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Paul Wilmott Introduces Quantitative Finance by Paul Wilmott
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Paul Wilmott Introduces Quantitative Finance [Paperback]

by Paul Wilmott
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Description of Paul Wilmott Introduces Quantitative Finance

Paul Wilmott Introduces Quantitative Finance, Second Edition is an accessible introduction to the classical side of quantitative finance specifically for university students. Adapted from the comprehensive, even epic, works Derivatives and Paul Wilmott on Quantitative Finance, Second Edition, it includes carefully selected chapters to give the student a thorough understanding of futures, options and numerical methods. Software is included to help visualize the most important ideas and to show how techniques are implemented in practice. There are comprehensive end-of-chapter exercises to test students on their understanding.

In praise of Paul Wilmott and his previous works

Some people write for fame, some for money. Most academics write books to impress the professor down the corridor so that one day they will be the professor down the corridor everyone is trying to impress. Uniquely, Paul Wilmott writes to inform and educate his readers, to convey ideas, and, most importantly, to show them how to do it. His greatest admirers are his readers. So, instead of endorsements from the great and the good, here are the words of his fans. Their sometimes unique spelling has been retained.

I found it to be easily the best book that I have read/worked through on the subject.

I thought it might amuse you to know that I think your book got me a job!

I'd like to say that this is a great book but you already know that!

I'm a junior derivatives trader in Mexico City. I've seen your book and I have only one coment: SEXY!

Loved your book, which is a breath of fresh air, amongst all those arid derivatives books!! It really is in a class of its own. I have wasted so much money on stupid derivative books which too elementary or way too complicated.

Purchased both Quant Finance and Derivatives a couple of days ago. Will not be able to afford steak or wine for weeks as a result.

BTW, I want to congratulate you for the ∗best∗ book in Financial Engineering I've read in the last years.

After reading the book I'd like to follow one of your courses, but they are way too expensive.

Congratulations for your brilliant book.

What I like about it is that it has this no-nonsense kind of approach that you'd expect in a physics text and it spells out the "stuff between the equations".

Congratulation to your book Derivatives !!! The way you describe, present, and deliver Derivative knowledge is unique! One can feel your passion on the topic. It's a pleasure to read, study, re-read...

Congratulations on a great new book - 'PW on Quant Finance'. I bought the DERIVATIVES one but cannot afford this one!!

I am fanatical follower of your book "Derivatives". You are best and this not flattery. Sorry from my English!

We use it for the part of our Banking and Risk Management course and it's much more comprehensive than the books that we have recommended in our study guide.

Your book “Derivatives: the Theory and Practice of Financial Engineering” is the best in the market so far.

I shall waste no more precious words but to say that I am very simpathetic to your humor and irony...what most don't always seem to understand: irony is one of the GREAT filters to access knowledge in this world and an elegant one for that matter.

your book rocks

Congratulations to the success of your book (I got my copy of it for Christmas).

I would like to thank you for writing Derivatives.

Derivatives is the Greatest! Thank you, thank you, thank you!

Just read the first 7 chapters of Derivatives, and it speaks to me.

complete, brilliant and amusing, stimulating for some original ideas and examples, didactically ready to be used by Students; it employs mathematical tools as tools only, not as a target; it is the last but the best book on derivatives in my library.

You're book truly struck me as fun, informative and brilliant! Us American would say 'Awesome Dude!!!'

I had a course on derivatives and your book was not suggested by the teacher (a stupid teacher).

Love you for ever, baby. xxx M

Title Information

ISBN:
9780470319581
Pages:
728 pages
Format:
Paperback
Product Code:
168530
Publisher:
John Wiley & Sons Ltd
Published:
29/06/2007
Edition:
2nd Edition

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About Paul Wilmott

Paul Wilmott, described by the Financial Times as 'cult derivatives lecturer,' is one of the world's leading experts on quantitative finance and derivatives. He is the proprietor of an innovative magazine on quantitative finance and a highly popular community website (www.wilmott.com). He is the principal of the financial consultancy and training firm, Wilmott Associates, and the Course Director for the Certificate in Quantitative Finance. He has researched and published widely on financial engineering.

Contents of Paul Wilmott Introduces Quantitative Finance

1. Products and Markets: Equities, Commodities, Exchange Rates, Forwards and Futures
1.1 Introduction
1.2 Equities
1.2.1 Dividends
1.2.2 Stock splits
1.3 Commodities
1.4 Currencies
1.5 Indices
1.6 The time value of money
1.7 Fixed-income securities
1.8 Inflation-proof bonds
1.9 Forwards and futures
1.9.1 A first example of no arbitrage
1.10 More about futures
1.10.1 Commodity futures
1.10.2 FX futures
1.10.3 Index futures
1.11 Summary

2. 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
2.10 Speculation and gearing
2.11 Early exercise
2.12 Put-call parity
2.13 Binaries or digitals
2.14 Bull and bear spreads
2.15 Straddles and strangles
2.16 Risk reversal
2.17 Butterflies and condors
2.18 Calendar spreads
2.19 LEAPS and FLEX
2.20 Warrants
2.21 Convertible bonds
2.22 Over the counter options
2.23 Summary

3. The Binomial Model
3.1 Introduction
3.2 Equities can go down as well as up
3.3 The option value
3.4 Which part of our 'model' didn't we need?
3.5 Why should this 'theoretical price' be the 'market price'?
3.5.1 The role of expectations
3.6 How did I know to sell ½ of the stock for hedging?
3.6.1 The general formula for ?
3.7 How does this change if interest rates are non-zero?
3.8 Is the stock itself correctly priced?
3.9 Complete markets
3.10 The real and risk-neutral worlds
3.10.1 Non-zero interest rates
3.11 And now using symbols
3.11.1 Average asset change
3.11.2 Standard deviation of asset price change
3.12 An equation for the value of an option
3.12.1 Hedging
3.12.2 No arbitrage
3.13 Where did the probability p go?
3.14 Counter-intuitive?
3.15 The binomial tree
3.16 The asset price distribution
3.17 Valuing back down the tree
3.18 Programming the binomial method
3.19 The greeks
3.20 Early exercise
3.21 The continuous-time limit
3.22 Summary

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 Itô and Taylor
5.13 Itô 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
6.8 Options on dividend-paying equities
6.9 Currency options
6.10 Commodity options
6.11 Expectations and Black-Scholes
6.12 Some other ways of deriving the Black-Scholes equation
6.12.1 The martingale approach 1
6.12.2 The binomial model
6.12.3 CAPM/utility
6.13 No arbitrage in the binomial, Black-Scholes and 'other' worlds
6.14 Forwards and futures
6.14.1 Forward contracts
6.15 Futures contracts
6.15.1 When interest rates are known, forward prices and futures prices are the same
6.16 Options on futures
6.17 Summary

7. Partial Differential Equations
7.1 Introduction
7.2 Putting the Black-Scholes equation into historical perspective
7.3 The meaning of the terms in the Black-Scholes equation
7.4 Boundary and initial/final conditions
7.5 Some solution methods
7.5.1 Transformation to constant coefficient diffusion equation
7.5.2 Green's functions
7.5.3 Series solution
7.6 Similarity reductions
7.7 Other analytical techniques
7.8 Numerical solution
7.9 Summary

8. The Black-Scholes Formulæ and the 'Greeks'
8.1 Introduction
8.2 Derivation of the formulæ for calls, puts and simple digitals
8.2.1 Formula for a call
8.2.2 Formula for a put
8.2.3 Formula for a binary call
8.2.4 Formula for a binary put
8.3 Delta
8.4 Gamma
8.5 Theta
8.6 Speed
8.7 Vega
8.8 Rho
8.9 Implied volatility
8.10 A classification of hedging types
8.10.1 Why hedge?
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 hedgin
8.10.8 Crash (Platinum) hedging
8.11 Summary

9. Overview of Volatility Modeling
9.1 Introduction
9.2 The different types of volatility
9.2.1 Actual volatility
9.2.2 Historical or realized volatility
9.2.3 Implied volatility
9.2.4 Forward volatility
9.3 Volatility estimation by statistical means
9.3.1 The simplest volatility estimate: constant volatility/moving window
9.3.2 Incorporating mean reversion.
9.3.3 Exponentially weighted moving average.
9.3.4 A simple GARCH model
9.3.5 Expected future volatility
9.3.6 Beyond close-close estimators: range-based estimation of volatility
9.4 Maximum likelihood estimation
9.4.1 A simple motivating example: taxi numbers
9.4.2 Three hats
9.4.3 The math behind this: find the standard deviation
9.4.4 Quants' salaries
9.5 Skews and smiles
9.5.1 Sensitivity of the straddle to skews and smiles
9.5.2 Sensitivity of the risk reversal to skews and smiles
9.6 Different approaches to modeling volatility
9.6.1 To calibrate or not?
9.6.2 Deterministic volatility surfaces
9.6.3 Stochastic volatility
9.6.4 Uncertain parameters
9.6.5 Static hedging
9.6.6 Stochastic volatility and mean-variance analysis
9.6.7 Asymptotic analysis of volatility
9.7 The choices of volatility models
9.8 Summary

10. How to Delta Hedge
10.1 Introduction
10.2 What if implied and actual volatilities are different?
10.3 Implied versus actual, delta hedging but using which volatility?
10.4 Case 1: Hedge with actual volatility, s
10.5 Case 2: Hedge with implied volatility, ˜s
10.5.1 The expected profit after hedging using implied volatility
10.5.2 The variance of profit after hedging using implied volatility
10.6 Hedging with different volatilities
10.6.1 Actual volatility = Implied volatility
10.6.2 Actual volatility > Implied volatility
10.6.3 Actual volatility < Implied volatility
10.7 Pros and cons of hedging with each volatility
10.7.1 Hedging with actual volatility
10.7.2 Hedging with implied volatility
10.7.3 Hedging with another volatility
10.8 Portfolios when hedging with implied volatility
10.8.1 Expectation
10.8.2 Variance
10.8.3 Portfolio optimization possibilities
10.9 How does implied volatility behave?
10.9.1 Sticky strike
10.9.2 Sticky delta
10.9.3 Time-periodic behavior
10.10 Summary

11. An Introduction to Exotic and Path-dependent Options
11.1 Introduction
11.2 Option classification
11.3 Time dependence
11.4 Cashflows
11.5 Path dependence
11.5.1 Strong path dependence
11.5.2 Weak path dependence
11.6 Dimensionality
11.7 The order of an option
11.8 Embedded decisions
11.9 Classification tables
11.10 Examples of exotic options
11.10.1 Compounds and choosers
11.10.2 Range notes
11.10.3 Barrier options
11.10.4 Asian options
11.10.5 Lookback options
11.11 Summary of math/coding consequences
11.12 Summary

12. Multi-asset Options
12.1 Introduction
12.2 Multidimensional lognormal random walks
12.3 Measuring correlations
12.4 Options on many underlyings
12.5 The pricing formula for European non-path-dependent options on dividend-paying assets
12.6 Exchanging one asset for another: a similarity solution
12.7 Two examples
12.8 Realities of pricing basket options
12.8.1 Easy problems
12.8.2 Medium problems
12.8.3 Hard problems
12.9 Realities of hedging basket options
12.10 Correlation versus cointegration
12.11 Summary

13. Barrier Options
13.1 Introduction
13.2 Different types of barrier options
13.3 Pricing methodologies
13.3.1 Monte Carlo simulation
13.3.2 Partial differential equations
13.4 Pricing barriers in the partial differential equation framework
13.4.1 'Out' barriers
13.4.2 'In' barriers
13.5 Examples
13.5.1 Some more examples
13.6 Other features in barrier-style options
13.6.1 Early exercise
13.6.2 Repeated hitting of the barrier
13.6.3 Resetting of barrier
13.6.4 Outside barrier options
13.6.5 Soft barriers
13.6.6 Parisian options
13.7 Market practice: what volatility should I use?
13.8 Hedging barrier options
13.8.1 Slippage costs
13.9 Summary

14. Fixed-income Products and Analysis: Yield, Duration and Convexity
14.1 Introduction
14.2 Simple fixed-income contracts and features
14.2.1 The zero-coupon bond
14.2.2 The coupon-bearing bond
14.2.3 The money market account
14.2.4 Floating rate bonds
14.2.5 Forward rate agreements
14.2.6 Repos
14.2.7 STRIPS
14.2.8 Amortization
14.2.9 Call provision
14.3 International bond markets
14.3.1 United States of America
14.3.2 United Kingdom
14.3.3 Japan
14.4 Accrued interest
14.5 Day-count conventions
14.6 Continuously and discretely compounded interest
14.7 Measures of yield
14.7.1 Current yield
14.7.2 The yield to maturity (YTM) or internal rate of return (IRR).
14.8 The yield curve
14.9 Price/yield relationship
14.10 Duration
14.11 Convexity
14.12 An example
14.13 Hedging
14.14 Time-dependent interest rate
14.15 Discretely paid coupons
14.16 Forward rates and bootstrapping
14.16.1 Discrete data
14.16.2 On a spreadsheet
14.17 Interpolation
14.18 Summary

15. Swaps
15.1 Introduction
15.2 The vanilla interest rate swap
15.3 Comparative advantage
15.4 The swap curve
15.5 Relationship between swaps and bonds
15.6 Bootstrapping
15.7 Other features of swaps contracts
15.8 Other types of swap
15.8.1 Basis rate swap
15.8.2 Equity swaps
15.8.3 Currency swaps
15.9 Summary

16. One-factor Interest Rate Modeling
16.1 Introduction
16.2 Stochastic interest rates
16.3 The bond pricing equation for the general model
16.4 What is the market price of risk?
16.5 Interpreting the market price of risk, and risk neutrality
16.6 Named models
16.6.1 Vasicek
16.6.2 Cox, Ingersoll & Ross
16.6.3 Ho & Lee
16.6.4 Hull & White
16.7 Equity and FX forwards and futures when rates are stochastic
16.7.1 Forward contracts
16.8 Futures contracts
16.8.1 The convexity adjustment
16.9 Summary

17. Yield Curve Fitting
17.1 Introduction
17.2 Ho & Lee
17.3 The extended Vasicek model of Hull & White
17.4 Yield-curve fitting: for and against
17.4.1 For
17.4.2 Against
17.5 Other models
17.6 Summary

18. Interest Rate Derivatives
18.1 Introduction
18.2 Callable bonds
18.3 Bond options
18.3.1 Market practice
18.4 Caps and floors
18.4.1 Cap/floor parity
18.4.2 The relationship between a caplet and a bond option
18.4.3 Market practice
18.4.4 Collars
18.4.5 Step-up swaps, caps and floors
18.5 Range notes
18.6 Swaptions, captions and floortions
18.6.1 Market practice
18.7 Spread options
18.8 Index amortizing rate swaps
18.8.1 Other features in the index amortizing rate swap
18.9 Contracts with embedded decisions
18.10 Some examples
18.11 More interest rate derivatives
18.12 Summary

19. The Heath, Jarrow & Morton and Brace, Gatarek & Musiela Models
19.1 Introduction
19.2 The forward rate equation
19.3 The spot rate process
19.3.1 The non-Markov nature of HJM
19.4 The market price of risk
19.5 Real and risk neutral
19.5.1 The relationship between the risk-neutral forward rate drift and volatility
19.6 Pricing derivatives
19.7 Simulations
19.8 Trees
19.9 The Musiela parameterization
19.10 Multi-factor HJM
19.11 Spreadsheet implementation
19.12 A simple one-factor example: Ho & Lee
19.13 Principal Component Analysis
19.13.1 The power method
19.14 Options on equities, etc.
19.15 Non-infinitesimal short rate
19.16 The Brace, Gatarek & Musiela model
19.17 Simulations
19.18 PVing the cashflows.
19.19 Summary

20. Investment Lessons from Blackjack and Gambling
20.1 Introduction
20.2 The rules of blackjack
20.3 Beating the dealer
20.3.1 Summary of winning at blackjack
20.4 The distribution of profit in blackjack
20.5 The Kelly criterion
20.6 Can you win at roulette?
20.7 Horse race betting and no arbitrage
20.7.1 Setting the odds in a sporting game
20.7.2 The mathematics
20.8 Arbitrage
20.8.1 How best to profit from the opportunity?
20.9 How to bet
20.10 Summary

21. Portfolio Management
21.1 Introduction
21.2 Diversification
21.2.1 Uncorrelated assets
21.3 Modern portfolio theory
21.3.1 Including a risk-free investment
21.4 Where do I want to be on the efficient frontier?
21.5 Markowitz in practice
21.6 Capital Asset Pricing Model
21.6.1 The single-index model
21.6.2 Choosing the optimal portfolio
21.7 The multi-index model
21.8 Cointegration
21.9 Performance measurement
21.10 Summary

22. 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

23. Credit Risk
23.1 Introduction
23.2 The Merton model: equity as an option on a company's assets
23.3 Risky bonds
23.4 Modeling the risk of default
23.5 The Poisson process and the instantaneous risk of default
23.5.1 A note on hedging
23.6 Time-dependent intensity and the term structure of default
23.7 Stochastic risk of default
23.8 Positive recovery
23.9 Hedging the default
23.10 Credit rating
23.11 A model for change of credit rating
23.12 Copulas: pricing credit derivatives with many underlyings
23.12.1 The copula function
23.12.2 The mathematical definition
23.12.3 Examples of copulas
23.13 Collateralized debt obligations
23.14 Summary

24. RiskMetrics and CreditMetrics
24.1 Introduction
24.2 The RiskMetrics datasets
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
5.4 CrashMetrics
25.5 CrashMetrics for one stock
25.6 Portfolio optimization and the Platinum hedge
25.6.1 Other 'cost' functions
25.7 The multi-asset/single-index mode
25.7.1 Assuming Taylor series for the moment
25.8 Portfolio optimization and the Platinum hedge in the multi-asset model
25.8.1 The marginal effect of an asset
5.9 The multi-index model
25.10 Incorporating time value
25.11 Margin calls and margin hedging
25.11.1 What is margin?
25.11.2 Modeling margin
25.11.3 The single-index model
5.12 Counterparty risk
25.13 Simple extensions to CrashMetrics
25.14 The CrashMetrics Index (CMI)
25.15 Summary

26. Derivatives **** Ups
26.1 Introduction
26.2 Orange County
26.3 Proctor and Gamble
26.4 Metallgesellschaft
26.4.1 Basis risk
26.5 Gibson Greetings
26.6 Barings
26.7 Long-Term Capital Management
26.8 Summary

27. Overview of Numerical Methods
27.1 Introduction
27.2 Finite-difference methods
27.2.1 Efficiency
27.2.2 Program of study
27.3 Monte Carlo methods
27.3.1 Efficiency
27.3.2 Program of study
27.4 Numerical integration
27.4.1 Efficiency
27.4.2 Program of study
27.5 Summary

28. Finite-difference Methods for One-factor Models
28.1 Introduction
28.2 Grids
28.3 Differentiation using the grid
28.4 Approximating ?
28.5 Approximating ?
28.6 Approximating +
28.7 Example
28.8 Bilinear interpolation
28.9 Final conditions and payoffs
28.10 Boundary conditions
28.11 The explicit finite-difference method
28.11.1 The Black-Scholes equation
28.11.2 Convergence of the explicit method
28.12 The Code #1: European option
28.13 The Code #2: American exercise
28.14 The Code #3: 2-D output
28.15 Upwind differencing
28.16 Summary

29. Monte Carlo Simulation
29.1 Introduction
29.2 Relationship between derivative values and simulations: equities, indices, currencies, commodities
29.3 Generating paths
29.4 Lognormal underlying, no path dependency
29.5 Advantages of Monte Carlo simulation
29.6 Using random numbers
29.7 Generating Normal variables
29.7.1 Box-Muller
29.8 Real versus risk neutral, speculation versus hedging
29.9 Interest rate products
29.10 Calculating the greeks
29.11 Higher dimensions: Cholesky factorization
29.12 Calculation time
29.13 Speeding up convergence
29.13.1 Antithetic variables
29.13.2 Control variate technique
29.14 Pros and cons of Monte Carlo simulations
29.15 American options
29.16 Longstaff & Schwartz regression approach for American options
29.17 Basis functions
29.18 Summary

30. Numerical Integration
30.1 Introduction
30.2 Regular grid
30.3 Basic Monte Carlo integration
30.4 Low-discrepancy sequences
30.5 Advanced techniques
30.6 Summary

A. All the Math You Need. . . and No More (An Executive Summary)
A.1 Introduction
A.2 e
A.3 log
A.4 Differentiation and Taylor series
A.5 Differential equations
A.6 Mean, standard deviation and distributions
A.7 Summary

B. Forecasting the Markets? A Small Digression
B.1 Introduction
B.2 Technical analysis
B.2.1 Plotting
B.2.2 Support and resistance
B.2.3 Trendlines
B.2.4 Moving averages
B.2.5 Relative strength
B.2.6 Oscillators
B.2.7 Bollinger bands
B.2.8 Miscellaneous patterns
B.2.9 Japanese candlesticks
B.2.10 Point and figure charts
B.3 Wave theory
B.3.1 Elliott waves and Fibonacci numbers
B.3.2 Gann charts
B.4 Other analytics
B.5 Market microstructure modeling
B.5.1 Effect of demand on price
B.5.2 Combining market microstructure and option theory
B.5.3 Imitation
B.6 Crisis prediction
B.7 Summary

C. A Trading Game
C.1 Introduction
C.2 Aims
C.3 Object of the game
C.4 Rules of the game
C.5 Notes
C.6 How to fill in your trading sheet
C.6.1 During a trading round
C.6.2 At the end of the game

D. Contents of CD accompanying Paul Wilmott Introduces Quantitative Finance, second edition

E. What you get if (when) you upgrade to PWOQF2

Bibliography
Index


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