Paul Wilmott introduces quantitative finance:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2008
|
| Ausgabe: | 2. ed., reprint. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIV, 695 S. Ill., graph. Darst. CD-ROM (12 cm) |
| ISBN: | 9780470319581 |
Internformat
MARC
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| 245 | 1 | 0 | |a Paul Wilmott introduces quantitative finance |
| 246 | 1 | 3 | |a Quantitative finance |
| 250 | |a 2. ed., reprint. | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2008 | |
| 300 | |a XXIV, 695 S. |b Ill., graph. Darst. |e CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804138057396387840 |
|---|---|
| adam_text | contents
Preface
xxiii
1
Products
and Markets: Equities, Commodities, Exchange Rates,
Forwards and Futures
1
1.1
Introduction
2
1.2
Equities
2
1.2.1
Dividends
7
1.2.2
Stocksplits
8
1.3
Commodities
9
1.4
Currencies
9
1.5
Indices
11
1.6
The time value of money
11
1.7
Fixed-income securities
17
1.8
Inflation-proof bonds
17
1.9
Forwards and futures
19
1.9.1
A first example of no arbitrage
20
1.10
More about futures
22
1.10.1
Commodity futures
23
1.10.2
FX futures
23
1.10.3
Index futures
24
1.11
Summary
24
27
28
28
33
34
34
39
39
39
40
41
Derivatives
2.1
Introduction
2.2
Options
2.3
Definition of common terms
2.4
Payoff diagrams
2.4.1
Other representations of value
2.5
Writing options
2.6
Margin
2.7
Market conventions
2.8
The value of the option before expiry
2.9
Factors affecting derivative prices
VÉii contents
2.10
Speculation and gearing
42
2.11
Early exercise
44
2.12
Put-call parity
44
2.13
Binaries or digitals
47
2.14
Bull and bear spreads
48
2.15
Straddles and strangles
50
2.16
Risk reversal 52
2.17
Butterflies and condors
53
2.18
Calendar spreads
53
2.19
LEAPS and FLEX
55
2.20
Warrants
55
2.21
Convertible bonds
55
2.22
Over the counter options
56
2.23
Summary
57
3
The Binomial Model
59
3.1
Introduction
60
3.2
Equities can go down as well as up
61
3.3
The option value
63
3.4
Which part of our model didn t we need?
65
3.5
Why should this theoretical price be the market price ?
65
3.5.1
The role of expectations
66
3.6
How did I know to sell of the stock for hedging?
66
3.6.1
The general formula for
Δ
67
3.7
How does this change if interest rates are non-zero?
67
3.8
Is the stock itself correctly priced?
68
3.9
Complete markets
69
3.10
The real and risk-neutral worlds
69
3.10.1
Non-zero interest rates
72
3.11
And now using symbols
73
3.11.1
Average asset change
74
3.11.2
Standard deviation of asset price change
74
3.12
An equation for the value of an option
75
3.12.1
Hedging
75
3.12.2
No arbitrage
76
3.13
Where did the probability
ρ
go?
77
3.14
Counter-intuitive?
77
3.15
The binomial tree
78
3.16
The asset price distribution
78
3.17
Valuing back down the tree
80
3.18
Programming the binomial method
85
3.19
The greeks
86
3.20
Early exercise
88
3.21
The continuous-time limit
90
3.22
Summary
90
contents
ix
4
The Random Behavior of Assets
4.1
Introduction
4.2
The popular forms of analysis
4.3
Why we need a model for randomness: Jensen s inequality
4.4
Similarities between equities, currencies, commodities and indices
4.5
Examining returns
4.6
Timescales
4.6.1
The drift
4.6.2
The volatility
4.7
Estimating volatility
4.8
The random walk on a spreadsheet
4.9
The Wiener process
4.10
The widely accepted model for equities, currencies, commodities and
indices
4.11
Summary
5
Elementary Stochastic Calculus
5.1
Introduction
5.2
A motivating example
5.3
The Markov property
5.4
The martingale property
5.5
Quadratic variation
5.6
Brownian motion
5.7
Stochastic integration
5.8
Stochastic differential equations
5.9
The mean square limit
5.10
Functions of stochastic variables and
Itô s
lemma
5.11
Interpretation of
Itô s
lemma
5.12
Ito
and Taylor
5.13
Ito in
higher dimensions
5.14
Some pertinent examples
5.14.1
Brownian motion with drift
5.14.2
The
lognormal
random walk
5.14.3
A mean-reverting random walk
5.14.4
And another mean-reverting random walk
5.15
Summary
6
The Black-Scholes Model
6.1
Introduction
6.2
A very special portfolio
6.3
Elimination of risk: delta hedging
6.4
No arbitrage
6.5
The Black-Scholes equation
6.6
The Black-Scholes assumptions
6.7
Final conditions
95
96
96
97
99
100
105
107
108
109
109
111
112
115
117
118
118
120
120
120
121
122
123
124
124
127
127
130
130
131
132
134
135
136
139
140
140
142
142
143
145
146
к
contents
6.
б
6.
9
6.
10
6.
.11
6
.12
6.13
6
.14
Options on dividend-paying equities
147
Currency options
147
Commodity options
148
Expectations and Black-Scholes
148
Some other ways of deriving the Black-Scholes equation
149
6.12.1
The martingale approach
149
6.12.2
The binomial model
149
6.12.3
CAPM/utility
149
No arbitrage in the binomial, Black-Scholes and other worlds
150
Forwards and futures
151
6.14.1
Forward contracts
151
6.15
Futures contracts
152
6.15.1
When interest rates are known, forward prices and futures
prices are the same
153
6.16
Options on futures
153
6.17
Summary
153
7
Partial Differential Equations
157
7.1
Introduction
158
7.2
Putting the Black-Scholes equation into historical perspective
158
7.3
The meaning of the terms in the Black-Scholes equation
159
7.4
Boundary and initial/final conditions
159
7.5
Some solution methods
160
7.5.1
Transformation to constant coefficient diffusion equation
160
7.5.2
Green s functions
161
7.5.3
Series solution
161
7.6
Similarity reductions
163
7.7
Other analytical techniques
163
7.8
Numerical solution
164
7.9
Summary
164
8
The Black-Scholes Formulae and the Greeks
169
8.1
Introduction
170
8.2
Derivation of the formulae for calls, puts and simple digitals
170
8.2.1
Formula for a call
175
8.2.2
Formula for a put
179
8.2.3
Formula for a binary call
181
8.2.4
Formula for a binary put
182
8.3
Delta
182
8.4
Gamma
184
8.5
Theta
187
8.6
Speed
187
8.7 Vega 188
8.8
Rho
190
8.9
Implied volatility
191
8.10
A classification of hedging types
194
8.10.1
Why hedge?
194
Contents xi
8.10.2
The two main classifications
8.10.3
Delta hedging
8.10.4
Gamma hedging
8.10.5
Vega
hedging
8.10.6
Static hedging
8.10.7
Margin hedging
8.10.8
Crash (Platinum) hedging
194
195
195
195
195
196
196
8.11
Summary
196
9
Overview of Volatility Modeling
203
9.1
Introduction
204
9.2
The different types of volatility
204
9.2.1
Actual volatility
204
9.2.2
Historical or realized volatility
204
9.2.3
Implied volatility
205
9.2.4
Forward volatility
205
9.3
Volatility estimation by statistical means
205
9.3.1
The simplest volatility estimate: constant volatility/moving
window
205
9.3.2
Incorporating mean reversion
206
9.3.3
Exponentially weighted moving average
206
9.3.4
A simple GARCH model
207
9.3.5
Expected future volatility
207
9.3.6
Beyond close-close estimators: range-based estimation of
volatility
209
9.4
Maximum likelihood estimation
211
9.4.1
A simple motivating example: taxi numbers
211
9.4.2
Three hats
211
9.4.3
The math behind this: find the standard deviation
213
9.4.4
Quants salaries
214
9.5
Skews and smiles
215
9.5.1
Sensitivity of the straddle to skews and smiles
216
9.5.2
Sensitivity of the risk reversal to skews and smiles
216
9.6
Different approaches to modeling volatility
217
9.6.1
To calibrate or not?
217
9.6.2
Deterministic volatility surfaces
218
9.6.3
Stochastic volatility
219
9.6.4
Uncertain parameters
219
9.6.5
Static hedging
220
9.6.6
Stochastic volatility and mean-variance analysis
220
9.6.7
Asymptotic analysis of volatility
220
9.7
The choices of volatility models
221
9.8
Summary
221
10
How to Delta Hedge
225
10.1
Introduction
226
10.2
What if implied and actual volatilities are different?
227
xli
contents
10.3
Implied versus actual, delta hedging but using which volatility?
228
10.4
Case
1:
Hedge with actual volatility,
σ
228
10.5
Case
2:
Hedge with implied volatility,
σ
231
10.5.1
The expected profit after hedging using implied volatility
232
10.5.2
The variance of profit after hedging using implied volatility
233
10.6
Hedging with different volatilities
235
10.6.1
Actual volatility
=
Implied volatility
236
10.6.2
Actual volatility
>
Implied volatility
236
10.6.3
Actual volatility
<
Implied volatility
238
10.7
Pros and cons of hedging with each volatility
238
10.7.1
Hedging with actual volatility
238
10.7.2
Hedging with implied volatility
239
10.7.3
Hedging with another volatility
239
10.8
Portfolios when hedging with implied volatility
239
10.8.1
Expectation
240
10.8.2
Variance
240
10.8.3
Portfolio optimization possibilities
241
10.9
How does implied volatility behave?
241
10.9.1
Sticky strike
242
10.9.2
Sticky delta
242
10.9.3
Time-periodic behavior
243
10.10
Summary
245
11
An Introduction to Exotic and Path-dependent Options
247
11.1
Introduction
248
11.2
Option classification
248
11.3
Time dependence
249
11.4
Cashflows
250
11.5
Path dependence
252
11.5.1
Strong path dependence
252
11.5.2
Weak path dependence
253
11.6
Dimensionality
254
11.7
The order of an option
255
11.8
Embedded decisions
256
11.9
Classification tables
258
11.10
Examples of exotic options
258
11.10.1
Compounds and choosers
258
11.10.2
Range notes
262
11.10.3
Barrier options
264
11.10.4
Asian options
265
11.10.5
Lookback
options
265
11.11
Summary of math/coding consequences
266
11.12
Summary
267
12
Multi-asset Options
271
12.1
Introduction
272
12.2
Multidimensional
lognormal
random walks
272
contents
Xiii
12.3
Measuring correlations
274
12.4
Options on many underlyings
277
12.5
The pricing formula for European non-path-dependent options on
dividend-paying assets
278
12.6
Exchanging one asset for another: a similarity solution
278
12.7
Two examples
280
12.8
Realities of pricing basket options
282
12.8.1
Easy problems
283
12.8.2
Medium problems
283
12.8.3
Hard problems
283
12.9
Realities of hedging basket options
283
12.10
Correlation versus
cointegration
283
12.11
Summary
284
13
Barrier Options
287
13.1
Introduction
288
13.2
Different types of barrier options
288
13.3
Pricing methodologies
289
13.3.1
Monte Carlo simulation
289
13.3.2
Partial differential equations
290
13.4
Pricing barriers in the partial differential equation framework
290
13.4.1
Out barriers
291
13.4.2
In barriers
292
13.5
Examples
293
13.5.1
Some more examples
294
13.6
Other features in barrier-style options
300
13.6.1
Early exercise
300
13.6.2
Repeated hitting of the barrier
301
13.6.3
Resetting of barrier
301
13.6.4
Outside barrier options
301
13.6.5
Soft barriers
301
13.6.6
Parisian options
301
13.7
Market practice: what volatility should I use?
302
13.8
Hedging barrier options
305
13.8.1
Slippage costs
306
13.9
Summary
307
14
Fixed-income Products and Analysis: Yield, Duration and Convexity
319
14.1
Introduction
320
14.2
Simple fixed-income contracts and features
320
14.2.1
The zero-coupon bond
320
14.2.2
The coupon-bearing bond
321
14.2.3
The money market account
321
14.2.4
Floating rate bonds
322
14.2.5
Forward rate agreements
323
14.2.6
Repos
323
14.2.7
STRIPS
324
xiv
contents
14.2.8
Amortization
324
14.2.9
Call provision
324
14.3
International bond markets
324
14.3.1
United States of America
324
14.3.2
United Kingdom
325
14.3.3
Japan
325
14.4
Accrued interest
325
14.5
Day-count conventions
325
14.6
Continuously and discretely compounded interest
326
14.7
Measures of yield
327
14.7.1
Current yield
327
14.7.2
The yield to maturity (YTM) or internal rate of return
(IRR)
327
14.8
The yield curve
329
14.9
Price/yield relationship
329
14.10
Duration
331
14.11
Convexity
333
14.12
An example
335
14.13
Hedging
335
14.14
Time-dependent interest rate
338
14.15
Discretely paid coupons
339
14.16
Forward rates and bootstrapping
339
14.16.1
Discrete data
340
14.16.2
On a spreadsheet
342
14.17
Interpolation
344
14.18
Summary
346
15
Swaps
349
15.1
Introduction
350
15.2
The vanilla interest rate swap
350
15.3
Comparative advantage
351
15.4
The swap curve
353
15.5
Relationship between swaps and bonds
354
15.6
Bootstrapping
355
15.7
Other features of swaps contracts
356
15.8
Other types of swap
357
15.8.1
Basis rate swap
357
15.8.2
Equity swaps
357
15.8.3
Currency swaps
357
15.9
Summary
358
16
One-factor Interest Rate Modeling
359
16.1
Introduction
360
16.2
Stochastic interest rates
361
16.3
The bond pricing equation for the general model
362
16.4
What is the market price of risk?
365
16.5
Interpreting the market price of risk, and risk neutrality
366
16.6
Named models
366
Contents xv
16.
.6.1
Vasicek
16.6.2
Cox, Ingersoll
&
Ross
16,
.6.3
Ho
&
Lee
16.
.6.4
Hull
&
White
366
367
368
369
16.7
Equity and FX forwards and futures when rates are stochastic
369
16.7.1
Forward contracts
369
16.8
Futures contracts
370
16.8.1
The convexity adjustment
371
16.9
Summary
372
17
Yield Curve Fitting
373
17.1
Introduction
374
17.2
Ho
&
Lee
374
17.3
The extended Vasicek model of Hull
&
White
375
17.4
Yield-curve fitting: For and against
376
17.4.1
For
376
17.4.2
Against
376
17.5
Other models
380
17.6
Summary
380
18
Interest Rate Derivatives
383
18.1
Introduction
384
18.2
Callable bonds
384
18.3
Bond options
385
18.3.1
Market practice
387
18.4
Caps and floors
389
18.4.1
Cap/floor parity
389
18.4.2
The relationship between a caplet and a bond option
391
18.4.3
Market practice
391
18.4.4
Collars
391
18.4.5
Step-up swaps, caps and floors
392
18.5
Range notes
392
18.6
Swaptions, captions and
f
loortions
392
18.6.1
Market practice
392
18.7
Spread options
394
18.8
Index amortizing rate swaps
394
18.8.1
Other features in the index amortizing rate swap
396
18.9
Contracts with embedded decisions
397
18.10
Some examples
398
18.11
More interest rate derivatives.
.. 400
18.12
Summary
401
19
The Heath, Jarrow
&
Morton and Brace, Gatarek
&
Musiela Models
403
19.1
Introduction
404
19.2
The forward rate equation
404
19.3
The spot rate process
404
19.3.1
The non-Markov nature of HJM
406
xvi
contents
19.4
The
market
price of risk 406
19.5
Real and risk neutral 407
19.5.1
The relationship between the risk-neutral forward rate drift
and volatility 4°7
19.6
Pricing derivatives 408
19.7
Simulations 408
19.8
Trees 41°
19.9
The Musiela parameterization 411
19.10
Multi-factor
H
JM
411
19.11
Spreadsheet implementation
411
19.12
A simple one-factor example: Ho
&
Lee 412
19.13
Principal Component Analysis 413
19.13.1
The power method 415
19.14
Options on equities, etc.
416
19.15
Non-infinitesimal short rate 416
19.16
The Brace, Gatarek
&
Musiela model 417
19.17
Simulations 419
19.18
PVing the cashflows 419
19.19
Summary 420
20
Investment Lessons from Blackjack and Gambling
423
20.1
Introduction 424
20.2
The rules of blackjack 424
20.3
Beating the dealer 426
20.3.1
Summary of winning at blackjack 427
20.4
The distribution of profit in blackjack 428
20.5
The Kelly criterion
429
20.6
Can you win at roulette? 432
20.7
Horse race betting and no arbitrage 433
20.7.1
Setting the odds in a sporting game 433
20.7.2
The mathematics 434
20.8
Arbitrage
434
20.8.1
How best to profit from the opportunity?
436
20.9
How to bet
436
20.10
Summary
438
21
Portfolio Management
441
21.1
Introduction
442
21.2
Diversification
442
21.2.1
Uncorrelated assets
443
21.3
Modern portfolio theory
445
21.3.1
Including a risk-free investment
447
21.4
Where do I want to be on the efficient frontier?
447
21.5 Markowitz
in practice
450
21.6
Capital Asset Pricing Model
451
21.6.1
The single-index model
451
21.6.2
Choosing the optimal portfolio
453
Contents xvii
Value
at Risk
22.1
Introduction
22.2
Definition of Value at Risk
22.3
VaR for a single asset
22.4
VaR for a portfolio
22.5
VaR for derivatives
22.5.1
The delta approximation
22.5.2
The delta/gamma approximation
22.5.3
Use of valuation models
22.5.4
Fixed-income portfolios
22.6
Simulations
22.6.1
Monte Carlo
22.6.2
Bootstrapping
22.7
Use of VaR as a performance measure
22.8
Introductory Extreme Value Theory
22.8.1
Some EVT results
22.9
Coherence
22.10
Summary
21.7
The multi-index model
454
21.8
Cointegration
454
21.9
Performance measurement
455
21.10
Summary
456
459
460
460
461
463
464
464
464
466
466
466
467
467
468
469
469
470
470
23
Credit Risk
473
23.1
Introduction
474
23.2
The Merton model: equity as an option on a company s assets
474
23.3
Risky bonds
475
23.4
Modeling the risk of default
476
23.5
The
Poisson
process and the instantaneous risk of default
477
23.5.1
A note on hedging
481
23.6
Time-dependent intensity and the term structure of default
481
23.7
Stochastic risk of default
482
23.8
Positive recovery
484
23.9
Hedging the default
485
23.10
Credit rating
486
23.11
A model for change of credit rating
488
23.12
Copulas: pricing credit derivatives with many underlyings
488
23.12.1
The copula function
489
23.12.2
The mathematical definition
489
23.12.3
Examples of copulas
490
23.13
Collateralized debt obligations
490
23.14
Summary
492
24
RiskMetrics and CreditMetrics
495
24.1
Introduction
496
24.2
The RiskMetrics
datasets
496
xviii
contents
24.3
Calculating the parameters the RiskMetrics way
24.3.1
Estimating volatility
24.3.2
Correlation
24.4
The CreditMetrics
dataset
24.4.1
Yield curves
24.4.2
Spreads
24.4.3
Transition matrices
24.4.4
Correlations
24.5
The CreditMetrics methodology
24.6
A portfolio of risky bonds
24.7
CreditMetrics model outputs
24.8
Summary
25
CrashMetrics
25.1
Introduction
25.2
Why do banks go broke?
25.3
Market crashes
25.4
CrashMetrics
25.5
CrashMetrics for one stock
25.6
Portfolio ODtimization and the Platinum hedae
496
497
498
498
499
500
500
500
501
501
502
502
505
506
506
506
507
508
510
25.6.1
Other cost functions
511
25.7
The multi-asset/single-index model
511
25.7.1
Assuming Taylor series for the moment
517
25.8
Portfolio optimization and the Platinum hedge in the multi-asset
model
519
25.8.1
The marginal effect of an asset
520
25.9
The multi-index model
520
25.10
Incorporating time value
521
25.11
Margin calls and margin hedging
522
25.11.1
What is margin?
522
25.11.2
Modeling margin
522
25.11.3
The single-index model
524
25.12
Counterparty risk
524
25.13
Simple extensions to CrashMetrics
524
25.14
The CrashMetrics Index
(CMI)
525
25.15
Summary
526
26
Derivatives
****
Ups
527
26.1
Introduction
528
26.2
Orange County
528
26.3
Proctor and Gamble
529
26.4 Metallgesellschaft 532
26.4.1
Basis risk
533
26.5
Gibson Greetings
533
26.6
Barings
536
26.7
Long-Term
Capital Management
537
26.8
Summary
54O
contents
Xix
27
Overview of Numerical Methods
541
27.1
Introduction
542
27.2
Finite-difference methods
542
27.2.1
Efficiency
543
27.2.2
Program of study
543
27.3
Monte Carlo methods
544
27.3.1
Efficiency
545
27.3.2
Program of study
545
27.4
Numerical integration
546
27.4.1
Efficiency
546
27.4.2
Program of study
546
27.5
Summary
547
28
Finite-difference Methods for One-factor Models
549
28.1
Introduction
550
28.2
Grids
550
28.3
Differentiation using the grid
553
28.4
Approximating
θ
553
28.5
Approximating
Δ
554
28.6
Approximating
Γ
557
28.7
Example
557
28.8
Bilinear interpolation
558
28.9
Final conditions and payoffs
559
28.10
Boundary conditions
560
28.11
The explicit finite-difference method
562
28.11.1
The Black-Scholes equation
565
28.11.2
Convergence of the explicit method
565
28.12
The Code
#1 :
European option
567
28.13
The Code
#2:
American exercise
571
28.14
The Code
#3:
2-D output
573
28.15
Upwind differencing
575
28.16
Summary
578
29
Monte Carlo Simulation
581
29.1
Introduction
582
29.2
Relationship between derivative values and simulations: equities,
indices, currencies, commodities
582
29.3
Generating paths
583
29.4 Lognormal
underlying, no path dependency
584
29.5
Advantages of Monte Carlo simulation
585
29.6
Using random numbers
586
29.7
Generating Normal variables
587
29.7.1
Box-Muller
587
29.8
Real versus risk neutral, speculation versus hedging
588
29.9
Interest rate products
590
29.10
Calculating the greeks
593
29.11
Higher dimensions: Cholesky factorization
594
xx
contents
29.12
Calculation time 596
29.13
Speeding up convergence
596
29.13.1
Antithetic variables
597
29.13.2
Control
variate
technique
597
29.14
Pros and cons of Monte Carlo simulations
598
29.15
American options
598
29.16
Longstaff
&
Schwartz regression approach for American options
599
29.17
Basis functions 603
29.18
Summary 603
30
Numerical Integration
605
30.1
Introduction 606
30.2
Regular grid
606
30.3
Basic Monte Carlo integration
607
30.4
Low-discrepancy sequences
609
30.5
Advanced techniques
613
30.6
Summary
614
A All the Math You Need.
..
and No More (An Executive Summary)
617
A.1 Introduction
618
A.2
e
618
A.3 log
618
A.4 Differentiation and Taylor series
620
A.5 Differential equations
623
A.6 Mean, standard deviation and distributions
623
A.7 Summary
626
В
Forecasting the Markets? A Small Digression
627
B.1 Introduction
628
B.2 Technical analysis
628
B.2.1 Plotting
628
B.2.2 Support and resistance
628
B.2.3
Trendlines 629
B.2.4 Moving averages
629
B.2.5 Relative strength
632
B.2.6 Oscillators
632
B.2.7 Bollinger bands
632
B.2.8 Miscellaneous patterns
633
B.2
.9
Japanese candlesticks
635
B.2.1
0
Point and figure charts
635
B.3 Wave theory
637
B.3.1 Elliott waves and Fibonacci numbers
638
B.3.2 Gann charts
638
B.4 Other analytics
638
B.5 Market
microstructure
modeling
640
B.5.1 Effect of demand on price
640
contents
xxi
В.5.2
Combining market
microstructure
and option theory
641
B.5.3 Imitation
641
B.6 Crisis prediction
641
B.7 Summary
641
С
A Trading Game
643
C.1 Introduction
643
C.2 Aims
643
C.3 Object of the game
643
C.4 Rules of the game
643
C.5 Notes
644
C.6 How to fill in your trading sheet
645
C.6.1 During a trading round
645
C.6.2 At the end of the game
645
D
Contents of CD accompanying Paul Wilmott Introduces Quantitative
Finance, second edition
649
E
What you get if (when) you upgrade to PWOQF2
653
Bibliography
659
Index
683
|
| adam_txt |
contents
Preface
xxiii
1
Products
and Markets: Equities, Commodities, Exchange Rates,
Forwards and Futures
1
1.1
Introduction
2
1.2
Equities
2
1.2.1
Dividends
7
1.2.2
Stocksplits
8
1.3
Commodities
9
1.4
Currencies
9
1.5
Indices
11
1.6
The time value of money
11
1.7
Fixed-income securities
17
1.8
Inflation-proof bonds
17
1.9
Forwards and futures
19
1.9.1
A first example of no arbitrage
20
1.10
More about futures
22
1.10.1
Commodity futures
23
1.10.2
FX futures
23
1.10.3
Index futures
24
1.11
Summary
24
27
28
28
33
34
34
39
39
39
40
41
Derivatives
2.1
Introduction
2.2
Options
2.3
Definition of common terms
2.4
Payoff diagrams
2.4.1
Other representations of value
2.5
Writing options
2.6
Margin
2.7
Market conventions
2.8
The value of the option before expiry
2.9
Factors affecting derivative prices
VÉii contents
2.10
Speculation and gearing
42
2.11
Early exercise
44
2.12
Put-call parity
44
2.13
Binaries or digitals
47
2.14
Bull and bear spreads
48
2.15
Straddles and strangles
50
2.16
Risk reversal 52
2.17
Butterflies and condors
53
2.18
Calendar spreads
53
2.19
LEAPS and FLEX
55
2.20
Warrants
55
2.21
Convertible bonds
55
2.22
Over the counter options
56
2.23
Summary
57
3
The Binomial Model
59
3.1
Introduction
60
3.2
Equities can go down as well as up
61
3.3
The option value
63
3.4
Which part of our 'model' didn't we need?
65
3.5
Why should this 'theoretical price' be the 'market price'?
65
3.5.1
The role of expectations
66
3.6
How did I know to sell \ of the stock for hedging?
66
3.6.1
The general formula for
Δ
67
3.7
How does this change if interest rates are non-zero?
67
3.8
Is the stock itself correctly priced?
68
3.9
Complete markets
69
3.10
The real and risk-neutral worlds
69
3.10.1
Non-zero interest rates
72
3.11
And now using symbols
73
3.11.1
Average asset change
74
3.11.2
Standard deviation of asset price change
74
3.12
An equation for the value of an option
75
3.12.1
Hedging
75
3.12.2
No arbitrage
76
3.13
Where did the probability
ρ
go?
77
3.14
Counter-intuitive?
77
3.15
The binomial tree
78
3.16
The asset price distribution
78
3.17
Valuing back down the tree
80
3.18
Programming the binomial method
85
3.19
The greeks
86
3.20
Early exercise
88
3.21
The continuous-time limit
90
3.22
Summary
90
contents
ix
4
The Random Behavior of Assets
4.1
Introduction
4.2
The popular forms of 'analysis'
4.3
Why we need a model for randomness: Jensen's inequality
4.4
Similarities between equities, currencies, commodities and indices
4.5
Examining returns
4.6
Timescales
4.6.1
The drift
4.6.2
The volatility
4.7
Estimating volatility
4.8
The random walk on a spreadsheet
4.9
The Wiener process
4.10
The widely accepted model for equities, currencies, commodities and
indices
4.11
Summary
5
Elementary Stochastic Calculus
5.1
Introduction
5.2
A motivating example
5.3
The Markov property
5.4
The martingale property
5.5
Quadratic variation
5.6
Brownian motion
5.7
Stochastic integration
5.8
Stochastic differential equations
5.9
The mean square limit
5.10
Functions of stochastic variables and
Itô's
lemma
5.11
Interpretation of
Itô's
lemma
5.12
Ito
and Taylor
5.13
Ito in
higher dimensions
5.14
Some pertinent examples
5.14.1
Brownian motion with drift
5.14.2
The
lognormal
random walk
5.14.3
A mean-reverting random walk
5.14.4
And another mean-reverting random walk
5.15
Summary
6
The Black-Scholes Model
6.1
Introduction
6.2
A very special portfolio
6.3
Elimination of risk: delta hedging
6.4
No arbitrage
6.5
The Black-Scholes equation
6.6
The Black-Scholes assumptions
6.7
Final conditions
95
96
96
97
99
100
105
107
108
109
109
111
112
115
117
118
118
120
120
120
121
122
123
124
124
127
127
130
130
131
132
134
135
136
139
140
140
142
142
143
145
146
к
contents
6.
б
6.
9
6.
10
6.
.11
6
.12
6.13
6
.14
Options on dividend-paying equities
147
Currency options
147
Commodity options
148
Expectations and Black-Scholes
148
Some other ways of deriving the Black-Scholes equation
149
6.12.1
The martingale approach
149
6.12.2
The binomial model
149
6.12.3
CAPM/utility
149
No arbitrage in the binomial, Black-Scholes and 'other' worlds
150
Forwards and futures
151
6.14.1
Forward contracts
151
6.15
Futures contracts
152
6.15.1
When interest rates are known, forward prices and futures
prices are the same
153
6.16
Options on futures
153
6.17
Summary
153
7
Partial Differential Equations
157
7.1
Introduction
158
7.2
Putting the Black-Scholes equation into historical perspective
158
7.3
The meaning of the terms in the Black-Scholes equation
159
7.4
Boundary and initial/final conditions
159
7.5
Some solution methods
160
7.5.1
Transformation to constant coefficient diffusion equation
160
7.5.2
Green's functions
161
7.5.3
Series solution
161
7.6
Similarity reductions
163
7.7
Other analytical techniques
163
7.8
Numerical solution
164
7.9
Summary
164
8
The Black-Scholes Formulae and the 'Greeks'
169
8.1
Introduction
170
8.2
Derivation of the formulae for calls, puts and simple digitals
170
8.2.1
Formula for a call
175
8.2.2
Formula for a put
179
8.2.3
Formula for a binary call
181
8.2.4
Formula for a binary put
182
8.3
Delta
182
8.4
Gamma
184
8.5
Theta
187
8.6
Speed
187
8.7 Vega 188
8.8
Rho
190
8.9
Implied volatility
191
8.10
A classification of hedging types
194
8.10.1
Why hedge?
194
Contents xi
8.10.2
The two main classifications
8.10.3
Delta hedging
8.10.4
Gamma hedging
8.10.5
Vega
hedging
8.10.6
Static hedging
8.10.7
Margin hedging
8.10.8
Crash (Platinum) hedging
194
195
195
195
195
196
196
8.11
Summary
196
9
Overview of Volatility Modeling
203
9.1
Introduction
204
9.2
The different types of volatility
204
9.2.1
Actual volatility
204
9.2.2
Historical or realized volatility
204
9.2.3
Implied volatility
205
9.2.4
Forward volatility
205
9.3
Volatility estimation by statistical means
205
9.3.1
The simplest volatility estimate: constant volatility/moving
window
205
9.3.2
Incorporating mean reversion
206
9.3.3
Exponentially weighted moving average
206
9.3.4
A simple GARCH model
207
9.3.5
Expected future volatility
207
9.3.6
Beyond close-close estimators: range-based estimation of
volatility
209
9.4
Maximum likelihood estimation
211
9.4.1
A simple motivating example: taxi numbers
211
9.4.2
Three hats
211
9.4.3
The math behind this: find the standard deviation
213
9.4.4
Quants' salaries
214
9.5
Skews and smiles
215
9.5.1
Sensitivity of the straddle to skews and smiles
216
9.5.2
Sensitivity of the risk reversal to skews and smiles
216
9.6
Different approaches to modeling volatility
217
9.6.1
To calibrate or not?
217
9.6.2
Deterministic volatility surfaces
218
9.6.3
Stochastic volatility
219
9.6.4
Uncertain parameters
219
9.6.5
Static hedging
220
9.6.6
Stochastic volatility and mean-variance analysis
220
9.6.7
Asymptotic analysis of volatility
220
9.7
The choices of volatility models
221
9.8
Summary
221
10
How to Delta Hedge
225
10.1
Introduction
226
10.2
What if implied and actual volatilities are different?
227
xli
contents
10.3
Implied versus actual, delta hedging but using which volatility?
228
10.4
Case
1:
Hedge with actual volatility,
σ
228
10.5
Case
2:
Hedge with implied volatility,
σ
231
10.5.1
The expected profit after hedging using implied volatility
232
10.5.2
The variance of profit after hedging using implied volatility
233
10.6
Hedging with different volatilities
235
10.6.1
Actual volatility
=
Implied volatility
236
10.6.2
Actual volatility
>
Implied volatility
236
10.6.3
Actual volatility
<
Implied volatility
238
10.7
Pros and cons of hedging with each volatility
238
10.7.1
Hedging with actual volatility
238
10.7.2
Hedging with implied volatility
239
10.7.3
Hedging with another volatility
239
10.8
Portfolios when hedging with implied volatility
239
10.8.1
Expectation
240
10.8.2
Variance
240
10.8.3
Portfolio optimization possibilities
241
10.9
How does implied volatility behave?
241
10.9.1
Sticky strike
242
10.9.2
Sticky delta
242
10.9.3
Time-periodic behavior
243
10.10
Summary
245
11
An Introduction to Exotic and Path-dependent Options
247
11.1
Introduction
248
11.2
Option classification
248
11.3
Time dependence
249
11.4
Cashflows
250
11.5
Path dependence
252
11.5.1
Strong path dependence
252
11.5.2
Weak path dependence
253
11.6
Dimensionality
254
11.7
The order of an option
255
11.8
Embedded decisions
256
11.9
Classification tables
258
11.10
Examples of exotic options
258
11.10.1
Compounds and choosers
258
11.10.2
Range notes
262
11.10.3
Barrier options
264
11.10.4
Asian options
265
11.10.5
Lookback
options
265
11.11
Summary of math/coding consequences
266
11.12
Summary
267
12
Multi-asset Options
271
12.1
Introduction
272
12.2
Multidimensional
lognormal
random walks
272
contents
Xiii
12.3
Measuring correlations
274
12.4
Options on many underlyings
277
12.5
The pricing formula for European non-path-dependent options on
dividend-paying assets
278
12.6
Exchanging one asset for another: a similarity solution
278
12.7
Two examples
280
12.8
Realities of pricing basket options
282
12.8.1
Easy problems
283
12.8.2
Medium problems
283
12.8.3
Hard problems
283
12.9
Realities of hedging basket options
283
12.10
Correlation versus
cointegration
283
12.11
Summary
284
13
Barrier Options
287
13.1
Introduction
288
13.2
Different types of barrier options
288
13.3
Pricing methodologies
289
13.3.1
Monte Carlo simulation
289
13.3.2
Partial differential equations
290
13.4
Pricing barriers in the partial differential equation framework
290
13.4.1
'Out'barriers
291
13.4.2
'In' barriers
292
13.5
Examples
293
13.5.1
Some more examples
294
13.6
Other features in barrier-style options
300
13.6.1
Early exercise
300
13.6.2
Repeated hitting of the barrier
301
13.6.3
Resetting of barrier
301
13.6.4
Outside barrier options
301
13.6.5
Soft barriers
301
13.6.6
Parisian options
301
13.7
Market practice: what volatility should I use?
302
13.8
Hedging barrier options
305
13.8.1
Slippage costs
306
13.9
Summary
307
14
Fixed-income Products and Analysis: Yield, Duration and Convexity
319
14.1
Introduction
320
14.2
Simple fixed-income contracts and features
320
14.2.1
The zero-coupon bond
320
14.2.2
The coupon-bearing bond
321
14.2.3
The money market account
321
14.2.4
Floating rate bonds
322
14.2.5
Forward rate agreements
323
14.2.6
Repos
323
14.2.7
STRIPS
324
xiv
contents
14.2.8
Amortization
324
14.2.9
Call provision
324
14.3
International bond markets
324
14.3.1
United States of America
324
14.3.2
United Kingdom
325
14.3.3
Japan
325
14.4
Accrued interest
325
14.5
Day-count conventions
325
14.6
Continuously and discretely compounded interest
326
14.7
Measures of yield
327
14.7.1
Current yield
327
14.7.2
The yield to maturity (YTM) or internal rate of return
(IRR)
327
14.8
The yield curve
329
14.9
Price/yield relationship
329
14.10
Duration
331
14.11
Convexity
333
14.12
An example
335
14.13
Hedging
335
14.14
Time-dependent interest rate
338
14.15
Discretely paid coupons
339
14.16
Forward rates and bootstrapping
339
14.16.1
Discrete data
340
14.16.2
On a spreadsheet
342
14.17
Interpolation
344
14.18
Summary
346
15
Swaps
349
15.1
Introduction
350
15.2
The vanilla interest rate swap
350
15.3
Comparative advantage
351
15.4
The swap curve
353
15.5
Relationship between swaps and bonds
354
15.6
Bootstrapping
355
15.7
Other features of swaps contracts
356
15.8
Other types of swap
357
15.8.1
Basis rate swap
357
15.8.2
Equity swaps
357
15.8.3
Currency swaps
357
15.9
Summary
358
16
One-factor Interest Rate Modeling
359
16.1
Introduction
360
16.2
Stochastic interest rates
361
16.3
The bond pricing equation for the general model
362
16.4
What is the market price of risk?
365
16.5
Interpreting the market price of risk, and risk neutrality
366
16.6
Named models
366
Contents xv
16.
.6.1
Vasicek
16.6.2
Cox, Ingersoll
&
Ross
16,
.6.3
Ho
&
Lee
16.
.6.4
Hull
&
White
366
367
368
369
16.7
Equity and FX forwards and futures when rates are stochastic
369
16.7.1
Forward contracts
369
16.8
Futures contracts
370
16.8.1
The convexity adjustment
371
16.9
Summary
372
17
Yield Curve Fitting
373
17.1
Introduction
374
17.2
Ho
&
Lee
374
17.3
The extended Vasicek model of Hull
&
White
375
17.4
Yield-curve fitting: For and against
376
17.4.1
For
376
17.4.2
Against
376
17.5
Other models
380
17.6
Summary
380
18
Interest Rate Derivatives
383
18.1
Introduction
384
18.2
Callable bonds
384
18.3
Bond options
385
18.3.1
Market practice
387
18.4
Caps and floors
389
18.4.1
Cap/floor parity
389
18.4.2
The relationship between a caplet and a bond option
391
18.4.3
Market practice
391
18.4.4
Collars
391
18.4.5
Step-up swaps, caps and floors
392
18.5
Range notes
392
18.6
Swaptions, captions and
f
loortions
392
18.6.1
Market practice
392
18.7
Spread options
394
18.8
Index amortizing rate swaps
394
18.8.1
Other features in the index amortizing rate swap
396
18.9
Contracts with embedded decisions
397
18.10
Some examples
398
18.11
More interest rate derivatives.
. 400
18.12
Summary
401
19
The Heath, Jarrow
&
Morton and Brace, Gatarek
&
Musiela Models
403
19.1
Introduction
404
19.2
The forward rate equation
404
19.3
The spot rate process
404
19.3.1
The non-Markov nature of HJM
406
xvi
contents
19.4
The
market
price of risk 406
19.5
Real and risk neutral 407
19.5.1
The relationship between the risk-neutral forward rate drift
and volatility 4°7
19.6
Pricing derivatives 408
19.7
Simulations 408
19.8
Trees 41°
19.9
The Musiela parameterization 411
19.10
Multi-factor
H
JM
411
19.11
Spreadsheet implementation
411
19.12
A simple one-factor example: Ho
&
Lee 412
19.13
Principal Component Analysis 413
19.13.1
The power method 415
19.14
Options on equities, etc.
416
19.15
Non-infinitesimal short rate 416
19.16
The Brace, Gatarek
&
Musiela model 417
19.17
Simulations 419
19.18
PVing the cashflows 419
19.19
Summary 420
20
Investment Lessons from Blackjack and Gambling
423
20.1
Introduction 424
20.2
The rules of blackjack 424
20.3
Beating the dealer 426
20.3.1
Summary of winning at blackjack 427
20.4
The distribution of profit in blackjack 428
20.5
The Kelly criterion
429
20.6
Can you win at roulette? 432
20.7
Horse race betting and no arbitrage 433
20.7.1
Setting the odds in a sporting game 433
20.7.2
The mathematics 434
20.8
Arbitrage
434
20.8.1
How best to profit from the opportunity?
436
20.9
How to bet
436
20.10
Summary
438
21
Portfolio Management
441
21.1
Introduction
442
21.2
Diversification
442
21.2.1
Uncorrelated assets
443
21.3
Modern portfolio theory
445
21.3.1
Including a risk-free investment
447
21.4
Where do I want to be on the efficient frontier?
447
21.5 Markowitz
in practice
450
21.6
Capital Asset Pricing Model
451
21.6.1
The single-index model
451
21.6.2
Choosing the optimal portfolio
453
Contents xvii
Value
at Risk
22.1
Introduction
22.2
Definition of Value at Risk
22.3
VaR for a single asset
22.4
VaR for a portfolio
22.5
VaR for derivatives
22.5.1
The delta approximation
22.5.2
The delta/gamma approximation
22.5.3
Use of valuation models
22.5.4
Fixed-income portfolios
22.6
Simulations
22.6.1
Monte Carlo
22.6.2
Bootstrapping
22.7
Use of VaR as a performance measure
22.8
Introductory Extreme Value Theory
22.8.1
Some EVT results
22.9
Coherence
22.10
Summary
21.7
The multi-index model
454
21.8
Cointegration
454
21.9
Performance measurement
455
21.10
Summary
456
459
460
460
461
463
464
464
464
466
466
466
467
467
468
469
469
470
470
23
Credit Risk
473
23.1
Introduction
474
23.2
The Merton model: equity as an option on a company's assets
474
23.3
Risky bonds
475
23.4
Modeling the risk of default
476
23.5
The
Poisson
process and the instantaneous risk of default
477
23.5.1
A note on hedging
481
23.6
Time-dependent intensity and the term structure of default
481
23.7
Stochastic risk of default
482
23.8
Positive recovery
484
23.9
Hedging the default
485
23.10
Credit rating
486
23.11
A model for change of credit rating
488
23.12
Copulas: pricing credit derivatives with many underlyings
488
23.12.1
The copula function
489
23.12.2
The mathematical definition
489
23.12.3
Examples of copulas
490
23.13
Collateralized debt obligations
490
23.14
Summary
492
24
RiskMetrics and CreditMetrics
495
24.1
Introduction
496
24.2
The RiskMetrics
datasets
496
xviii
contents
24.3
Calculating the parameters the RiskMetrics way
24.3.1
Estimating volatility
24.3.2
Correlation
24.4
The CreditMetrics
dataset
24.4.1
Yield curves
24.4.2
Spreads
24.4.3
Transition matrices
24.4.4
Correlations
24.5
The CreditMetrics methodology
24.6
A portfolio of risky bonds
24.7
CreditMetrics model outputs
24.8
Summary
25
CrashMetrics
25.1
Introduction
25.2
Why do banks go broke?
25.3
Market crashes
25.4
CrashMetrics
25.5
CrashMetrics for one stock
25.6
Portfolio ODtimization and the Platinum hedae
496
497
498
498
499
500
500
500
501
501
502
502
505
506
506
506
507
508
510
25.6.1
Other'cost'functions
511
25.7
The multi-asset/single-index model
511
25.7.1
Assuming Taylor series for the moment
517
25.8
Portfolio optimization and the Platinum hedge in the multi-asset
model
519
25.8.1
The marginal effect of an asset
520
25.9
The multi-index model
520
25.10
Incorporating time value
521
25.11
Margin calls and margin hedging
522
25.11.1
What is margin?
522
25.11.2
Modeling margin
522
25.11.3
The single-index model
524
25.12
Counterparty risk
524
25.13
Simple extensions to CrashMetrics
524
25.14
The CrashMetrics Index
(CMI)
525
25.15
Summary
526
26
Derivatives
****
Ups
527
26.1
Introduction
528
26.2
Orange County
528
26.3
Proctor and Gamble
529
26.4 Metallgesellschaft 532
26.4.1
Basis risk
533
26.5
Gibson Greetings
533
26.6
Barings
536
26.7
Long-Term
Capital Management
537
26.8
Summary
54O
contents
Xix
27
Overview of Numerical Methods
541
27.1
Introduction
542
27.2
Finite-difference methods
542
27.2.1
Efficiency
543
27.2.2
Program of study
543
27.3
Monte Carlo methods
544
27.3.1
Efficiency
545
27.3.2
Program of study
545
27.4
Numerical integration
546
27.4.1
Efficiency
546
27.4.2
Program of study
546
27.5
Summary
547
28
Finite-difference Methods for One-factor Models
549
28.1
Introduction
550
28.2
Grids
550
28.3
Differentiation using the grid
553
28.4
Approximating
θ
553
28.5
Approximating
Δ
554
28.6
Approximating
Γ
557
28.7
Example
557
28.8
Bilinear interpolation
558
28.9
Final conditions and payoffs
559
28.10
Boundary conditions
560
28.11
The explicit finite-difference method
562
28.11.1
The Black-Scholes equation
565
28.11.2
Convergence of the explicit method
565
28.12
The Code
#1 :
European option
567
28.13
The Code
#2:
American exercise
571
28.14
The Code
#3:
2-D output
573
28.15
Upwind differencing
575
28.16
Summary
578
29
Monte Carlo Simulation
581
29.1
Introduction
582
29.2
Relationship between derivative values and simulations: equities,
indices, currencies, commodities
582
29.3
Generating paths
583
29.4 Lognormal
underlying, no path dependency
584
29.5
Advantages of Monte Carlo simulation
585
29.6
Using random numbers
586
29.7
Generating Normal variables
587
29.7.1
Box-Muller
587
29.8
Real versus risk neutral, speculation versus hedging
588
29.9
Interest rate products
590
29.10
Calculating the greeks
593
29.11
Higher dimensions: Cholesky factorization
594
xx
contents
29.12
Calculation time 596
29.13
Speeding up convergence
596
29.13.1
Antithetic variables
597
29.13.2
Control
variate
technique
597
29.14
Pros and cons of Monte Carlo simulations
598
29.15
American options
598
29.16
Longstaff
&
Schwartz regression approach for American options
599
29.17
Basis functions 603
29.18
Summary 603
30
Numerical Integration
605
30.1
Introduction 606
30.2
Regular grid
606
30.3
Basic Monte Carlo integration
607
30.4
Low-discrepancy sequences
609
30.5
Advanced techniques
613
30.6
Summary
614
A All the Math You Need.
.
and No More (An Executive Summary)
617
A.1 Introduction
618
A.2
e
618
A.3 log
618
A.4 Differentiation and Taylor series
620
A.5 Differential equations
623
A.6 Mean, standard deviation and distributions
623
A.7 Summary
626
В
Forecasting the Markets? A Small Digression
627
B.1 Introduction
628
B.2 Technical analysis
628
B.2.1 Plotting
628
B.2.2 Support and resistance
628
B.2.3
Trendlines 629
B.2.4 Moving averages
629
B.2.5 Relative strength
632
B.2.6 Oscillators
632
B.2.7 Bollinger bands
632
B.2.8 Miscellaneous patterns
633
B.2
.9
Japanese candlesticks
635
B.2.1
0
Point and figure charts
635
B.3 Wave theory
637
B.3.1 Elliott waves and Fibonacci numbers
638
B.3.2 Gann charts
638
B.4 Other analytics
638
B.5 Market
microstructure
modeling
640
B.5.1 Effect of demand on price
640
contents
xxi
В.5.2
Combining market
microstructure
and option theory
641
B.5.3 Imitation
641
B.6 Crisis prediction
641
B.7 Summary
641
С
A Trading Game
643
C.1 Introduction
643
C.2 Aims
643
C.3 Object of the game
643
C.4 Rules of the game
643
C.5 Notes
644
C.6 How to fill in your trading sheet
645
C.6.1 During a trading round
645
C.6.2 At the end of the game
645
D
Contents of CD accompanying Paul Wilmott Introduces Quantitative
Finance, second edition
649
E
What you get if (when) you upgrade to PWOQF2
653
Bibliography
659
Index
683 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Wilmott, Paul |
| author_facet | Wilmott, Paul |
| author_role | aut |
| author_sort | Wilmott, Paul |
| author_variant | p w pw |
| building | Verbundindex |
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| classification_rvk | QP 700 SK 980 |
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| ctrlnum | (OCoLC)263419474 (DE-599)BVBBV035097223 |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed., reprint. |
| format | Book |
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| spelling | Wilmott, Paul Verfasser aut Paul Wilmott introduces quantitative finance Quantitative finance 2. ed., reprint. Chichester [u.a.] Wiley 2008 XXIV, 695 S. Ill., graph. Darst. CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Optionshandel (DE-588)4126185-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Optionshandel (DE-588)4126185-9 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Derivat Wertpapier (DE-588)4381572-8 s Optionspreistheorie (DE-588)4135346-8 s 2\p DE-604 Finanzmathematik (DE-588)4017195-4 s 3\p DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016765254&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wilmott, Paul Paul Wilmott introduces quantitative finance Finanzmathematik (DE-588)4017195-4 gnd Optionspreistheorie (DE-588)4135346-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Optionshandel (DE-588)4126185-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4135346-8 (DE-588)4381572-8 (DE-588)4126185-9 (DE-588)4114528-8 (DE-588)4151278-9 |
| title | Paul Wilmott introduces quantitative finance |
| title_alt | Quantitative finance |
| title_auth | Paul Wilmott introduces quantitative finance |
| title_exact_search | Paul Wilmott introduces quantitative finance |
| title_exact_search_txtP | Paul Wilmott introduces quantitative finance |
| title_full | Paul Wilmott introduces quantitative finance |
| title_fullStr | Paul Wilmott introduces quantitative finance |
| title_full_unstemmed | Paul Wilmott introduces quantitative finance |
| title_short | Paul Wilmott introduces quantitative finance |
| title_sort | paul wilmott introduces quantitative finance |
| topic | Finanzmathematik (DE-588)4017195-4 gnd Optionspreistheorie (DE-588)4135346-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Optionshandel (DE-588)4126185-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Finanzmathematik Optionspreistheorie Derivat Wertpapier Optionshandel Mathematisches Modell Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016765254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wilmottpaul paulwilmottintroducesquantitativefinance AT wilmottpaul quantitativefinance |