Paul Wilmott Introduces Quantitative Finance,9780471498629

Paul Wilmott Introduces Quantitative Finance

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Edition: CD
ISBN13: 9780471498629
ISBN10: 0471498629
Format: Paperback
Pub. Date: 2001-06-01
Publisher(s): WILEY
List Price: $69.95

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Summary

In this updated student edition, Paul Wilmott updates and extends his earlier classic, Derivatives: The Theory and Practice of Financial Engineering. Included on CD are numerous Bloomberg screen dumps to illustrate, in real terms, the points raised in the book, along with essential Visual basic code, spreadsheet explanations of the models, and the reproduction of term sheets and option classification tables. The author presents all the current financial theories in a manner designed to make them easy to understand and implement.

Author Biography

<B>PAUL WILLMOTT</B>, described by the Financial Times as 'cult derivatives lecturer,' is one of the world's leading experts on quantitative finance and derivatives. <P> He is proprietor of an innovative magazine on quantitative finance and principal of the financial consultancy and training firm, Wilmott Associates. He has written and published widely on quantitative finance. See also his personal website <BR> <BR>

Table of Contents

Preface xix
Products and Markets: Equities, Commodities, Exchange Rates, Forwards and Futures
1(26)
Introduction
2(1)
Equities
2(7)
Dividends
5(4)
Stock splits
9(1)
Commodities
9(1)
Currencies
10(2)
Indices
12(2)
The time value of money
14(4)
Fixed-income secrities
18(1)
Inflation-proof bonds
19(1)
Forwards and futures
20(4)
A first example of no arbitrage
21(3)
More about futures
24(1)
Commodity futures
24(1)
FX futures
25(1)
Index futures
25(1)
Summary
25(2)
Derivatives
27(32)
Introduction
28(1)
Options
28(5)
Definition of common terms
33(1)
Payoff diagrams
34(4)
Other representations of value
38(1)
Writing options
38(1)
Margin
39(1)
Market conventions
40(1)
The value of the option before expiry
40(1)
Factors affecting derivative prices
41(2)
Speculation and gearing
43(1)
Early exercise
44(1)
Put-call parity
44(2)
Binaries for digitals
46(2)
Bull and bear spreads
48(1)
Straddles and strangles
49(2)
Risk reversal
51(1)
Butterflies and condors
51(2)
Calendar spreads
53(1)
LEAPS and FLEX
54(1)
Warrants
55(1)
Convertible bonds
55(1)
Over the counter options
55(1)
Summary
56(3)
Predicting the Markets? A Small Digression
59(16)
Introduction
60(1)
Technical analysis
60(7)
Plotting
60(1)
Support and resistance
60(1)
Trendlines
61(1)
Moving averages
61(1)
Relative strength
62(2)
Oscillators
64(1)
Bollinger bands
64(1)
Miscellaneous patterns
64(3)
Japanese candlesticks
67(1)
Point and figure charts
67(1)
Wave theory
67(4)
Elliott waves and Fibonacci numbers
69(2)
Gann charts
71(1)
Other analytics
71(1)
Market microstructure modeling
71(1)
Effect of demand on price
71(1)
Combining market microstructure and option theory
72(1)
Imitation
72(1)
Crisis prediction
72(1)
Summary
73(2)
All the Math You Need...and No More (An Executive Summary)
75(10)
Introduction
76(1)
e
76(1)
log
76(2)
Differentiation and Taylor series
78(3)
Differential equations
81(1)
Mean, standard deviation and distributions
81(1)
Summary
82(3)
The Binomial Model
85(16)
Introduction
86(1)
Equities can go down as well as up
86(2)
Let's generalize
88(1)
Average asset change
89(1)
Standard deviation of asset price change
89(1)
The binomial tree
89(1)
The asset price distribution
90(1)
An equation for the value of an option
90(3)
Hedging
92(1)
No arbitrage
92(1)
Where did the probability p go?
93(1)
Other choices for u, v and p
93(1)
Valuing back down the tree
94(2)
Early exercise
96(2)
The continuous-time limit
98(1)
Summary
99(2)
The Random Behavior of Assets
101(18)
Introduction
102(1)
Similarities between equities, currencies, commodities and indices
102(1)
Examining returns
103(5)
Timescales
108(4)
The drift
110(1)
The volatility
111(1)
Estimating volatility
112(1)
The random walk on a spreadsheet
112(2)
The Wiener process
114(1)
The widely accepted model for equities, currencies, commodities and indices
115(3)
Summary
118(1)
Elementary Stochastic Calculus
119(20)
Introduction
120(1)
A motivating example
120(2)
The Markov property
122(1)
The martingale property
122(1)
Quadratic variation
122(1)
Brownian motion
123(1)
Stochastic integration
124(1)
Stochastic differential equations
125(1)
The mean square limit
125(1)
Functions of stochastic variables and Ito's lemma
126(3)
Ito and Taylor
129(1)
Ito in higher dimensions
130(1)
Some pertinent examples
131(5)
Brownian motion with drift
131(1)
The lognormal random walk
132(1)
A mean-reverting random walk
133(2)
And another mean-reverting random walk
135(1)
Summary
136(3)
The Black--Scholes Model
139(16)
Introduction
140(1)
A very special portfolio
140(2)
Elimination of risk: delta hedging
142(1)
No arbitrage
142(1)
The Black--Scholes equation
143(2)
The Black--Scholes assumptions
145(1)
Final conditions
146(1)
Options on dividend-paying equities
147(1)
Currency options
147(1)
Commodity options
147(1)
Expectations and Black--Scholes
148(1)
Some other ways of deriving the Black--Scholes equation
149(1)
The martingale approach
149(1)
The binomial model
149(1)
CAPM/utility
149(1)
No arbitrage in the binomial, Black--Scholes and `other' worlds
150(1)
Forwards and futures
151(1)
Forward contracts
151(1)
Futures contracts
152(1)
When interest rates are known, forward prices and futures prices are the same
152(1)
Options on futures
152(1)
Summary
153(2)
Partial Differential Equations
155(8)
Introduction
156(1)
Putting the Black--Scholes equation into historical perspective
156(1)
The Meaning of the terms in the Black--Scholes equation
157(1)
Boundary and initial/final conditions
157(1)
Some solution methods
158(2)
Transformation to constant coefficient diffusion equation
158(1)
Green's functions
159(1)
Series solution
159(1)
Similarity reductions
160(1)
Other analytical techniques
161(1)
Numerical solution
161(1)
Summary
162(1)
The Black--Scholes Formulas and the `Greeks'
163(30)
Introduction
164(1)
Derivation of the formulas for calls, puts and simple digitals
164(12)
Formula for a call
169(4)
Formula for a put
173(2)
Formula for a binary call
175(1)
Formula for a binary put
176(1)
Delta
176(2)
Gamma
178(1)
Theta
179(1)
Vega
180(3)
Rho
183(1)
Implied volatility
183(3)
A classification of hedging types
186(3)
Why hedge?
186(1)
The two main classifications
186(1)
Delta hedging
187(1)
Gamma hedging
187(1)
Vega hedging
187(1)
Static hedging
188(1)
Margin hedging
188(1)
Crash (Platinum) hedging
188(1)
Summary
189(4)
Multi-Asset Options
193(14)
Introduction
194(1)
Multidimensional lognormal random walks
194(2)
Measuring correlations
196(3)
Options on many underlyings
199(1)
The pricing formula for European non-path-dependent options on dividend-paying assets
200(1)
Exchanging one asset for another: a similarity solution
200(2)
Two examples
202(2)
Realities of pricing basket options
204(1)
Easy problems
205(1)
Medium problems
205(1)
Hard problems
205(1)
Realities of hedging basket options
205(1)
Correlation versus cointegration
205(1)
Summary
206(1)
An Introduction to Exotic and Path-Dependent Options
207(20)
Introduction
208(1)
Discrete cashflows
208(1)
Early exercise
209(1)
Weak path dependence
210(1)
Strong path dependence
211(1)
Time dependence
212(1)
Dimensionality
212(1)
The order of an option
213(1)
Decisions, decisions
214(1)
Classification tables
215(1)
Compounds and choosers
215(1)
Range options
216(2)
Barrier options
218(3)
Asian options
221(1)
Lookback options
221(1)
Summary
222(5)
Barrier Options
227(24)
Introduction
228(1)
Different types of barrier options
228(1)
Pricing barriers in the partial differential equation framework
229(3)
`Out' barriers
230(1)
`In' barriers
231(1)
Examples
232(3)
Some more examples
235(1)
Other features in barrier-style options
235(3)
Early exercise
235(1)
Repeated hitting of the barrier
236(1)
Resetting of barrier
236(1)
Outside barrier options
237(1)
Soft barriers
237(1)
Parisian options
238(1)
Market practice: What volatility should I use?
238(3)
Hedging barrier options
241(6)
Slippage costs
244(3)
Summary
247(4)
Fixed-Income Products and Analysis: Yield, Duration and Convexity
251(24)
Introduction
252(1)
Simple fixed-income contracts and featues
252(3)
The zero-coupon bond
252(1)
The coupon-bearing bond
252(1)
The money market account
252(1)
Floating rate bonds
253(1)
Forward rate agreements
254(1)
Repos
254(1)
STRIPS
254(1)
Amortization
254(1)
Call provision
255(1)
International bond markets
255(1)
United States of America
255(1)
United Kingdom
255(1)
Japan
255(1)
Accrued interest
255(1)
Day-count conventions
256(1)
Continuously and discretely compounded interest
256(1)
Measures of yield
257(2)
Current yield
257(1)
The yield to maturity (YTM) or internal rate of return (IRR)
258(1)
The yield curve
259(2)
Price/yield relationship
261(1)
Duration
262(1)
Convexity
263(1)
An example
264(1)
Hedging
265(2)
Time-dependent interest rate
267(2)
Discretely paid coupons
269(1)
Forward rates and bootstrapping
269(3)
Interpolation
272(1)
Summary
272(3)
Swaps
275(10)
Introduction
276(1)
The vanilla interest rate swap
276(1)
Comparative advantage
277(2)
The swap curve
279(1)
Relationship between swaps and bonds
280(2)
Bootstrapping
282(1)
Other features of swaps contracts
282(1)
Other types of swap
283(1)
Basis rate swap
283(1)
Equity swaps
283(1)
Currency swaps
284(1)
Summary
284(1)
One-Factor Interest Rate Modeling
285(14)
Introduction
286(1)
Stochastic interest rates
287(1)
The bond pricing equation for the general model
288(3)
What is the market price of risk?
291(1)
Interpreting the market price of risk, and risk neutrality
291(1)
Named models
292(3)
Vasicek
292(1)
Cox, Ingersoll & Ross
293(1)
Ho & lee
294(1)
Hull & White
295(1)
Equity and FX forwards and futures when rates are stochastic
295(1)
Forward contracts
295(1)
Futures contracts
296(1)
The convexity adjustment
297(1)
Summary
297(2)
Interest Rate Derivatives
299(20)
Introduction
300(1)
Callable bonds
300(1)
Bond options
301(4)
Market practice
303(2)
Caps and floors
305(3)
Cap/floor parity
306(1)
The relationship between a caplet and a bond option
306(1)
Market practice
307(1)
Collars
307(1)
Step-up swaps, caps and floors
307(1)
Range notes
308(1)
Swaptions, captions and floortions
308(2)
Market practice
308(2)
Spread options
310(1)
Index amortizing rate swaps
310(3)
Other features in the index amortizing rate swap
312(1)
Contracts with embedded decisions
313(1)
Some more exotics
314(1)
Some examples
315(2)
Summary
317(2)
Health, Jarrow and Morton
319(16)
Introduction
320(1)
The forward rate equation
320(1)
The spot rate process
321(1)
The non-Markov nature of HJM
322(1)
The market price of risk
322(1)
Real and risk neutral
323(1)
The relationship between the risk-neutral forward rate drift and volatility
323(1)
Pricing derivatives
324(1)
Simulations
324(1)
Trees
325(1)
The Musiela parametrization
326(1)
Multifactor HJM
327(1)
A simple one-factor example: Ho & Lee
327(1)
Principal component analysis
328(3)
The power method
330(1)
Options on equities etc.
331(1)
Nonninfinitesimal short rate
331(1)
The Brace, Gatarek & Musiela model
332(1)
Summary
333(2)
Portfolio Management
335(20)
Introduction
336(1)
The Kelly criterion
336(2)
Diversification
338(3)
Uncorrelated assets
339(2)
Modern Portfolio Theory
341(2)
Including a risk-free investment
343(1)
Where do I want to be on the efficient frontier?
343(3)
Markowitz in practice
346(1)
Capital Asset Pricing Model
346(3)
The single-index model
346(3)
Choosing the optimal protfolio
349(1)
The multi-index model
349(1)
Cointegration
350(1)
Performance measurement
351(1)
Summary
352(3)
Value at Risk
355(12)
Introduction
356(1)
Definition of Value at Risk
356(1)
VaR for a single asset
357(2)
VaR for a portfolio
359(1)
VaR for derivatives
360(3)
The delta approximation
360(1)
The delta/gamma approximation
360(2)
Use of valuation models
362(1)
Fixed-income portfolios
362(1)
Simulations
363(2)
Monte Carlo
363(1)
Bootstrapping
363(2)
Use of VaR as a performance measure
365(1)
Summary
365(2)
Credit Risk
367(16)
Introduction
368(1)
Risky bonds
368(1)
Modeling the risk of default
369(1)
The Poisson process and the instantaneous risk of default
369(4)
A note on hedging
373(1)
Time-dependent intensity and the term structure of default
373(2)
Stochastic risk of default
375(2)
Positive recovery
377(1)
Hedging the default
378(1)
Credit rating
379(1)
A model for change of credit rating
379(2)
Summary
381(2)
RiskMetrics and CreditMetrics
383(10)
Introduction
384(1)
The RiskMetrics datasets
384(1)
Calculating parameters the RiskMetrics way
384(2)
Estimating volatility
384(2)
Correlation
386(1)
The CreditMetrics dataset
386(3)
Yield curves
387(1)
Spreads
388(1)
Transition matrices
388(1)
Correlations
388(1)
The CreditMetrics methodology
389(1)
A portfolio of risky bonds
389(1)
CreditMetrics model outputs
390(1)
Summary
391(2)
CrashMetrics
393(20)
Introduction
394(1)
Why do banks go broke?
394(1)
Market crashes
394(1)
CrashMetrics
394(2)
CrashMetrics for one stock
396(3)
Portfolio optimization and the Platinum hedge
398(1)
The multi-asset/single-index model
399(8)
Portfolio optimization and the Platinum hedge in the multi-asset model
406(1)
The marginal effect of an asset
406(1)
The multi-index model
407(1)
Incorporating time value
408(1)
Margin calls and margin hedging
408(3)
What is margin?
409(1)
Modeling margin
409(1)
The single-index model
410(1)
Counterparty risk
411(1)
Simple extensions to CrashMetrics
411(1)
The CrashMetrics Index (CMI)
411(1)
Summary
412(1)
Derivatives****Ups
413(14)
Introduction
414(1)
Orange County
414(1)
Procter and Gamble
415(3)
Metallgesellschaft
418(1)
Basis risk
419(1)
Gibson Greetings
419(2)
Barings
421(2)
Long-Term Capital Management
423(3)
Summary
426(1)
Finite-Difference Methods for One-Factor Models
427(26)
Introduction
428(1)
Grids
428(3)
Differentiation using the grid
431(1)
Approximating &thetas;
431(1)
Approximating Δ
432(2)
Approximating Γ
434(1)
Bilinear interpolation
435(1)
Final conditions and payoffs
436(1)
Boundary conditions
437(2)
The explicit finite-difference method
439(9)
The Black--Scholes equation
442(1)
Convergence of the explicit method
442(6)
Upwind differencing
448(2)
Summary
450(3)
Monte Carlo Simulation and Related Methods
453(26)
Introduction
454(1)
Relationship between derivative values and simulations; equities, indices, currencies, commodities
454(3)
Advantages of Monte Carlo simulation
457(1)
Using random numbers
458(1)
Generating normal variables
459(1)
Real versus risk neutral, speculation versus hedging
459(4)
Interest rate products
463(2)
Calculating the greeks
465(1)
Higher dimensions: Cholesky factorization
466(1)
Speeding up convergence
467(1)
Antithetic variables
467(1)
Control variate technique
467(1)
Pros and cons of Monte Carlo simulations
468(1)
American options
469(1)
Numerical integration
469(1)
Regular grid
470(1)
Basic Monte Carlo integration
470(3)
Low-discrepancy sequences
473(4)
Advanced techniques
477(1)
Summary
478(1)
Appendix A A Trading Game 479(6)
A.1 Introduction
479(1)
A.2 Aims
479(1)
A.3 Object of the game
479(1)
A.4 Rules of the game
479(1)
A.5 Notes
480(1)
A.6 How to fill in your trading sheet
481(4)
A.6.1 During a trading round
481(1)
A.6.2 At the end of the game
481(4)
Appendix B What You Get If (When) You Upgrade... 485(4)
Contents of the CD 489(2)
Bibliography 491(16)
Index 507

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