Global derivatives: products, theory and practice
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2007
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| Beschreibung: | XXVI, 384 S. Ill., graph. Darst. |
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| 020 | |a 9789812566898 |c hbk : £ 41.00 |9 978-981-256-689-8 | ||
| 020 | |a 9812566899 |9 981-256-689-9 | ||
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| 245 | 1 | 0 | |a Global derivatives |b products, theory and practice |c ed.: Eric Benhamou |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific Publ. |c 2007 | |
| 300 | |a XXVI, 384 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Finanzderivat / Finanzinnovation / Finanzmarkt / Financial Futures / Hedging | |
| 650 | 4 | |a Lehrbuch / Textbook - 28 | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Derivative securities |x Mathematical models | |
| 650 | 4 | |a Structured notes (Securities) |x Mathematical models | |
| 650 | 0 | 7 | |a Derivat |g Wertpapier |0 (DE-588)4381572-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | |C b |5 DE-604 | |
| 700 | 1 | |a Benhamou, Eric |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015820737&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015820737 | ||
Datensatz im Suchindex
| _version_ | 1804136771820191744 |
|---|---|
| adam_text | CONTENTS
PREFACE v
ABOUT THE AUTHORS
Іх
1.
STANDARD PRODUCTS AND MARKETS
1
1.1.
Introduction to Financial Markets
.......... 1
1.1.1.
Definition of financial markets
........ 1
1.1.2.
The different derivatives markets
....... 2
1.1.3.
Importance of the derivatives
......... 3
1.1.4.
Cash or spot vs. derivatives markets
..... 5
1.1.5.
History of financial markets
......... 6
1.1.6.
Listed markets vs. OTC markets
....... 8
1.1.7.
Shares and dividends
............. 8
1.1.8.
Typology of the markets participants
.... 10
1.2.
Presentation of the Trading Room and Group
Description
....................... 11
1.2.1.
Different functionality of the trading room
. 11
1.2.2.
Job description
................. 11
1.2.2.1.
Trader
................ 11
1.2.2.2.
Sales/originators/structurors
.... 12
1.2.2.3.
Quant/IT/analyst support
..... 12
1.2.2
A. Middle office/back office support
. 12
1.3.
Flow Business, Prop Trading and Exotic
...... 13
xiv
Global
Derivatives:
Products,
Theory and Practice
1.3.1.
Definition
.................... 13
1.3.2.
Hedge fund business
.............. 13
1.3.3.
Key differences
................. 13
1.3.4.
Market making
................. 14
1.3.5.
ECN and electronic trading platform
.... 14
1.4.
Ethic and Deontology
................. 15
1.4.1.
History
..................... 15
1.4.1.1.
Barings
................ 15
1.4.1.2.
ENRON
............... 16
1.4.1.3.
LTCM
................ 17
1.4.2.
Insider trading
................. 18
1.4.3.
Money laundering
............... 19
1.5.
Summary
........................ 19
References
.......................... 20
2.
THE VANILLA PRODUCTS
21
2.1.
Interest and Usage of Products
........... 22
2.1.1.
Interest and usage of products
........ 22
2.1.2.
Derivatives description
............ 22
2.1.3.
The hedging purpose
............. 23
2.1.3.1.
Hedging with forward contract
... 23
2.1.3.2.
Hedging with options
........ 24
2.1.4.
The speculation
................ 25
2.1.5.
The arbitrage
................. 26
2.2.
Pricing of Future Contract
.............. 27
2.2.1.
Trading futures: Margin call and trading
account
..................... 27
2.2.1.1.
The future contract
......... 27
2.2.1.2.
Product specification
........ 28
2.2.2.
Futures vs. forward
.............. 30
2.2.3.
Forward and futures prices
.......... 30
2.2.3.1.
Forward pricing
........... 30
2.2.3.2.
Futures prices
............ 31
2.3.
Options
......................... 33
2.3.1.
Definition and features
............ 33
2.3.2.
Call-put parity
................ 35
Contents xv
2.3.3. Option
strategies: call, put, straddle,
strangle, spread and butterfly
........ 35
2.3.3.1.
Call/put option
........... 36
2.3.3.2.
Straddle
............... 37
2.3.3.3.
Strangle
............... 38
2.3.3.4.
Butterfly
............... 39
2.3.4.
Warrants
.................... 40
2.4.
Summary
........................ 41
References
.......................... 42
3.
INTRODUCTION TO FINANCIAL MODELING
43
3.1.
A Bit of History
.................... 43
3.2.
Usage of Models
.................... 48
3.2.1.
Risk categories
................. 48
3.2.1.1.
Market risk
............. 48
3.2.1.2.
Counterparty risk
.......... 50
3.2.1.3.
Operational risk
........... 50
3.2.1.4.
Model risk
.............. 52
3.2.2.
What are models for?
............. 53
3.2.2.1.
As a predictor
............ 53
3.2.2.2.
As an interpolator or
extrapolator
............ 53
3.2.3.
Simple versus complicated models
...... 55
3.2.4.
Warnings
.................... 56
3.2.5.
Special warnings: calibration issues
..... 58
3.3.
Reasonable Mathematical Basis for Financial
Modeling
........................ 59
3.3.1.
Modeling framework
.............. 59
3.3.1.1.
Words on probability
........ 60
3.3.1.2.
Types of computations
....... 61
3.3.1.3.
Ito
processes and Ito/Doblin
formula
................ 62
3.3.1.4.
Usage of Brownian motion
..... 64
3.3.2.
Risk neutral probability
............ 67
3.3.2.1.
Example of the one factor case
. . . 67
3.3.2.2.
The
η
factor case
.......... 69
xvi
Global
Derivatives:
Products,
Theory and Practice
3.3.2.3.
The two currency case
....... 73
3.4.
Summary
........................ 77
References
.......................... 78
4.
THE BLACK-SCHOLES MODEL
79
4.1.
Model History
..................... 79
4.2.
Initial Problems
.................... 80
4.3.
Model Hypothesis
................... 82
4.3.1. Lognormal
distribution and constant
volatility
.................... 82
4.3.2.
Assumptions
.................. 82
4.4.
Black-Scholes Partial Differential Equation
..... 83
4.5.
Black-Scholes Formulae for Call and Put Options
. 85
4.6.
Implied Volatility and Smile
............. 86
4.7.
Hedging Strategies
.................. 86
4.7.1.
Naked and cover positions
.......... 87
4.7.2.
Delta hedging
................. 87
4.7.3.
Stop and loss strategy
............. 87
4.8.
The Derivative Function of the Price or Greeks
. . 90
4.8.1.
Delta
...................... 90
4.8.2.
Theta
...................... 91
4.8.3.
Gamma
..................... 92
4.8.4. Vega...................... 92
4.9.
Black-Scholes Robustness
.............. 94
4.10.
Black-Scholes Extensions
............... 95
4.10.1.
Volatility: deterministic function of time
. . 95
4.10.2.
Dividend
................... 95
4.10.3.
Normal and shifted
lognormal
models
... 96
4.11.
Summary
........................ 97
References
.......................... 98
5.
FIXED INCOME BASIS
99
5.1
Simple Instruments
.................. 99
5.1.1.
Markets conventions
.............. 99
5.1.2.
LIBOR
rates
.................. 100
5.1.3.
Repo
rate
.................... 101
Contents xvii
5.1.4.
Duration
.................... 102
5.2
Bootstrapping and Curve Fitting
.......... 104
5.3
Introduction to Swaps
................ 105
5.3.1.
Vanilla swaps
................. 105
5.3.2.
Cross-currency swaps
............. 106
5.3.3.
Forward starting swaps
............ 109
5.3.4.
LIBOR-in-arrears swaps
........... 110
5.3.5.
CMT and CMS swaps
............. 110
5.4
Convexity Adjustment
................
Ill
5.4.1.
Convexity correction
.............
Ill
5.4.2.
LIBOR-in-arrears swap
............ 112
5.4.3.
CMS/CMT/spread lock
............ 114
5.4.4.
Replication
................... 116
5.5
Vanilla Interest Rate Options
............ 120
5.5.1.
Interest rate caps and floors
......... 120
5.5.2.
European swaptions
.............. 122
5.5.3.
Spread options
................. 123
5.6
Summary
........................ 123
References
.......................... 124
6.
SMILE MODELING
125
6.1.
Smile and Digital Models
............... 125
6.1.1.
Target market
................. 126
6.2.
Smile Models (Basic European Models)
....... 127
6.2.1.
The Merton model
............... 128
6.2.1.1.
Influence of the jumps (a la Merton)
on the smile
............. 129
6.2.2.
Local volatility models (a la Dupire)
..... 129
6.2.3.
The CEV model
................ 131
6.2.3.1.
Extrapolation issues
......... 133
6.2.3.2.
Robustness issues
.......... 133
6.2.4.
Stochastic volatility models
.......... 134
6.2.4.1.
An analytical formula
........ 135
6.2.4.2.
Heston model and Fourier
transform
.............. 136
xviii
Global
Derivatives:
Products,
Theory and Practice
6.2.4.3.
Lewis model and the preservative
approach
............... 136
6.2.4.4.
SABR model and link to
Riemannian geometry
........ 138
6.2.5.
Connection between the SABR and the
complex BS models
............. 142
6.2.5.1.
Expected local time and vanilla
option prices
............. 142
6.2.5.2.
Expected local time and probability
density
................ 144
6.2.5.3.
Explicit computation of the local
time for stochastic models
..... 145
6.2.5.4.
Fast computation of the SABR
stochastic integral and connection
with BS model
............ 146
6.2.5.5.
Application to CMS replication
pricing
................ 148
6.2.6.
Volatility and variance swap: Log and
parabola contracts
............... 152
6.2.6.1.
Contract definition
......... 152
6.2.6.2.
Replication strategy and pricing
. . 153
6.2.6.3.
Variance swap in the Heston
model
................. 154
6.2.6.4.
Variance swap in the mean
reverting
lognormal
model
..... 154
6.2.6.5.
Application
1:
Computation of
expected volatility
.......... 155
6.2.6.6.
Application
2:
Computation of the
variance call
............. 156
6.3.
Summary
........................ 156
References
.......................... 157
7.
YIELD CURVE MODELING
159
7.1.
Model Typology
.................... 159
7.1.1.
Short rates
................... 159
7.1.2.
Market
(LIBOR
and swap rate) models
... 160
7.1.3.
Markov functional models
.......... 161
Contents xix
7.2. Heath-Jarrow-Morton
Framework
.......... 163
7.2.1.
Philosophy
................... 163
7.2.2.
Forward bond volatility and drift
...... 164
7.3.
Short Rate Models
.................. 165
7.3.1.
HW
1,2,...
,nF
................. 165
7.3.1.1.
Diffusion equation
.......... 165
7.3.1.2.
Model s calibration
......... 167
7.3.1.3.
Pricing of caplets
.......... 167
7.3.1.4.
Pricing of swaptions
......... 168
7.3.1.5.
Example of calibration of the
model
................. 169
7.3.2.
Cox-Ingersoll-Ross model
.......... 170
7.3.2.1.
Diffusion equation
.......... 170
7.3.2.2.
Reconstruction formulae
...... 170
7.3.2.3.
Remark
............... 171
7.3.3.
Black-Karasinski model
............ 172
7.3.3.1.
Diffusion equation
.......... 172
7.3.3.2.
Remarks
............... 172
7.4.
Market Model (BGM)
................ 173
7.4.1.
Motivations
.................. 173
7.4.2.
Diffusion
.................... 173
7.4.3.
Interpolation
.................. 175
7.4.4.
Handling drift
................. 177
7.4.5.
Calibration: Relation
vol
Swap
voi Fra .
. . 178
7.5.
Extension to Smile
.................. 180
7.5.1.
Short-rate model extension and Cheyette
. . 180
7.5.1.1.
Quadratic Gaussian model
..... 180
7.5.1.2.
Cheyette model
........... 181
7.5.1.3.
Swaption pricing approximation in
Cheyette
............... 182
7.5.2.
BGM extension: constant elasticity of
variance (CEV) (Cox and Ross,
1976),
SFRM
..................... 183
7.5.3.
Stochastic volatility with BGM models
... 184
7.6.
Summary
........................ 184
References
.......................... 186
xx
Global
Derivatives:
Products,
Theory and Practice
8.
INFLATION
187
8.1.
Vanilla Products
.................... 187
8.1.1.
History of inflation markets
.......... 187
8.1.2.
Swap: YoY, zero coupon and bond
...... 188
8.1.3.
Option: Cap, floor and swaption
....... 189
8.1.4.
Pricing example
................ 191
8.2.
Vanilla Product Pricing
................ 192
8.2.1.
Presentation
.................. 192
8.2.2.
Curve modeling
................ 193
8.2.3.
Convexity adjustment
............. 194
8.3.
Seasonality
....................... 194
8.3.1.
Motivations and static seasonality
modeling
.................... 194
8.3.2.
Parametric estimation of seasonality
..... 198
8.3.3.
Parametric vs. non-parametric
........ 200
8.3.4.
Pricing impact on various inflation linked
derivatives
................... 205
8.4.
Hybrid model
..................... 207
8.4.1.
Jarrow-Yildirim model
............ 207
8.4.2.
Mercurio
model
................ 210
8.4.3.
Market model
................. 213
8.4.4.
Index equity model
.............. 218
8.5.
Summary
........................ 219
References
.......................... 219
9.
HYBRID MODELS
221
9.1.
Basis Hybrid
...................... 221
9.1.1.
Bermuda option
................ 222
9.1.2.
Model
...................... 222
9.1.2.1.
Forward forex rate
......... 222
9.1.2.2.
Basis margin
............. 225
9.2.
Forex Hybrids
..................... 226
9.2.1.
Market, products and models
......... 226
9.2.2.
Short rates model
............... 228
9.2.2.1.
Theoretical model
.......... 228
Contents xxi
9.2.2.2.
Underlying future price
....... 229
9.2.2.3.
Implementation details
....... 230
9.2.2.4.
Basis curves
............. 232
9.2.2.5.
Smile issue
.............. 233
9.2.3.
LIBOR
market model
............. 235
9.2.3.1.
Diffusion overview
.......... 235
9.2.3.2.
Pricing method
........... 236
9.2.4.
Equity hybrids
................. 237
9.2.5.
Credit hybrids
................. 238
9.2.6.
Alternative structured products
....... 240
9.3.
Summary
........................ 240
References
.......................... 241
10.
PRODUCT CATALOG AND USAGE
243
10.1.
Typology
........................ 243
10.1.1.
Investment vs. hedging
........... 243
10.1.2.
Investment products: high-risk products
. 245
10.1.2.1.
High-coupon strategy
...... 245
10.1.2.2.
Yield curve slope strategy
. . . 245
10.1.2.3.
Callability
............ 245
10.1.2.4.
Bet strategy: corridor and
digital
.............. 245
10.1.2.5.
Quanto
strategy
......... 245
10.1.2.6.
Currency convergence trade
. . 246
10.1.2.7.
Hedging products: low
premium
............. 246
10.1.2.8.
Zero-premium strategy
..... 246
10.1.2.9.
Customized products
...... 247
10.1.2.10.
Barrier options
......... 247
10.1.3.
Product typology
.............. 248
10.2.
Products Catalog
................... 248
10.2.1.
European options
.............. 248
10.2.2.
Asian options
................ 250
10.2.3.
Hawaiian options
.............. 253
10.2.4.
Barrier options
............... 253
10.2.5.
Lookback
and extensions
.......... 254
xxii
Global
Derivatives:
Products, Theory and Practice
10.2.6.
PNL and passport options
......... 254
10.2.7.
Simple correlation/multi-asset options
. . 255
10.2.8.
Option on options
.............. 256
10.2.9.
Chooser options
............... 256
10.3.
Equity Derivatives
................... 257
10.3.1.
Complex correlation/multi-asset options
. 257
10.4.
Exotic Interest Rates Products
............ 262
10.4.1.
Averaging amortizing compounding/
accreting swap
................ 262
10.4.2.
Autocap, chooser cap, flexi cap
...... 262
10.4.3.
Callable reverse floater
........... 263
10.4.4.
Target redemption note (TARN)
..... 264
10.4.5.
Callable snowball
.............. 270
10.4.6.
Callable spread options
........... 273
10.4.7.
New types of underlying and options
. . . 273
10.4.8.
Management of a trading book
...... 273
10.4.9.
Risk class
.................. 274
10.4.9.1.
Interest rate risk
......... 274
10.4.9.2.
Volatility risk
.......... 274
10.4.9.3.
Basis risk
............. 274
10.4.9.4.
Smile
............... 274
10.4.9.5.
Correlation
............ 275
10.4.9.6.
Foreign exchange
........ 275
10.4.10.
Risk management
.............. 275
10.4.10.1.
Delta, Gamma,
Vega
hedging
. 276
10.4.11.
PNL explanations (Greeks)
........ 276
10.5.
Summary
........................ 276
References
.......................... 276
11.
THIRD GENERATION TRADING
SYSTEM AND ITS UNDERMINING
COPERNICAN REVOLUTION
279
11.1.
The New Generation of Trading Systems
...... 279
11.2.
Motivation for a Generic Pricer
........... 281
11.2.1.
Product innovation
............. 281
11.2.2.
Reactivity, flexibility and efficiency
.... 282
Contents xxiii
11.2.3.
Maintenance
and evolution
......... 283
11.2.4.
Front to back, enterprise wide
....... 283
11.3.
Example of an Architecture
............. 284
11.3.1.
Price-it®, the Pricing Partners generic
pricer solution
................ 284
11.3.2.
Cash flows vs. events
............ 285
11.3.3.
Decomposition: security, model and
numerical methods
............. 286
11.3.4.
Critical tasks for a generic pricer
..... 287
11.3.5.
Parsing system and financial language
. . 288
11.3.5.1.
Interest of
a meta
language
. . . 288
11.3.5.2.
Description of the cash flows
with
a meta
language
...... 288
11.3.5.3.
Referencing
........... 292
11.3.5.4.
Components of the
meta
language: Functions and
operators
............. 293
11.3.5.5.
Standard programming
operators
............. 294
11.3.5.6.
Financial operators
....... 294
11.3.5.7.
Parsing the grammar and
creating a syntax
........ 296
11.3.5.8.
Example of table of cash flows
in
a meta
language
....... 298
11.3.5.9.
Split between models and
numerical methods
....... 299
11.3.5.10.
Generic code and design
.... 300
11.3.5.11.
Split between models and
calibration
............ 300
A. TECHNICAL TOOLBOX
303
A.I. Stochastic Calculus
.................. 303
A.I.I.
Ito
formula
.................. 303
A.1.2. Girsanov theorem
.............. 304
A.1.3. Feynman-Kac
................ 305
A.1.4. Tanaka and local time
........... 307
xxiv
Global
Derivatives:
Products,
Theory and Practice
A.I.
5.
Markov property
.............. 309
A.1.6. Risk neutral and numeraire
........ 310
A.1.7. Copula
.................... 313
A.2. Econometrics
..................... 315
A.2.1. Time series
................. 315
A.2.2. GARCH and Nelson result
......... 316
A.3. Numerical Analysis
.................. 318
A.3.1. PCA, Cholesky
............... 318
A.3.2. Minimizing the errors: Newton-Raphson
search
.................... 320
A.3.3. Optimizer: BFGS, conjugate and steepest
gradient
................... 322
A.4. Expansion Technique
................. 326
A.
4.1.
Perturbation theory
............. 326
A.4.2. Taylor series with Malliavin weights
.... 327
A.4.3. Singular perturbation and the WKB
expansion
.................. 328
A.4.4. Spectral expansion
............. 329
A.4.5. Gram Charlier/Edgeworth
......... 332
ΑΑδ.Ι.
Cumulants............
332
A.4.5.2. The
cumulant
modifying
operator (CMO)
......... 333
A.4.5.3. Application to pricing
...... 333
A.
5.
Summary
........................ 334
References
.......................... 335
B. MONTE CARLO
337
B.I. Monte Carlo
...................... 337
B.I.I. Theoretical background: central limit
theorem
................... 337
B.I.
2.
Pricing European securities using Monte
Carlo
..................... 338
B.1.3. Random numbers and quasi Monte Carlo
. 339
8.1.3.1.
Box-Muller............
339
6.1.3.2.
Cumulated density inverse
. . . 339
B.1.4. Notion of discrepancy
............ 340
Contents xxv
В.
1.5.
Examples of random numbers generation
. 341
B.l.ö.l.
The combined MRG of order
5 . 341
B.I.
6.
Examples of quasi-random numbers
generation
.................. 342
В. 1.6.1.
Halton
quasi-random
sequences
............. 342
B.I.
6.2.
Square quasi-random
sequences
............. 343
B.
1.6.3.
Sobol
sequence
.......... 344
B.I.?. Variance reduction techniques
....... 344
B.I.
7.1.
Control
variate
......... 344
6.1.7.2.
Importance sampling
...... 345
B.l.7.3. Antithetic control
........ 347
B.1.8. Computation of Greeks in Monte Carlo
. . 348
В. 1.8.1.
Finite differences
........ 348
6.1.8.2.
Path-wise method
........ 349
B.l.8.3. Likelihood ratio method
.... 350
6.1.8.4.
Malliavin calculus
........ 351
8.1.8.5.
Stochastic analysis
....... 351
B.1.9. Extension of Monte Carlo methods for
American-style securities pricing
...... 352
B.l.9.1. Andersen method
........ 353
B.I.
9.2.
Longstaff-Schwartz method
. . 356
B.2. Summary
........................ 357
References
.......................... 357
С
TREE AND PDE METHODS
359
C.I. Trees
.......................... 359
C.I.I. Arrow Debreu prices
............ 359
C.1.2. Computing probabilities in a generated
trees
..................... 359
C.1.3. Geometry and boundaries
......... 364
C.1.4. Smoothing
.................. 366
C.2. Partial Differential Equations
............ 366
C.2.1. Motivation
.................. 366
C.2.2. Finite difference
............... 368
xxvi
Global
Derivatives:
Products,
Theory and Practice
C.2.3. Crank Nicholson
.............. 370
C.2.4. Stability and robustness
.......... 370
C.2.5. Finite differences schemes for
multi-dimensional PDE: alternating
direction iterative (ADI)
.......... 372
C.2.6. Finite elements
............... 376
C.3. Summary
........................ 378
References
.......................... 378
INDEX
379
|
| adam_txt |
CONTENTS
PREFACE v
ABOUT THE AUTHORS
Іх
1.
STANDARD PRODUCTS AND MARKETS
1
1.1.
Introduction to Financial Markets
. 1
1.1.1.
Definition of financial markets
. 1
1.1.2.
The different derivatives markets
. 2
1.1.3.
Importance of the derivatives
. 3
1.1.4.
Cash or spot vs. derivatives markets
. 5
1.1.5.
History of financial markets
. 6
1.1.6.
Listed markets vs. OTC markets
. 8
1.1.7.
Shares and dividends
. 8
1.1.8.
Typology of the markets participants
. 10
1.2.
Presentation of the Trading Room and Group
Description
. 11
1.2.1.
Different functionality of the trading room
. 11
1.2.2.
Job description
. 11
1.2.2.1.
Trader
. 11
1.2.2.2.
Sales/originators/structurors
. 12
1.2.2.3.
Quant/IT/analyst support
. 12
1.2.2
A. Middle office/back office support
. 12
1.3.
Flow Business, Prop Trading and Exotic
. 13
xiv
Global
Derivatives:
Products,
Theory and Practice
1.3.1.
Definition
. 13
1.3.2.
Hedge fund business
. 13
1.3.3.
Key differences
. 13
1.3.4.
Market making
. 14
1.3.5.
ECN and electronic trading platform
. 14
1.4.
Ethic and Deontology
. 15
1.4.1.
History
. 15
1.4.1.1.
Barings
. 15
1.4.1.2.
ENRON
. 16
1.4.1.3.
LTCM
. 17
1.4.2.
Insider trading
. 18
1.4.3.
Money laundering
. 19
1.5.
Summary
. 19
References
. 20
2.
THE VANILLA PRODUCTS
21
2.1.
Interest and Usage of Products
. 22
2.1.1.
Interest and usage of products
. 22
2.1.2.
Derivatives description
. 22
2.1.3.
The hedging purpose
. 23
2.1.3.1.
Hedging with forward contract
. 23
2.1.3.2.
Hedging with options
. 24
2.1.4.
The speculation
. 25
2.1.5.
The arbitrage
. 26
2.2.
Pricing of Future Contract
. 27
2.2.1.
Trading futures: Margin call and trading
account
. 27
2.2.1.1.
The future contract
. 27
2.2.1.2.
Product specification
. 28
2.2.2.
Futures vs. forward
. 30
2.2.3.
Forward and futures prices
. 30
2.2.3.1.
Forward pricing
. 30
2.2.3.2.
Futures prices
. 31
2.3.
Options
. 33
2.3.1.
Definition and features
. 33
2.3.2.
Call-put parity
. 35
Contents xv
2.3.3. Option
strategies: call, put, straddle,
strangle, spread and butterfly
. 35
2.3.3.1.
Call/put option
. 36
2.3.3.2.
Straddle
. 37
2.3.3.3.
Strangle
. 38
2.3.3.4.
Butterfly
. 39
2.3.4.
Warrants
. 40
2.4.
Summary
. 41
References
. 42
3.
INTRODUCTION TO FINANCIAL MODELING
43
3.1.
A Bit of History
. 43
3.2.
Usage of Models
. 48
3.2.1.
Risk categories
. 48
3.2.1.1.
Market risk
. 48
3.2.1.2.
Counterparty risk
. 50
3.2.1.3.
Operational risk
. 50
3.2.1.4.
Model risk
. 52
3.2.2.
What are models for?
. 53
3.2.2.1.
As a predictor
. 53
3.2.2.2.
As an "interpolator" or
"extrapolator"
. 53
3.2.3.
Simple versus complicated models
. 55
3.2.4.
Warnings
. 56
3.2.5.
Special warnings: calibration issues
. 58
3.3.
Reasonable Mathematical Basis for Financial
Modeling
. 59
3.3.1.
Modeling framework
. 59
3.3.1.1.
Words on probability
. 60
3.3.1.2.
Types of computations
. 61
3.3.1.3.
Ito
processes and Ito/Doblin
formula
. 62
3.3.1.4.
Usage of Brownian motion
. 64
3.3.2.
Risk neutral probability
. 67
3.3.2.1.
Example of the one factor case
. . . 67
3.3.2.2.
The
η
factor case
. 69
xvi
Global
Derivatives:
Products,
Theory and Practice
3.3.2.3.
The two currency case
. 73
3.4.
Summary
. 77
References
. 78
4.
THE BLACK-SCHOLES MODEL
79
4.1.
Model History
. 79
4.2.
Initial Problems
. 80
4.3.
Model Hypothesis
. 82
4.3.1. Lognormal
distribution and constant
volatility
. 82
4.3.2.
Assumptions
. 82
4.4.
Black-Scholes Partial Differential Equation
. 83
4.5.
Black-Scholes Formulae for Call and Put Options
. 85
4.6.
Implied Volatility and Smile
. 86
4.7.
Hedging Strategies
. 86
4.7.1.
Naked and cover positions
. 87
4.7.2.
Delta hedging
. 87
4.7.3.
Stop and loss strategy
. 87
4.8.
The Derivative Function of the Price or Greeks
. . 90
4.8.1.
Delta
. 90
4.8.2.
Theta
. 91
4.8.3.
Gamma
. 92
4.8.4. Vega. 92
4.9.
Black-Scholes Robustness
. 94
4.10.
Black-Scholes Extensions
. 95
4.10.1.
Volatility: deterministic function of time
. . 95
4.10.2.
Dividend
. 95
4.10.3.
Normal and shifted
lognormal
models
. 96
4.11.
Summary
. 97
References
. 98
5.
FIXED INCOME BASIS
99
5.1
Simple Instruments
. 99
5.1.1.
Markets conventions
. 99
5.1.2.
LIBOR
rates
. 100
5.1.3.
Repo
rate
. 101
Contents xvii
5.1.4.
Duration
. 102
5.2
Bootstrapping and Curve Fitting
. 104
5.3
Introduction to Swaps
. 105
5.3.1.
Vanilla swaps
. 105
5.3.2.
Cross-currency swaps
. 106
5.3.3.
Forward starting swaps
. 109
5.3.4.
LIBOR-in-arrears swaps
. 110
5.3.5.
CMT and CMS swaps
. 110
5.4
Convexity Adjustment
.
Ill
5.4.1.
Convexity correction
.
Ill
5.4.2.
LIBOR-in-arrears swap
. 112
5.4.3.
CMS/CMT/spread lock
. 114
5.4.4.
Replication
. 116
5.5
Vanilla Interest Rate Options
. 120
5.5.1.
Interest rate caps and floors
. 120
5.5.2.
European swaptions
. 122
5.5.3.
Spread options
. 123
5.6
Summary
. 123
References
. 124
6.
SMILE MODELING
125
6.1.
Smile and Digital Models
. 125
6.1.1.
Target market
. 126
6.2.
Smile Models (Basic European Models)
. 127
6.2.1.
The Merton model
. 128
6.2.1.1.
Influence of the jumps (a la Merton)
on the smile
. 129
6.2.2.
Local volatility models (a la Dupire)
. 129
6.2.3.
The CEV model
. 131
6.2.3.1.
Extrapolation issues
. 133
6.2.3.2.
Robustness issues
. 133
6.2.4.
Stochastic volatility models
. 134
6.2.4.1.
An analytical formula
. 135
6.2.4.2.
Heston model and Fourier
transform
. 136
xviii
Global
Derivatives:
Products,
Theory and Practice
6.2.4.3.
Lewis model and the preservative
approach
. 136
6.2.4.4.
SABR model and link to
Riemannian geometry
. 138
6.2.5.
Connection between the SABR and the
"complex" BS models
. 142
6.2.5.1.
Expected local time and vanilla
option prices
. 142
6.2.5.2.
Expected local time and probability
density
. 144
6.2.5.3.
Explicit computation of the local
time for stochastic models
. 145
6.2.5.4.
Fast computation of the SABR
stochastic integral and connection
with BS model
. 146
6.2.5.5.
Application to CMS replication
pricing
. 148
6.2.6.
Volatility and variance swap: Log and
parabola contracts
. 152
6.2.6.1.
Contract definition
. 152
6.2.6.2.
Replication strategy and pricing
. . 153
6.2.6.3.
Variance swap in the Heston
model
. 154
6.2.6.4.
Variance swap in the mean
reverting
lognormal
model
. 154
6.2.6.5.
Application
1:
Computation of
expected volatility
. 155
6.2.6.6.
Application
2:
Computation of the
variance call
. 156
6.3.
Summary
. 156
References
. 157
7.
YIELD CURVE MODELING
159
7.1.
Model Typology
. 159
7.1.1.
Short rates
. 159
7.1.2.
Market
(LIBOR
and swap rate) models
. 160
7.1.3.
Markov functional models
. 161
Contents xix
7.2. Heath-Jarrow-Morton
Framework
. 163
7.2.1.
Philosophy
. 163
7.2.2.
Forward bond volatility and drift
. 164
7.3.
Short Rate Models
. 165
7.3.1.
HW
1,2,.
,nF
. 165
7.3.1.1.
Diffusion equation
. 165
7.3.1.2.
Model's calibration
. 167
7.3.1.3.
Pricing of caplets
. 167
7.3.1.4.
Pricing of swaptions
. 168
7.3.1.5.
Example of calibration of the
model
. 169
7.3.2.
Cox-Ingersoll-Ross model
. 170
7.3.2.1.
Diffusion equation
. 170
7.3.2.2.
Reconstruction formulae
. 170
7.3.2.3.
Remark
. 171
7.3.3.
Black-Karasinski model
. 172
7.3.3.1.
Diffusion equation
. 172
7.3.3.2.
Remarks
. 172
7.4.
Market Model (BGM)
. 173
7.4.1.
Motivations
. 173
7.4.2.
Diffusion
. 173
7.4.3.
Interpolation
. 175
7.4.4.
Handling drift
. 177
7.4.5.
Calibration: Relation
vol
Swap
voi Fra .
. . 178
7.5.
Extension to Smile
. 180
7.5.1.
Short-rate model extension and Cheyette
. . 180
7.5.1.1.
Quadratic Gaussian model
. 180
7.5.1.2.
Cheyette model
. 181
7.5.1.3.
Swaption pricing approximation in
Cheyette
. 182
7.5.2.
BGM extension: constant elasticity of
variance (CEV) (Cox and Ross,
1976),
SFRM
. 183
7.5.3.
Stochastic volatility with BGM models
. 184
7.6.
Summary
. 184
References
. 186
xx
Global
Derivatives:
Products,
Theory and Practice
8.
INFLATION
187
8.1.
Vanilla Products
. 187
8.1.1.
History of inflation markets
. 187
8.1.2.
Swap: YoY, zero coupon and bond
. 188
8.1.3.
Option: Cap, floor and swaption
. 189
8.1.4.
Pricing example
. 191
8.2.
Vanilla Product Pricing
. 192
8.2.1.
Presentation
. 192
8.2.2.
Curve modeling
. 193
8.2.3.
Convexity adjustment
. 194
8.3.
Seasonality
. 194
8.3.1.
Motivations and static seasonality
modeling
. 194
8.3.2.
Parametric estimation of seasonality
. 198
8.3.3.
Parametric vs. non-parametric
. 200
8.3.4.
Pricing impact on various inflation linked
derivatives
. 205
8.4.
Hybrid model
. 207
8.4.1.
Jarrow-Yildirim model
. 207
8.4.2.
Mercurio
model
. 210
8.4.3.
Market model
. 213
8.4.4.
Index equity model
. 218
8.5.
Summary
. 219
References
. 219
9.
HYBRID MODELS
221
9.1.
Basis Hybrid
. 221
9.1.1.
Bermuda option
. 222
9.1.2.
Model
. 222
9.1.2.1.
Forward forex rate
. 222
9.1.2.2.
Basis margin
. 225
9.2.
Forex Hybrids
. 226
9.2.1.
Market, products and models
. 226
9.2.2.
Short rates model
. 228
9.2.2.1.
Theoretical model
. 228
Contents xxi
9.2.2.2.
Underlying future price
. 229
9.2.2.3.
Implementation details
. 230
9.2.2.4.
Basis curves
. 232
9.2.2.5.
Smile issue
. 233
9.2.3.
LIBOR
market model
. 235
9.2.3.1.
Diffusion overview
. 235
9.2.3.2.
Pricing method
. 236
9.2.4.
Equity hybrids
. 237
9.2.5.
Credit hybrids
. 238
9.2.6.
Alternative structured products
. 240
9.3.
Summary
. 240
References
. 241
10.
PRODUCT CATALOG AND USAGE
243
10.1.
Typology
. 243
10.1.1.
Investment vs. hedging
. 243
10.1.2.
Investment products: high-risk products
. 245
10.1.2.1.
High-coupon strategy
. 245
10.1.2.2.
Yield curve slope strategy
. . . 245
10.1.2.3.
Callability
. 245
10.1.2.4.
Bet strategy: corridor and
digital
. 245
10.1.2.5.
Quanto
strategy
. 245
10.1.2.6.
Currency convergence trade
. . 246
10.1.2.7.
Hedging products: low
premium
. 246
10.1.2.8.
Zero-premium strategy
. 246
10.1.2.9.
Customized products
. 247
10.1.2.10.
Barrier options
. 247
10.1.3.
Product typology
. 248
10.2.
Products Catalog
. 248
10.2.1.
European options
. 248
10.2.2.
Asian options
. 250
10.2.3.
Hawaiian options
. 253
10.2.4.
Barrier options
. 253
10.2.5.
Lookback
and extensions
. 254
xxii
Global
Derivatives:
Products, Theory and Practice
10.2.6.
PNL and passport options
. 254
10.2.7.
Simple correlation/multi-asset options
. . 255
10.2.8.
Option on options
. 256
10.2.9.
Chooser options
. 256
10.3.
Equity Derivatives
. 257
10.3.1.
Complex correlation/multi-asset options
. 257
10.4.
Exotic Interest Rates Products
. 262
10.4.1.
Averaging amortizing compounding/
accreting swap
. 262
10.4.2.
Autocap, chooser cap, flexi cap
. 262
10.4.3.
Callable reverse floater
. 263
10.4.4.
Target redemption note (TARN)
. 264
10.4.5.
Callable snowball
. 270
10.4.6.
Callable spread options
. 273
10.4.7.
New types of underlying and options
. . . 273
10.4.8.
Management of a trading book
. 273
10.4.9.
Risk class
. 274
10.4.9.1.
Interest rate risk
. 274
10.4.9.2.
Volatility risk
. 274
10.4.9.3.
Basis risk
. 274
10.4.9.4.
Smile
. 274
10.4.9.5.
Correlation
. 275
10.4.9.6.
Foreign exchange
. 275
10.4.10.
Risk management
. 275
10.4.10.1.
Delta, Gamma,
Vega
hedging
. 276
10.4.11.
PNL explanations (Greeks)
. 276
10.5.
Summary
. 276
References
. 276
11.
THIRD GENERATION TRADING
SYSTEM AND ITS UNDERMINING
COPERNICAN REVOLUTION
279
11.1.
The New Generation of Trading Systems
. 279
11.2.
Motivation for a Generic Pricer
. 281
11.2.1.
Product innovation
. 281
11.2.2.
Reactivity, flexibility and efficiency
. 282
Contents xxiii
11.2.3.
Maintenance
and evolution
. 283
11.2.4.
Front to back, enterprise wide
. 283
11.3.
Example of an Architecture
. 284
11.3.1.
Price-it®, the Pricing Partners' generic
pricer solution
. 284
11.3.2.
Cash flows vs. events
. 285
11.3.3.
Decomposition: security, model and
numerical methods
. 286
11.3.4.
Critical tasks for a generic pricer
. 287
11.3.5.
Parsing system and financial language
. . 288
11.3.5.1.
Interest of
a meta
language
. . . 288
11.3.5.2.
Description of the cash flows
with
a meta
language
. 288
11.3.5.3.
Referencing
. 292
11.3.5.4.
Components of the
meta
language: Functions and
operators
. 293
11.3.5.5.
Standard programming
operators
. 294
11.3.5.6.
Financial operators
. 294
11.3.5.7.
Parsing the grammar and
creating a syntax
. 296
11.3.5.8.
Example of table of cash flows
in
a meta
language
. 298
11.3.5.9.
Split between models and
numerical methods
. 299
11.3.5.10.
Generic code and design
. 300
11.3.5.11.
Split between models and
calibration
. 300
A. TECHNICAL TOOLBOX
303
A.I. Stochastic Calculus
. 303
A.I.I.
Ito
formula
. 303
A.1.2. Girsanov theorem
. 304
A.1.3. Feynman-Kac
. 305
A.1.4. Tanaka and local time
. 307
xxiv
Global
Derivatives:
Products,
Theory and Practice
A.I.
5.
Markov property
. 309
A.1.6. Risk neutral and numeraire
. 310
A.1.7. Copula
. 313
A.2. Econometrics
. 315
A.2.1. Time series
. 315
A.2.2. GARCH and Nelson result
. 316
A.3. Numerical Analysis
. 318
A.3.1. PCA, Cholesky
. 318
A.3.2. Minimizing the errors: Newton-Raphson
search
. 320
A.3.3. Optimizer: BFGS, conjugate and steepest
gradient
. 322
A.4. Expansion Technique
. 326
A.
4.1.
Perturbation theory
. 326
A.4.2. Taylor series with Malliavin weights
. 327
A.4.3. Singular perturbation and the WKB
expansion
. 328
A.4.4. Spectral expansion
. 329
A.4.5. Gram Charlier/Edgeworth
. 332
ΑΑδ.Ι.
Cumulants.
332
A.4.5.2. The
cumulant
modifying
operator (CMO)
. 333
A.4.5.3. Application to pricing
. 333
A.
5.
Summary
. 334
References
. 335
B. MONTE CARLO
337
B.I. Monte Carlo
. 337
B.I.I. Theoretical background: central limit
theorem
. 337
B.I.
2.
Pricing European securities using Monte
Carlo
. 338
B.1.3. Random numbers and quasi Monte Carlo
. 339
8.1.3.1.
Box-Muller.
339
6.1.3.2.
Cumulated density inverse
. . . 339
B.1.4. Notion of discrepancy
. 340
Contents xxv
В.
1.5.
Examples of random numbers generation
. 341
B.l.ö.l.
The combined MRG of order
5 . 341
B.I.
6.
Examples of quasi-random numbers
generation
. 342
В. 1.6.1.
Halton
quasi-random
sequences
. 342
B.I.
6.2.
Square quasi-random
sequences
. 343
B.
1.6.3.
Sobol
sequence
. 344
B.I.?. Variance reduction techniques
. 344
B.I.
7.1.
Control
variate
. 344
6.1.7.2.
Importance sampling
. 345
B.l.7.3. Antithetic control
. 347
B.1.8. Computation of Greeks in Monte Carlo
. . 348
В. 1.8.1.
Finite differences
. 348
6.1.8.2.
Path-wise method
. 349
B.l.8.3. Likelihood ratio method
. 350
6.1.8.4.
Malliavin calculus
. 351
8.1.8.5.
Stochastic analysis
. 351
B.1.9. Extension of Monte Carlo methods for
American-style securities pricing
. 352
B.l.9.1. Andersen method
. 353
B.I.
9.2.
Longstaff-Schwartz method
. . 356
B.2. Summary
. 357
References
. 357
С
TREE AND PDE METHODS
359
C.I. Trees
. 359
C.I.I. Arrow Debreu prices
. 359
C.1.2. Computing probabilities in a generated
trees
. 359
C.1.3. Geometry and boundaries
. 364
C.1.4. Smoothing
. 366
C.2. Partial Differential Equations
. 366
C.2.1. Motivation
. 366
C.2.2. Finite difference
. 368
xxvi
Global
Derivatives:
Products,
Theory and Practice
C.2.3. Crank Nicholson
. 370
C.2.4. Stability and robustness
. 370
C.2.5. Finite differences schemes for
multi-dimensional PDE: alternating
direction iterative (ADI)
. 372
C.2.6. Finite elements
. 376
C.3. Summary
. 378
References
. 378
INDEX
379 |
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| spelling | Global derivatives products, theory and practice ed.: Eric Benhamou Singapore [u.a.] World Scientific Publ. 2007 XXVI, 384 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finanzderivat / Finanzinnovation / Finanzmarkt / Financial Futures / Hedging Lehrbuch / Textbook - 28 Mathematisches Modell Derivative securities Mathematical models Structured notes (Securities) Mathematical models Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Derivat Wertpapier (DE-588)4381572-8 s b DE-604 Benhamou, Eric Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015820737&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Global derivatives products, theory and practice Finanzderivat / Finanzinnovation / Finanzmarkt / Financial Futures / Hedging Lehrbuch / Textbook - 28 Mathematisches Modell Derivative securities Mathematical models Structured notes (Securities) Mathematical models Derivat Wertpapier (DE-588)4381572-8 gnd |
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| title | Global derivatives products, theory and practice |
| title_auth | Global derivatives products, theory and practice |
| title_exact_search | Global derivatives products, theory and practice |
| title_exact_search_txtP | Global derivatives products, theory and practice |
| title_full | Global derivatives products, theory and practice ed.: Eric Benhamou |
| title_fullStr | Global derivatives products, theory and practice ed.: Eric Benhamou |
| title_full_unstemmed | Global derivatives products, theory and practice ed.: Eric Benhamou |
| title_short | Global derivatives |
| title_sort | global derivatives products theory and practice |
| title_sub | products, theory and practice |
| topic | Finanzderivat / Finanzinnovation / Finanzmarkt / Financial Futures / Hedging Lehrbuch / Textbook - 28 Mathematisches Modell Derivative securities Mathematical models Structured notes (Securities) Mathematical models Derivat Wertpapier (DE-588)4381572-8 gnd |
| topic_facet | Finanzderivat / Finanzinnovation / Finanzmarkt / Financial Futures / Hedging Lehrbuch / Textbook - 28 Mathematisches Modell Derivative securities Mathematical models Structured notes (Securities) Mathematical models Derivat Wertpapier Lehrbuch |
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