2 Von
Neumann stability and the dimensionless heat equation 1
59
7.7
Explicit Finite Difference on
Nonuniform
Meshes
163
7.7.1
Mixed partial derivative terms on nonunilorm meshes
165
7.8
Implicit Finite Difference Scheme
165
7.9
The Crank-Nicolson Scheme
167
7.10
Numerical Schemes for Multidimensional PDEs
168
7.10.1
Two-dimensional Crank-Nicolson scheme
169
7.10.2
An early ADI scheme
-
Peaceman-Rachford splitting
169
7.10.3
Douglas-Rachford splitting
171
7.10.4
Craig-Sneyd splitting
172
7.1 1
Practical
Nonuniform
Grid Generation Schemes
173
7.11.1
Uniform grid generation
173
7.11.2
Uniform grid generation with required levels
173
7.11.3
Spatial grid generation
174
7.11.4
Temporal grid generation
175
7.12
Further Reading
176
8
First Generation Exotics
-
Binary and Barrier Options
177
8.
1 The Reflection Principle
179
8.2
European Barriers and Binaries
180
8.2.1
European barriers
180
8.2.2
Barrier parity relationships
182
8.2.3
European digitals
183
8.3
Continuously Monitored Binaries and Barriers
183
8.3.1
Domestic binaries
188
8.3.2
Foreign binaries
189
8.3.3
Instant one-touch products
190
8.3.4
Barrier products
191
8.3.5
KIKOs and ONTOs
194
8.4
Double Barrier Products
194
8.5
Sensitivity to Local and Stochastic Volatility
195
8.6
Barrier Bending
197
Contents xi
8.7
Value
Monitoring 202
8.7.1
Compounds
202
8.7.2
Americans
203
8.7.3
Bermudán
s
203
9
Second
Generation Exotics
205
9.1
Chooser Options
206
9.2
Range Accrual Options
206
9.3
Forward Start Options
207
9.3.1
Strike reset options
209
9.4
Lookback
Options
209
9.4.1
Double
lookback
options
211
9.5
Asian Options
212
9.5.1
Notes on seasoned Asians and fixing at expiry
214
9.6
Target Redemption Notes
214
9.7
Volatility and Variance Swaps
214
9.7.1
Volatility observation
215
9.7.2
Product specification and value at expiry
216
9.7.3
Variance swap product valuation
217
9.7.4
Volatility swap product valuation
219
10
Multicurrency Options
225
10.1
Correlations,
Triangulation
and Absence of Arbitrage
226
10.2
Exchange Options
229
10.3
Quantos
229
10.3.1
Self-quanto option
230
10.3.2
Self-quanto forward
231
10.3.3
General
quanto
options
231
10.4
Best-ofs and Worst-ofs
233
10.4.1
Two-asset best-of call
234
10.4.2
Three-asset best-of call
236
10.4.3
/V-asset best-of call
239
10.5
Basket Options
239
10.6
Numerical Methods
241
10.7
A Note on Multicurrency Greeks
242
10.8
Quantoing Untradeable Factors
243
10.9
Further Reading
244
11
Longdated FX
245
11.1
Currency Swaps
245
11.2
Basis Risk
247
.3
Forward Measure
249
.4
LIBOR
in Arrears
250
.5
Typical Longdated FX Products
253
11.5.1
Power reverse dual currency notes
253
I
1.5.2
FX target redemption notes
254
11.5.3
Effect on USDJPY volatility smile
255
xii Contents
1 1.6
The Three Factor Model
255
1
1
.7
Interest Rale Calibration ol the Three-Factor Model
237
I
1.7.1
Determination of drifts
25Ί
I
1.7.2
Determination ol Hull White volatilities
258
1
I .X Spot IX Calibration of the Three-1 actor Model
259
I I.S.I FX vanillas with
Unnormal
spot FX
260
I I .«S.2
1-Х
vanillas with CKV local volatility
261
1
Ï.H..1!
FX vanillas with Dnpire local volatility
262
I I
})
Conclusion
264
References
265
Further Reading
271
Index
273
|
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| id | DE-604.BV041547535 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:58:15Z |
| institution | BVB |
| isbn | 9780470683682 0470683686 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026993352 |
| oclc_num | 723450789 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-20 |
| owner_facet | DE-473 DE-BY-UBG DE-20 |
| physical | XVIII, 280 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley finance series |
| spelling | Clark, Iain J. Verfasser aut Foreign exchange option pricing a practitioner's guide Iain J. Clark 1. ed. Chichester [u.a.] Wiley 2011 XVIII, 280 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley finance series Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Optionspreis (DE-588)4115453-8 gnd rswk-swf Devisenmarkt (DE-588)4139011-8 gnd rswk-swf Devisenmarkt (DE-588)4139011-8 s Optionspreis (DE-588)4115453-8 s Finanzmathematik (DE-588)4017195-4 s DE-604 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026993352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Clark, Iain J. Foreign exchange option pricing a practitioner's guide Finanzmathematik (DE-588)4017195-4 gnd Optionspreis (DE-588)4115453-8 gnd Devisenmarkt (DE-588)4139011-8 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4115453-8 (DE-588)4139011-8 |
| title | Foreign exchange option pricing a practitioner's guide |
| title_auth | Foreign exchange option pricing a practitioner's guide |
| title_exact_search | Foreign exchange option pricing a practitioner's guide |
| title_full | Foreign exchange option pricing a practitioner's guide Iain J. Clark |
| title_fullStr | Foreign exchange option pricing a practitioner's guide Iain J. Clark |
| title_full_unstemmed | Foreign exchange option pricing a practitioner's guide Iain J. Clark |
| title_short | Foreign exchange option pricing |
| title_sort | foreign exchange option pricing a practitioner s guide |
| title_sub | a practitioner's guide |
| topic | Finanzmathematik (DE-588)4017195-4 gnd Optionspreis (DE-588)4115453-8 gnd Devisenmarkt (DE-588)4139011-8 gnd |
| topic_facet | Finanzmathematik Optionspreis Devisenmarkt |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026993352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT clarkiainj foreignexchangeoptionpricingapractitionersguide |