Paul Wilmott on Quantitative Finance, 2 Volume Set,,9780471874386

Paul Wilmott on Quantitative Finance, 2 Volume Set,

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Edition: 2nd
ISBN13: 9780471874386
ISBN10: 0471874388
Format: Hardcover
Pub. Date: 2000-01-01
Publisher(s): WILEY
List Price: $252.00

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Summary

The only comprehensive reference encompassing both traditional and new derivatives and financial engineering techniques Based on the author's hugely successful Derivatives: The Theory and Practice of Financial Engineering, Paul Wilmott on Quantitative Finance is the definitive guide to derivatives and related financial products. In addition to fully updated and expanded coverage of all the topics covered in the first book, this two-volume set also includes sixteen entirely new chapters covering such crucial areas as stochastic control and derivatives, utility theory, stochastic volatility and utility, mortgages, real options, power derivatives, weather derivatives, insurance derivatives, and more. Wilmott has also added clear, detailed explanations of all the mathematical procedures readers need to know in order to use the techniques he describes. Paul Wilmott, Dphil (Oxford, UK), is one of Europe's leading writers and consultants in the area of financial mathematics. He is also head of Wilmott Associates, a leading international financial consulting firm whose clients include Citibank, IBM, Bank of Montreal, Momura, Daiwa, Maxima, Dresdner Klienwort Benson, Origenes, and Siembra.

Table of Contents

Prolog xxv
PART ONE BASIC THEORY OF DERIVATIVES 1(308)
Products and Markets
3(20)
Introduction
3(1)
The time value of money
3(2)
Equities
5(7)
Dividends
10(1)
Stock splits
11(1)
Commodities
12(1)
Currencies
12(1)
Indices
13(2)
Fixed-income securities
15(2)
Inflation-proof bonds
17(2)
Forwards and futures
19(2)
A first example of no arbitrage
19(2)
Summary
21(2)
Derivatives
23(28)
Introduction
23(1)
Options
23(5)
Definition of common terms
28(1)
Payoff diagrams
29(5)
Other representations of value
29(5)
Writing options
34(1)
Margin
34(1)
Market conventions
35(1)
The value of the option before expiry
35(1)
Factors affecting derivative prices
36(1)
Speculation and gearing
37(1)
Early exercise
38(1)
Put--call parity
38(2)
Binaries or digitals
40(1)
Bull and bear spreads
41(1)
Straddles and strangles
42(3)
Risk reversal
45(1)
Butterflies and condors
46(1)
Calendar spreads
46(1)
LEAPS and FLEX
47(1)
Warrants
48(1)
Convertible bonds
48(1)
Over the counter options
48(1)
Summary
48(3)
The Random Behavior of Assets
51(14)
Introduction
51(1)
Similarities between equities, currencies, commodities and indices
51(1)
Examining returns
52(3)
Timescales
55(4)
The drift
57(1)
The volatility
58(1)
Estimating volatility
59(1)
Exponentially weighted
59(1)
Using highs and lows
59(1)
High-low-close estimator
60(1)
The random walk on a spreadsheet
60(1)
The Wiener process
61(1)
The widely accepted model for equities, currencies, commodities and indices
62(1)
Summary
63(2)
Elementary Stochastic Calculus
65(16)
Introduction
65(1)
A motivating example
65(2)
The Markov property
67(1)
The martingale property
67(1)
Quadratic variation
67(1)
Brownian motion
68(1)
Stochastic integration
69(1)
Stochastic differential equations
70(1)
The mean square limit
70(1)
Functions of stochastic variables and Ito's lemma
71(2)
Ito and Taylor
73(1)
Ito in higher dimensions
74(1)
Some pertinent examples
75(5)
Brownian motion with drift
75(1)
The lognormal random walk
75(3)
A mean-reverting random walk
78(1)
And another mean-reverting random walk
78(2)
Summary
80(1)
The Black--Scholes Model
81(10)
Introduction
81(1)
A very special portfolio
81(1)
Elimination of risk: delta hedging
82(1)
No arbitrage
83(1)
The Black--Scholcs equation
84(1)
The Black--Scholes assumptions
85(1)
Final conditions
86(1)
Options on dividend-paying equities
87(1)
Currency options
87(1)
Commodity options
87(1)
Options on futures
88(1)
Some other ways of deriving the Black--Scholes equation
88(1)
The martingale approach
82(6)
The binomial model
88(1)
CAPM/utility
88(1)
Summary
89(2)
Partial Differential Equations
91(8)
Introduction
91(1)
Putting the Black--Scholes equation into historical perspective
91(1)
The meaning of the terms in the Black--Scholes equation
92(1)
Boundary and initial/final conditions
93(1)
Some solution methods
93(2)
Transformation to constant coefficient diffusion equation
93(1)
Green's functions
94(1)
Series solution
94(1)
Similarity reductions
95(1)
Other analytical techniques
96(1)
Numerical solution
96(1)
Summary
97(2)
The Black--scholes Formulae and the `Greeks'
99(28)
Introduction
99(1)
Derivation of the formulae for calls, puts and simple digitals
100(11)
Formula for a call
104(3)
Formula for a put
107(2)
Formula for a binary call
109(2)
Formula for a binary put
111(1)
Delta
111(1)
Gamma
112(3)
Theta
115(1)
Vega
115(3)
Rho
118(1)
Implied volatility
119(3)
A classification of hedging types
122(2)
Why hedge?
122(1)
The two main classifications
122(1)
Delta hedging
122(1)
Gamma hedging
122(1)
Vega hedging
123(1)
Static hedging
123(1)
Margin hedging
123(1)
Crash (Platinum) hedging
124(1)
Summary
124(3)
Simple Generalizations of the Black--Scholes World
127(10)
Introduction
127(1)
Dividends, foreign interest and cost of carry
127(1)
Dividend structures
128(1)
Dividend payments and no arbitrage
128(1)
The behavior of an option value across a dividend date
129(2)
Time-dependent parameters
131(2)
Formulae for power options
133(1)
The log contract
134(1)
Summary
134(3)
Early Exercise and American Options
137(18)
Introduction
137(1)
The perpetual American put
137(4)
Perpetual American call with dividends
141(1)
Mathematical formulation for general payoff
142(2)
Local solution for call with constant dividend yield
144(2)
Other dividend structures
146(1)
One-touch options
147(2)
Other features in American-style contracts
149(2)
Bermudan options
149(1)
Make your mind up
150(1)
Other issues
151(1)
Nonlinearity
151(1)
Free boundary problems
151(1)
Numerical solution
152(1)
Summary
152(3)
Probability Density Functions and First Exit Times
155(12)
Introduction
155(1)
The transition probability density function
155(1)
A trinomial model for the random walk
156(1)
The forward equation
157(3)
The steady-state distribution
160(1)
The backward equation
160(1)
First exit times
160(1)
Cumulative distribution functions for first exit times
161(1)
Expected first exit times
162(1)
Another example of optimal stopping
163(1)
Expectations and Black--Scholes
164(1)
Summary
165(2)
Multi-asset Options
167(12)
Introduction
167(1)
Multi-dimensional lognormal random walks
167(1)
Measuring correlations
168(2)
Options on many underlyings
170(1)
The pricing formula for European non-path-dependent options on dividend-paying assets
171(1)
Exchanging one asset for another: a similarity solution
171(1)
Quantos
172(2)
Two examples
174(2)
Other features
176(1)
Realities of pricing basket options
177(1)
Easy problems
177(1)
Medium problems
177(1)
Hard problems
177(1)
Realities of hedging basket options
178(1)
Correlation versus cointegration
178(1)
Summary
178(1)
The Binomial Model
179(14)
Introduction
179(1)
Equities can go down as well as up
180(1)
The binomial tree
181(1)
The asset price distribution
182(1)
An equation for the value of an option
183(1)
Valuing back down the tree
184(3)
The greeks
187(2)
Early exercise
189(1)
The continuous-time limit
190(1)
No arbitrage in the binomial, Black-Scholes and `other' worlds
191(1)
Summary
192(1)
Predicting the Markets?
193(14)
Introduction
193(1)
Technical analysis
193(9)
Plotting
194(1)
Support and resistance
194(1)
Trendlines
195(1)
Moving averages
195(2)
Relative strength
197(1)
Oscillators
197(1)
Bollinger bands
198(1)
Miscellaneous patterns
198(1)
Japanese candlesticks
199(1)
Point and figure charts
200(2)
Wave theory
202(2)
Elliott waves and Fibonacci numbers
202(2)
Gann charts
204(1)
Other analytics
204(1)
Market microstructure modeling
204(1)
Effect of demand on price
205(1)
Combining market microstructure and option theory
205(1)
Imitation
205(1)
Crisis prediction
205(1)
Summary
206(1)
A Trading Game
207(6)
Introduction
207(1)
Aims
207(1)
Object of the game
207(1)
Rules of the game
207(1)
Notes
208(1)
How to fill in your trading sheet
208(5)
During a trading round
208(1)
At the end of the game
209(4)
PART TWO PATH DEPENDENCY
An Introduction to Exotic and Path-Dependent Options
213(16)
Introduction
213(1)
Discrete cashflows
214(1)
Early exercise
215(1)
Weak path dependence
215(1)
Strong path dependence
216(1)
Time dependence
217(1)
Dimensionality
217(1)
The order of an option
217(1)
Decisions, decisions
218(1)
Classification tables
218(1)
Compounds and choosers
219(4)
Range notes
223(1)
Barrier options
224(1)
Asian options
224(2)
Lookback options
226(1)
Summary
227(2)
Barrier Options
229(24)
Introduction
229(1)
Different types of barrier option
230(1)
Pricing barriers in the partial differential equation framework
231(5)
`Out' barriers
231(1)
`In' barriers
232(1)
Some formulae when volatility is constant
232(4)
Some more examples
236(1)
Other features of barrier-style options
236(7)
Early exercise
240(1)
The intermittent barrier
240(1)
Repeated hitting of the barrier
241(1)
Resetting of barrier
242(1)
Outside barrier options
242(1)
Soft barriers
242(1)
Parisian options
243(1)
First exit time
243(1)
Market practice: What volatility should I use?
244(2)
Hedging barrier options
246(4)
Slippage costs
249(1)
Summary
250(3)
Strongly Path-dependent Options
253(10)
Introduction
253(1)
Path-dependent quantities represented by an integral
254(1)
Examples
254(1)
Continuous sampling: The pricing equation
255(1)
Example
256(1)
Path-dependent quantities represented by an updating rule
256(1)
Examples
256(1)
Discrete sampling: The pricing equation
257(3)
Examples
258(1)
The algorithm for discrete sampling
259(1)
Higher dimensions
260(1)
Pricing via expectations
261(1)
Early exercise
261(1)
Summary
261(2)
Asian Options
263(14)
Introduction
263(1)
Payoff types
263(1)
Types of averaging
264(1)
Arithmetic or geometric
264(1)
Discrete or continuous
264(1)
Extending the Black--Scholes equation
265(6)
Continuously-sampled averages
265(1)
Discretely-sampled averages
266(4)
Exponentially-weighted and other averages
270(1)
The Asian tail
271(1)
Early exercise
271(1)
Asian options in higher dimensions
271(1)
Similarity reductions
272(2)
Put-call parity for the European average strike
273(1)
Some formulae
274(1)
Summary
275(2)
Lookback Options
277(8)
Introduction
277(1)
Types of payoff
277(1)
Continuous measurement of the maximum
277(3)
Discrete measurement of the maximum
280(1)
Similarity reduction
280(1)
Some formulae
281(2)
Summary
283(2)
Derivatives and Stochastic Control
285(8)
Introduction
285(1)
Perfect trader and passport options
285(3)
Similarity solution
287(1)
Limiting the number of trades
288(1)
Limiting the time between trades
289(1)
Non-optimal trading and the benefits to the writer
290(1)
Summary
291(2)
Miscellaneous Exotics
293(16)
Introduction
293(1)
Forward start options
293(2)
Shout options
295(1)
Capped lookbacks and Asians
296(1)
Combining path-dependent quantities: the lookback-Asian etc.
296(3)
The maximum of the asset and the average of the asset
297(1)
The average of the asset and the maximum of the average
298(1)
The maximum of the asset and the average of the maximum
298(1)
The volatility option
299(2)
The continuous-time limit
301(1)
Ladders
301(1)
Parisian options
301(4)
Examples
304(1)
Summary
305(4)
PART THREE EXTENDING BLACK--SCHOLES 309(214)
Defects in the Black--Scholes Model
311(8)
Introduction
311(1)
Discrete hedging
312(1)
Transaction costs
312(1)
Volatility smiles and surfaces
312(1)
Stochastic volatility
313(1)
Uncertain parameters
313(1)
Empirical analysis of volatility
313(1)
Jump diffusion
314(1)
Crash modeling
314(1)
Speculating with options
314(1)
Optimal static hedging
315(1)
The feedback effect of hedging in illiquid markets
315(1)
Utility theory
316(1)
More about American options and related matters
316(1)
Stochastic volatility and mean-variance analysis
316(1)
Advanced dividend modeling
317(1)
Summary
317(2)
Discrete Hedging
319(12)
Introduction
319(1)
A model for a discretely-hedged position
319(2)
A higher-order analysis
321(5)
Choosing the best Δ
323(1)
The hedging error
324(1)
Pricing the option
325(1)
The adjusted Δ and option value
325(1)
The real distribution of returns and the hedging error
326(2)
Total hedging error
328(1)
Summary
329(2)
Transaction Costs
331(26)
Introduction
331(1)
The effect of costs
331(1)
The model of Leland (1985)
332(1)
The model of Hoggard, Whalley & Wilmott (1992)
333(4)
Non-single-signed gamma
337(1)
The marginal effect of transaction costs
337(3)
Other cost structures
340(1)
Hedging to a bandwidth: the model of Whalley & Wilmott (1993) and Henrotte (1993)
340(1)
Utility-based models
341(3)
The model of Hodges & Neuberger (1989)
341(1)
The model of Davis, Panas & Zariphopoulou (1993)
342(1)
The asymptotic analysis of Whalley & Wilmott (1993)
342(1)
Arbitrary cost structure
343(1)
Interpretation of the models
344(2)
Nonlinearity
344(1)
Negative option prices
345(1)
Existence of solutions
346(1)
Non-normal returns
346(1)
Empirical testing
347(6)
Black--Scholes and Leland hedging
348(1)
Market movement or delta-tolerance strategy
349(1)
The utility strategy
349(2)
Using the real data
351(1)
And the winner is...
352(1)
Summary
353(4)
Volatility Smiles and Surfaces
357(16)
Introduction
357(1)
Implied volatility
357(2)
Time-dependent volatility
359(2)
Volatility smiles and skews
361(1)
Volatility surfaces
362(1)
Backing out the local volatility surface from European call option prices
362(4)
A simple volatility surface parameterization
366(1)
An approximate solution
367(1)
Volatility information contained in an at-the-money straddle
367(1)
Volatility information contained in a risk-reversal
368(1)
Time dependence
369(1)
A market convention
369(1)
How do I use the local volatility surface?
370(1)
Summary
370(3)
Stochastic Volatility
373(10)
Introduction
373(1)
Random volatility
373(1)
A stochastic differential equation for volatility
373(1)
The pricing equation
374(2)
The market price of volatility risk
376(1)
Aside: The market price of risk for traded assets
377(1)
An example
377(2)
Named models
379(1)
GARCH
379(1)
Stochastic implied volatility: the model of Schonbucher
379(2)
Summary
381(2)
Uncertain Parameters
383(12)
Introduction
383(2)
Best and worst cases
385(6)
Uncertain volatility: The model of Avellaneda, Levy & Paras and Lyons (1995)
385(2)
Example: An up-and-out call
387(2)
Uncertain interest rate
389(1)
Uncertain dividends
390(1)
Uncertain correlation
391(1)
Nonlinearity
391(1)
Summary
392(3)
Empirical Analysis of Volatility
395(8)
Introduction
395(1)
Stochastic volatility and uncertain parameters revisited
395(1)
Deriving an empirical stochastic volatility model
396(1)
Estimating the volatility of volatility
397(1)
Estimating the drift of volatility
398(1)
How to use the model
399(1)
Option pricing with stochastic volatility
399(1)
The time evolution of stochastic volatility
399(1)
Stochastic volatility, certainty bands and confidence limits
400(1)
Summary
400(3)
Jump Diffusion
403(12)
Introduction
403(1)
Evidence for jumps
403(3)
Poisson processes
406(2)
Hedging when there are jumps
408(1)
Hedging the diffusion
408(1)
Hedging the jumps
409(1)
Hedging the jumps and risk neutrality
410(1)
The downside of jump-diffusion models
411(1)
Jump volatility
411(1)
Jump volatility with deterministic decay
412(1)
Summary
413(2)
Crash Modeling
415(14)
Introduction
415(1)
Value at Risk
415(1)
A simple example: the hedged call
416(1)
A mathematical model for a crash
417(4)
Case I: Black--Scholes hedging
420(1)
Case II: Crash hedging
420(1)
An example
421(1)
Optimal static hedging: VaR reduction
422(1)
Continuous-time limit
423(1)
A range for the crash
423(1)
Multiple crashes
424(1)
Limiting the total number of crashes
424(1)
Limiting the frequency of crashes
424(1)
Crashes in a multi-asset world
425(1)
Fixed and floating exchange rates
425(1)
Summary
426(3)
Speculating with Options
429(16)
Introduction
429(1)
A simple model for the value of an option to a speculator
430(3)
The present value of expected payoff
430(1)
Standard deviation
431(2)
More sophisticated models for the return on an asset
433(5)
Diffusive drift
435(1)
Jump drift
435(3)
Early closing
438(3)
To hedge or not to hedge?
441(2)
Other issues
443(1)
Summary
443(2)
Static Hedging
445(16)
Introduction
445(1)
Static replicating portfolio
445(1)
Matching a `target' contract
446(1)
Static hedging: nonlinear governing equation
447(1)
Nonlinear equations
448(1)
Pricing with a nonlinear equation
448(1)
Static hedging
449(2)
Optimal static hedging
451(2)
Hedging path-dependent options with vanilla options
453(2)
Barrier options
453(1)
Pricing and optimally hedging a portfolio of barrier options
454(1)
The mathematics of optimization
455(5)
Downhill simplex method
455(4)
Simulated annealing
459(1)
Optimal portfolios for speculators
460(1)
Summary
460(1)
The Feedback Effect of Hedging in Illiquid Markets
461(16)
Introduction
461(1)
The trading strategy for option replication
462(1)
The excess demand function
463(1)
Incorporating the trading strategy
463(2)
The influence of replication
465(3)
The forward equation
468(2)
The boundaries
468(2)
Numerical results
470(4)
Time-independent trading strategy
471(2)
Put replication trading
473(1)
Summary
474(3)
Utility Theory
477(8)
Introduction
477(1)
Ranking events
477(1)
The utility function
478(1)
Risk aversion
479(1)
Special utility functions
479(1)
Certainty equivalent wealth
480(2)
Maximization of expected utility
482(1)
Ordinal and cardinal utility
482(1)
Summary
483(2)
More About American Options and Related Matters
485(20)
Introduction
485(1)
What Derivatives Week published
486(1)
Hold these thoughts
487(1)
Change of notation
487(1)
And finally, the paper...
488(1)
Introduction
488(2)
Preliminary: pricing and hedging
490(1)
Utility maximizing exercise time
491(4)
Constant Absolute Risk Aversion
493(1)
Hyperbolic Absolute Risk Aversion
494(1)
The expected return
495(1)
Profit from selling American options
495(3)
Concluding remarks
498(1)
FAQ
499(1)
Another situation where the same idea applies: passport options
499(4)
Recap
499(1)
Utility maximization in the passport option
500(3)
Summary
503(2)
Stochastic Volatility and Mean-variance Analysis
505(8)
Introduction
505(1)
The model for the asset and its volatility
506(1)
Analysis of the mean
506(1)
Analysis of the variance
506(1)
Choosing Δ to minimize the variance
507(1)
The mean and variance equations
507(1)
How to interpret and use the mean and variance
508(1)
Static hedging and portfolio optimization
508(1)
Example: Valuing and hedging an up-and-out call
509(4)
Static hedging
511(2)
Summary
513(1)
Advanced Dividend Modeling
513(10)
Introduction
513(1)
Why do we need dividend models?
513(2)
Effects of dividends on asset prices
515(2)
Market frictions
516(1)
Term structure of dividends
516(1)
Stochastic dividends
517(1)
Poisson jumps
518(1)
Uncertainty in dividend amount and timing
518(2)
Summary
520(3)
PART FOUR INTEREST RATES AND PRODUCTS 523(186)
Fixed-Income Products and Analysis: Yield, Duration and Convexity
525(20)
Introduction
525(1)
Simple fixed-income contracts and features
525(3)
The zero-coupon bond
525(1)
The coupon-bearing bond
526(1)
The money market account
526(1)
Floating rate bonds
526(1)
Forward-rate agreements
526(1)
Repos
527(1)
STRIPS
528(1)
Amortization
528(1)
Call provision
528(1)
International bond markets
528(1)
United States of America
528(1)
United Kingdom
529(1)
Japan
529(1)
Accrued interest
529(1)
Day count conventions
529(1)
Continuously- and discretely-compounded interest
529(1)
Measures of yield
530(2)
Current yield
520(11)
The Yield to Maturity (YTM) or Internal Rate of Return (IRR)
531(1)
The yield curve
532(1)
Price/yield relationship
533(1)
Duration
533(2)
Convexity
535(1)
An example
536(1)
Hedging
536(2)
Time-dependent interest rate
538(2)
Discretely-paid coupons
540(1)
Forward-rates and bootstrapping
541(2)
Interpolation
543(1)
Summary
544(1)
Swaps
545(10)
Introduction
545(1)
The vanilla interest rate swap
545(2)
Comparative advantage
547(1)
The swap curve
548(1)
Relationship between swaps and bonds
548(3)
Bootstrapping
551(1)
Other features of swaps contracts
551(1)
Other types of swap
552(1)
Basis rate swap
552(1)
Equity swaps
553(1)
Currency swaps
553(1)
Summary
553(2)
One-factor Interest Rate Modeling
555(14)
Introduction
555(1)
Stochastic interest rates
555(1)
The bond pricing equation for the general model
556(2)
What is the market price of risk?
558(11)
Interpreting the market price of risk, and risk neutrality
569(1)
Tractable models and solutions of the bond pricing equation
569
Solution for constant parameters
561(2)
Named models
563(4)
Vasicek
563(2)
Cox, Ingersoll & Ross
565(1)
Ho & Lee
566(1)
Hull & White
567(1)
Summary
567(2)
Yield Curve Fitting
569(8)
Introduction
569(1)
Ho & Lee
569(1)
The extended Vasicek model of Hull & White
570(1)
Yield-curve fitting: for and against
571(4)
For
571(1)
Against
572(3)
Other models
575(1)
Summary
575(2)
Interest Rate Derivatives
577(20)
Introduction
577(1)
Callable bonds
577(1)
Bond options
578(3)
Market practice
578(3)
Caps and floors
581(3)
Cap/floor parity
583(1)
The relationship between a caplet and a bond option
583(1)
Market practice
583(1)
Collars
584(1)
Step-up swaps, caps and floors
584(1)
Range notes
584(1)
Swaptions, captions and floortions
584(2)
Market practice
584(2)
Spread options
586(1)
Index amortizing rate swaps
586(4)
Similarity solution
588(1)
Other features in the index amortizing rate swap
589(1)
Contracts with embedded decisions
590(1)
When the interest rate is not the spot rate
591(1)
The relationship between the spot interest rate and other rates
592(1)
Some more exotics
592(1)
Some examples
593(2)
Summary
595(2)
Convertible Bonds
597(14)
Introduction
597(1)
Convertible bond basics
597(1)
Market practice
598(2)
What are CBs for?
600(1)
Pricing CBs with known interest rate
600(3)
Call and put features
601(2)
Two-factor modeling: convertible bonds with stochastic interest rate
603(4)
A special model
607(1)
Path dependence in convertible bonds
608(1)
Dilution
609(1)
Credit risk issues
609(1)
Summary
610(1)
Mortgage-backed Securities
611(10)
Introduction
611(1)
Individual mortgages
612(1)
Monthly payments in the fixed rate mortgage
612(1)
Prepayment
612(1)
Mortgage-backed securities
613(1)
The issuers
613(1)
Modeling prepayment
613(4)
The statistics of repayment
614(1)
The PSA model
615(1)
More realistic models
616(1)
Valuing MBSs
617(2)
Summary
619(2)
Multi-factor Interest Rate Modeling
621(12)
Introduction
621(1)
Theoretical framework for two factors
621(3)
Special case: modeling a long-term rate
623(1)
Special case: modeling the spread between the long and the short rate
624(1)
Popular models
624(2)
The phase plane in the absence of randomness
626(3)
The yield curve swap
629(1)
General multi-factor theory
630(2)
Tractable affine models
630(2)
Summary
632(1)
Empirical Behavior of the Spot Interest Rate
633(12)
Introduction
633(1)
Popular one-factor spot-rate models
634(1)
Implied modeling: one factor
635(1)
The volatility structure
636(1)
The drift structure
637(2)
The slope of the yield curve and the market price of risk
639(1)
What the slope of the yield curve tells us
640(1)
Properties of the forward-rate curve `on average'
641(2)
Implied modeling: two factor
643(1)
Summary
644(1)
Heath, Jarrow and Morton
645(14)
Introduction
645(1)
The forward-rate equation
645(1)
The spot rate process
646(1)
The non-Markov nature of HJM
647(1)
The market price of risk
647(1)
Real and risk neutral
648(1)
The relationship between the risk-neutral forward; rate drift and volatility
648(1)
Pricing derivatives
649(1)
Simulations
649(1)
Trees
650(1)
The Musiela parameterization
650(1)
Multi-factor HJM
650(1)
A simple one-factor example: Ho & Lee
651(1)
Principal component analysis
652(2)
The power method
654(1)
Options on equities etc.
654(1)
Non-infinitesimal short rate
655(1)
The Brace, Gatarek and Musiela model
655(2)
Summary
657(2)
Interest-rate Modeling Without Probabilities
659(20)
Introduction
659(1)
What do I want from an interest rate model?
660(1)
A non-probabilistic model for the behavior of the short-term interest rate
660(1)
Worst-case scenarios and a nonlinear equation
661(2)
Let's see that again in slow motion
662(1)
Examples of hedging: spreads for prices
663(6)
Hedging with one instrument
665(1)
Hedging with multiple instruments
666(3)
Generating the `Yield Envelope'
669(2)
Swaps
671(4)
Caps and floors
675(2)
Applications of the model
677(1)
Identifying arbitrage opportunities
677(1)
Establishing prices for the market maker
677(1)
Static hedging to reduce interest rate risk
677(1)
Risk management: a measure of absolute loss
678(1)
A remark on the validity of the model
678(1)
Summary
678(1)
Pricing and Optimal Hedging of Derivatives, the Non-Probabilistic Model Cont'd
679(18)
Introduction
679(1)
A real portfolio
679(4)
Bond options
683(5)
Pricing the European option on a zero-coupon bond
683(2)
Pricing and hedging American options
685(3)
Contracts with embedded decisions
688(2)
The index amortizing rate swap
690(3)
Convertible bonds
693(2)
Summary
695(2)
Extensions to the Non-probabilistic Interest-rate Model
697(12)
Introduction
697(1)
Fitting forward-rates
697(1)
Economic cycles
698(1)
Interest rate bands
699(2)
Estimating s from past data
700(1)
Crash modeling
701(4)
A maximum number of crashes
702(2)
A maximum frequency of crashes
704(1)
Estimating e from past data
705(1)
Liquidity
705(2)
Summary
707(2)
PART FIVE RISK MEASUREMENT AND MANAGEMENT 709(108)
Portfolio Management
711(16)
Introduction
711(1)
The Kelly criterion
712(1)
Diversification
713(2)
Uncorrelated assets
714(1)
Modern Portfolio Theory
715(2)
Including a risk-free investment
716(1)
Where do I want to be on the efficient frontier?
717(3)
Markowitz in practice
720(1)
Capital asset pricing model
720(2)
The single-index model
720(2)
Choosing the optimal portfolio
722(1)
The multi-index model
722(1)
Cointegration
722(2)
Performance measurement
724(1)
Summary
725(2)
Asset Allocation in Continuous Time
727(10)
Introduction
727(1)
One risk-free and one risky asset
727(5)
The wealth process
727(1)
Maximizing expected utility
728(1)
Stochastic control and the Bellman equation
729(1)
Constant Relative Risk Aversion
730(1)
Constant Absolute Risk Aversion
731(1)
Many assets
732(1)
Maximizing long-term growth
733(1)
A brief look at transaction costs
734(2)
Summary
736(1)
Value at Risk
737(10)
Introduction
737(1)
Definition of value at risk
737(1)
VaR for a single asset
738(2)
VaR for a portfolio
740(1)
VaR for derivatives
740(3)
The delta approximation
741(1)
The delta-gamma approximation
741(2)
Use of valuation models
743(1)
Fixed-income portfolios
743(1)
Simulations
743(1)
Monte Carlo
743(1)
Bootstrapping
744(1)
Use of VaR as a performance measure
744(2)
Summary
746(1)
Value of the Firm and the Risk of Default
747(8)
Introduction
747(1)
The value of the firm as a random variable
747(3)
Known interest rate
748(1)
Stochastic interest rates
749(1)
Modeling with measurable parameters and variables
750(1)
Calculating the value of the firm
751(2)
Summary
753(2)
Credit Risk
755(24)
Introduction
755(1)
Risky bonds
755(1)
Modeling the risk of default
756(1)
The Poisson process and the instantaneous risk of default
757(2)
A note on hedging
759(1)
Time-dependent intensity and the term structure of default
759(2)
Stochastic risk of default
761(2)
Positive recovery
763(1)
Special cases and yield curve fitting
763(1)
A case study: The Argentine Par bond
764(2)
Hedging the default
766(1)
Credit rating
767(2)
A model for change of credit rating
769(3)
The forward equation
770(2)
The backward equation
772(1)
The pricing equation
772(1)
Constant interest rates
772(1)
Stochastic interest rates
773(1)
Credit risk in CBs
773(2)
Bankruptcy when stock reaches a critical level
773(1)
Incorporating the instantaneous risk of default
773(2)
Modeling liquidity risk
775(1)
Summary
776(3)
Credit Derivatives
779(10)
Introduction
779(1)
Derivatives triggered by default
779(2)
Default swap
779(1)
Credit default swap
780(1)
Limited recourse note
780(1)
Asset swap
780(1)
Derivatives of the yield spread
781(1)
Default calls and puts
781(1)
Credit spread options
781(1)
Payment on change of rating
781(1)
Pricing credit derivatives
782(4)
An exchange option
783(1)
Payoff on change of rating
784(2)
Multi-factor derivatives
786(1)
Summary
786(3)
RiskMetrics and CreditMetrics
789(8)
Introduction
789(1)
The RiskMetrics datasets
790(1)
Calculating the parameters the RiskMetrics way
790(3)
Estimating volatility
790(1)
Correlation
791(2)
The CreditMetrics dataset
793(1)
Yield curves
793(1)
Spreads
793(1)
Transition matrices
794(1)
Correlations
794(1)
The CreditMetrics methodology
794(1)
A portfolio of risky bonds
795(1)
CreditMetrics model outputs
796(1)
Summary
796(1)
CrashMetrics
797(20)
Introduction
797(1)
Why do banks go broke?
797(1)
Market crashes
798(1)
CrashMetrics
799(1)
CrashMetrics for one stock
799(3)
Portfolio optimization and the Platinum Hedge
801(1)
The multi-asset/single-index model
802(8)
Portfolio optimization and the Platinum Hedge in the multi-asset model
809(1)
The marginal effect of an asset
810(1)
The multi-index model
810(1)
Incorporating time value
811(1)
Margin calls and margin hedging
811(2)
What is margin?
812(1)
Modeling margin
812(1)
The single-index model
813(1)
Counterparty risk
813(1)
Simple extensions to CrashMetrics
814(1)
The CrashMetrics Index (CMI)
814(1)
Summary
815(2)
PART SIX MISCELLANEOUS TOPICS 817(51)
Derivatives **** Ups
819(14)
Introduction
819(1)
Orange County
819(2)
Proctor and Gamble
821(2)
Metallgesellschaft
823(2)
Basis risk
824(1)
Gibson Greetings
825(2)
Barings
827(1)
Long-Term Capital Management
828(3)
Summary
831(2)
Bonus Time
833(14)
Introduction
833(1)
One bonus period
833(4)
Bonus depending on the Sharpe ratio
833(2)
Numerical results
835(2)
The skill factor
837(4)
Putting skill into the equation
841(2)
Example
842(1)
Summary
843(4)
Real Options
847(8)
Introduction
847(1)
Financial options and Real options
847(1)
An introductory example: Abandonment of a machine
847(2)
Optimal investment: simple example #2
849(1)
Temporary suspension of the project, costless
850(1)
Temporary suspension of the project, costly
850(1)
Sequential and incremental investment
851(1)
Summary
852(3)
Energy Derivatives
855(13)
Introduction
855(1)
The energy market
855(1)
What's so special about the energy markets?
856(3)
Why can't we apply Black--Scholes theory to energy derivatives?
859(1)
The convenience yield
860(1)
The Pilopovic two-factor model
860(2)
Fitting
862(1)
Energy derivatives
862(2)
One-day options
862(1)
Asian options
862(1)
Caps and floors
862(1)
Cheapest to deliver
863(1)
Basis spreads
863(1)
Swing options
863(1)
Spread options
864(1)
Summary
864(4)
PART SEVEN NUMERICAL METHODS 868(91)
Finite-difference Methods for One-factor Models
867(22)
Introduction
867(1)
Program of study
868(1)
Grids
869(1)
Differentiation using the grid
870(1)
Approximating &thetas;
871(1)
Approximating Δ
872(2)
Approximating Γ
874(1)
Bilinear interpolation
874(1)
Final conditions and payoffs
875(1)
Boundary conditions
875(3)
The explicit finite-difference method
878(7)
The Black--Scholes equation
881(1)
Convergence of the explicit method
881(4)
Upwind differencing
885(2)
Summary
887(2)
Further Finite-Difference Methods for One-Factor Models
889(24)
Introduction
889(1)
Implicit finite-difference methods
889(2)
The Crank--Nicolson method
891(10)
Boundary condition type I: Vko+1 given
893(1)
Boundary condition type II: relationship between Vko+1 and Vko+1
893(1)
Boundary condition type III: ∂2V/∂S2 = 0
894(1)
The matrix equation
895(1)
LU decomposition
895(3)
Successive over-relaxation, SOR
898(2)
Optimal choice of ω
900(1)
Comparison of finite-difference methods
901(1)
Other methods
901(1)
Douglas schemes
902(1)
Three time-level methods
903(1)
Richardson extrapolation
904(1)
Free boundary problems and American options
905(2)
Early exercise and the explicit method
906(1)
Early exercise and Crank-Nicolson
906(1)
Jump conditions
907(2)
A discrete cashflow
907(2)
Discretely-paid dividend
909(1)
Path-dependent options
909(2)
Discretely-sampled quantities
910(1)
Continuously-sampled quantities
910(1)
Summary
911(2)
Finite-difference Methods for Two-factor Models
913(10)
Introduction
913(1)
Two-factor models
913(2)
The explicit method
915(3)
Stability of the explicit method
918(1)
Alternating Direction Implicit
918(2)
The Hopscotch method
920(1)
Summary
921(2)
Monte Carlo Simulation and Related Methods
923(24)
Introduction
923(1)
Relationship between derivative values and simulations: Equities, indices, currencies, commodities
924(2)
Advantages of Monte Carlo simulation
926(1)
Using random numbers
927(1)
Generating normal variables
928(1)
Real versus risk neutral, speculation versus hedging
929(2)
Interest rate products
931(2)
Calculating the greeks
933(1)
Higher dimensions: Cholesky factorization
934(1)
Speeding up convergence
935(1)
Antithetic variables
935(1)
Control variate technique
935(1)
Pros and cons of Monte Carlo simulations
936(1)
American options
937(1)
Numerical integration
937(1)
Regular grid
938(1)
Basic Monte Carlo integration
938(2)
Low-discrepancy sequences
940(4)
Advanced techniques
944(1)
Summary
945(2)
Finite-difference Programs
947(12)
Introduction
947(1)
Explicit one-factor model for a convertible bond
947(1)
American call, implicit
948(1)
Explicit Parisian option
949(2)
Explicit stochastic volatility
951(1)
Crash modeling
952(1)
Explicit Epstein--Wilmott solution
953(1)
Risky-bond calculator
954(5)
Appendix A All the Math You Need... and No More (An Executive Summary) 959(8)
A.1 Introduction
959(1)
A.2 e
959(1)
A.3 log
960(1)
A.4 Differentiation and Taylor series
961(2)
A.5 Expectation and variance
963(2)
A.6 Another look at Black-Scholes
965(1)
A.7 Summary
966(1)
Epilog 967(2)
Bibliography 969(16)
Index 985

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