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Frequently Asked Questions in Quantitative Finance
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Year 2009
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Preface to the Second Edition
Preface to the First Edition
Chapter 1. The Quantitative Finance Timeline
1827 Brown
1900 Bachelier
1905 Einstein
1911 Richardson
1923 Wiener
1950s Samuelson
1951 Its
1952 Markowitz
1963 Sharpe, Lintner and Mossin
1966 Fama
1960s Sobol', Faure, Hammersley, Haselgrove and Halton...
1968 Thorp
1973 Black, Scholes and Merton
1974 Merton, again
1977 Boyle
1977 Vasicek
1979 Cox, Ross and Rubinstein
1979-81 Harrison, Kreps and Pliska
1986 Ho and Lee
1992 Heath, Jarrow and Morton
1990s Cheyette, Barrett, Moore and Wilmott
1994 Dupire, Rubinstein, Derman and Kani
1996 Avellaneda and Paras
1997 Brace, Gatarek and Musiela
2000 Li
2002 Hagan, Kumar, Lesniewski and Woodward
August 2007 quantitative finance in disrepute
And Now a Brief Unofficial History!
References and Further Reading
Chapter 2. FAQs
What are the Different Types of Mathematics Found in Quantitative Finance?
Probabilistic
Deterministic
Discrete/Continuous
Simulations
Discrimination methods
Approximations
Asymptotic analysis
Series solutions
Green's functions
What is Arbitrage?
What is Put-Call Parity?
What is the Central Limit Theorem and What are its Implications for Finance?
How is Risk Defined in Mathematical Terms?
What is Value at Risk and How is it Used?
What is Extreme Value Theory?
What is CrashMetrics?
What is a Coherent Risk Measure and What are its Properties?
Coherent measures
Attribution
What is Modern Portfolio Theory?
What is the Capital Asset Pricing Model?
What is Arbitrage Pricing Theory?
What is Maximum Likelihood Estimation?
Find the volatility
Quants' salaries
What is Cointegration?
What is the Kelly Criterion?
Why Hedge?
Delta hedging
Gamma hedging
Vega hedging
Static hedging
Superhedging
Margin hedging
Crash (Platinum) hedging
What is Marking to Market and How Does it Affect Risk Management in Derivatives Trading?
What is the Efficient Markets Hypothesis?
What are the Most Useful Performance Measures?
Sharpe ratio
Modigliani-Modigliani measure
Sortino ratio
Treynor ratio
Information ratio
What is a Utility Function and How is it Used?
What is the Difference between a Quant and an Actuary?
What is a Wiener Process/Brownian Motion and What are its Uses in Finance?
What is Jensen's Inequality and What is its Role in Finance?
What is Ito's Lemma?
Why Does Risk-Neutral Valuation Work?
What is Girsanov's Theorem, and Why is it Important in Finance?
What are the Greeks?
Delta
Gamma
Theta
Speed
Vega
Rho
Colour
Vanna
Vomma or Volga
Shadow greeks
Why do Quants like Closed-Form Solutions?
What are the Forward and Backward Equations?
The forward equation
The backward equation
Option prices
What is the Black—Scholes Equation?
Which Numerical Method should I Use and When?
Finite-difference methods
Number of dimensions
Functional form of coefficients
Boundary/final conditions
Decision features
Linear or non-linear
Efficiency
Programme of study
Monte Carlo methods
Number of dimensions
Functional form of coefficients
Boundary/final conditions
Decision features
Linear or non-linear
Efficiency
Programme of study
Numerical integration
Efficiency
Programme of study
Summary
What is Monte Carlo Simulation?
Exploring portfolio statistics
Pricing derivatives
What is the Finite-Difference Method?
What is a Poisson Process and What are its Uses in Finance?
What is a Jump-Diffusion Model and How does it Affect Option Values?
What is Meant by 'Complete' and 'Incomplete' Markets?
Can I use Real Probabilities to Price Derivatives?
What is Volatility?
Econometric models
Deterministic models
Stochastic volatility
Poisson processes
Uncertain volatility
What is the Volatility Smile?
What is GARCH?
What?
Why?
How?
Family members
How Do I Dynamically Hedge?
What is the correct delta?
How big is my hedging error?
Can I optimize my hedge?
How much will transaction costs reduce my profit?
Can I optimize my hedging when there are transaction costs?
What is Serial Autocorrelation and Does it Have a Role in Derivatives?
What is Dispersion Trading?
What is Bootstrapping using Discount Factors?
What is the LIBOR Market Model and its Principal Applications in Finance?
What is Meant by the 'Value' of a Contract?
What is Calibration?
What is Option Adjusted Spread?
What is the Market Price of Risk?
Can I Reverse Engineer a Partial Differential Equation to get at the Model and Contract?
Term independent of V
The V term
First-derivative terms
Second-derivative terms
Other terms?
What is the Difference Between the Equilibrium Approach and the No-Arbitrage Approach to Modelling?
How Good is the Assumption of Normal Distributions for Financial Returns?
How Robust is the Black-Scholes Model?
Hedging is continuous
There are no transaction costs
Volatility is constant
There are no arbitrage opportunities
The underlying is lognormally distributed
There are no costs associated with borrowing stock for going short
Returns are normally distributed
Why is the Lognormal Distribution Important?
What are Copulas and How are they Used in Quantitative Finance?
What is Asymptotic Analysis and How is it Used in Financial Modelling?
Transactions costs
SABR
Fast drift and high volatility in stochastic volatility models
What is a Free-Boundary Problem and What is the Optimal-Stopping Time for an American Option?
What are Low-Discrepancy Numbers?
Intuition
What are the Bastard Greeks?
What are the Stupidest Things People have Said about Risk Neutrality?
What is the Best-Kept Secret in Quantitative Finance?
Chapter 3. The Financial Modellers' Manifesto
Preface
Manifesto
Chapter 4. Essays
Science in Finance: Introduction
Science in Finance I Revisited: Supply and Demand, and Spoon Bending
Science in Finance II: '... ists'
Science in Finance IV: The Feedback Effect
Science in Finance VI: True Sensitivities, CDOs and Correlations
Science in Finance VII: Risk Management — What is the Point?
Science in Finance IX: In Defence of Black, Scholes and Merton
Magicians and Mathematicians
Volatility Arbitrage
The Same Old Same Old
Results and Ideas: Two Classical Putdowns
It Is and It Isn't
This is No Longer Funny
THERE WILL BE MORE ROQUE TRADERS
GOOD SALESMEN WILL HOODWINK SMART PEOPLE
CONVEXITY WILL BE MISSED
CORRELATION PRODUCTS WILL BLOW UP DRAMATICALLY
RISK MANAGEMENT WILL FAIL
VOLATILITY WILL INCREASE ENORMOUSLY AT TIMES FOR NO ECONOMIC REASON
TOO MUCH MONEY WILL GO INTO TOO FEW PRODUCTS
MORE HEDGE FUNDS WILL COLLAPSE
POLITICIANS AND GOVERNMENTS WILL REMAIN COMPLETELY IN THE DARK
Frustration
Ponzi Schemes, Auditors, Regulators, Credit Ratings, and Other Scams
Economics Makes My Brain Hurt
Name and Shame in Our New Blame Game!
Chapter 5. The Commonest Mistakes in Quantitative Finance: A Dozen Basic Lessons in Commonsense for Quants and Risk Managers and the Traders Who Rely on Them
Introduction
Quiz
Lesson 1: Lack of Diversification
Lesson 2: Supply and Demand
Lesson 3:Jensen's Inequality Arbitraje
Lesson 4: Sensitivity to Parameters
Lesson 5: Correlation
Lesson 6: Reliance on Continuous Hedging (Arguments)
Lesson 7: Feedback
Lesson 8: Reliance on Closed-Form Solutions
Lesson9: Valuation is Not Linear
Lesson 10: Calibration
Why is calibration unstable?
Lesson 11: Too Much Precision
Equity, FX and commodity markets
Fixed-income markets
Correlation markets
Credit markets
Lesson 12: Too Much Complexity
Bonus Lesson 13: The Binomial Method is Rubbish
Summary
Chapter 6. The Most Popular Probability Distributions and Their Uses in Finance
Normal or Gaussian
Lognormal
Poisson*
Chi square
Gumbel
Weibull
Student's t
Pareto
Uniform
Inverse normal
Gamma
Logistic
Laplace
Cauchy
Beta
Exponential
Chapter 7. Twelve Different Ways to Derive Black-Scholes
Hedging and the Partial Differential Equation
Martingales
Change of Numeraire
Local Time
Parameters as Variables
Continuous-Time Limit of the Binomial Model
CAPM
Utility Theory
Taylor Series
Mellin Transform
A Diffusion Equation
Black—Scholes for Accountants
Other Derivations
Chapter 8. Models and Equations
Equity, Foreign Exchange and Commodities
The lognormal random walk
Multi-dimensional lognormal random walks
Stochastic volatility
Hull & White (1987)
Square-root model/Heston (1993)
3/2 model
GARCH-diffusion
Ornstein-Uhlenbeck process
Asymptotic analysis
Schonbucher's stochastic implied volatility
Jump diffusion
Fixed Income
The yield to maturity (YTM) or internal rate of return (IRR)
Duration
Convexity
The spot rate and forward rates
Black 1976
Bond options
Caps and floors
Swaptions
Spot rate models
Vasicek
Cox, Injersoll & Ross
Ho & Lee
Hull & White
Black & Karasinski
Two-factor models
Brennan & Schwartz
Fong & Vasicek
Longstaff & Schwartz
Hull & White
The market price of risk as a random factor
SABR
Heath, Jarrow & Morton
Brace, Gatarek & Musiela
Prices as expectations
Credit
Structural models
Reduced form
Chapter 9. The Black-Scholes Formulae and the Greeks
Chapter 10. Common Contracts
Things to Look Out For in Exotic Contracts
Time dependence
Cash flows
Path dependence
Dimensionality
The order of an option
Embedded decisions
Examples
Accrual
American option
Asian option
Asset swap
Balloon option
Barrier option
Basis swap
Basket option
Bermudan option
Binary option
Break/Cancellable forward
Coupe option
Call option
Cap
Chooser option
Cliquet option
Constant Maturity Swap (CMS)
Collateralized Debt Obligation (CDO)
Collateralized Debt Obligation squared (CDO2)
Collateralized Mortgage Obligation (CMO)
Compound option
Contingent premium option
Convertible bond
Credit Default Swap (CDS)
Diff (erential) swap
Digital option
Exponential Collateralized Debt Obligation (ECDO)
Extendible option/swap
Floating Rate Note (FRN)
Floor
Forward
Forward Rate Agreement (FRA)
Forward-start option
Future
Hawai'ian option
Himalayan option
HYPER option
Index amortizing rate swap
Interest rate swap
Inverse floater
Knock-in/out option
LIBOR-in-arrears swap
Lookback option
Mortgage Backed Security (MBS)
Outperformance option
Parisian option
Pass through
Passport option
Put option
Quanto
Rainbow option
Range note
Ratchet
Repo
Reverse repo
Straddle
Strangle
STRIPS
Swap
Swaption
Total Return Swap (TRS)
Ultras
Variance swap
Chapter 11. Popular Quant Books
Paul Wilmott Introduces Quantitative Finance, Second Edition by Paul Wilmott
Paul Wilmott on Quantitative Finance, Second Edition by Paul Wilmott
Advanced Modelling in finance Using Excel and VBA by Mary Jackson and Mike Staunton
Option Valuation under Stochastic Volatility by Alan Lewis
The Concepts and Practice of Mathematical Finance by Mark Joshi
C++ Design Patterns and Derivatives Pricing by Mark Joshi
Heard on the Street by Timothy Crack
Monte Carlo Methods in Finance by Peter Jackel
Credit Derivatives Pricing Models by Philipp Schonbucher
Principles of Financial Engineering by Salih Neftci
Options, Futures, and Other Derivatives by John Hull
The Complete Guide to Option Pricing Formulas by Espen Gaarder Haug
Chapter 12. The Most Popular Search Words and Phrases on Wilmott.com
American option
Arbitrage
Asian option
Asset swap
Barrier option
Base correlation
Basket
Bermudan swaption
Calibration
Callable
Cap
CDO
CDS
CFA
CMS
Convertible
Convexity
Copula
Correlation
CQF
Default probability
Delta
Digital
Dispersion
Duration
Exotic
Expected loss
Finite difference
Gamma
GARCH
Hedge
Hybrid
Implied
Levy
LIBOR
Market maker
MBS
Mean reversion
Monte Carlo
Normal distribution
PDE
Quantlib
Quanto
Regression
Risk
Risk neutral
SABR
Skew
Smile
Sobol'
Stochastic
Structured products
Swap
Swaptions
Variance swap
Volatility
Yield curve
Esoterica
Chapter 13. Brainteasers
The Questions
Russian roulette
Matching birthdays
Another one about birthdays
Biased coins
Two heads
Balls in a bag
Sums of uniform random variables
Minimum and maximum correlation
Airforce One
Hit-and-run taxi
Annual returns
Dice game
100kgof berries
Urban planning
Closer to the edge or the centre?
Snowflake
The doors
Two thirds of the average
Ones and zeros
Bookworm
Compensation
Einstein's brainteaser
Gender ratio
Covering a chessboard with dominoes
Aircraft armour
Hanging a picture
Ages of three children
The Monty Hall problem
Ants on a circle
Four switches and a lightbulb
Turnover
Muddy faces
The Oracle at Delphi
Miss Moneypenny
Pirate puzzle
The Answers
Russian roulette
Matching birthdays
Another one about birthdays
Biased coins
Two heads
Balls in a bag
Sums of uniform random variables
Minimum and maximum correlation
Airforce One
Hit-and-run taxi
Annual returns
Dice game
100 kg of berries
Urban planning
Closer to the edge or the centre?
Snowflake
The doors
Two thirds of the average
Ones and zeros
Bookworm
Compensation
Einftein'f brainteaser
Gender ratio
Covering a chessboard with dominoes
Aircraft armour
Hanging a picture
Ages of three children
The Monty Hall problem
Ants on a circle
Four switches and a lightbulb
Turnover
Muddy faces
The Oracle at Delphi
Miss Moneypenny
Pirate puzzle
Chapter 14. Paul & Dominic's Guide to Getting a Quant Job
Introduction
Making a difference
Unberstanb the process
What you need to prove
Kissing frogs
Writing a CV
Read the job specification
Make sure you can be contacted
Get it checked
Covering letter
Fonts and layout
PDF
Name
Dates
Be honest
Show that you can do things
Interests and hobbies
Last job first
Paul & Dominic
Multiple CVs
Finding banks
Interviews
Be prepared
Be confident
Be punctual
Set traps
Show you can do things
Questions for the interviewer
Getting the message across
Find out more about the job
Appearance
Good clothes
Neatness is good
Colours
Jewellery
Perfume and aftershave
Make-up
What People Get Wrong
Zeroth law of holes
Sleep regularly, sleep often
Make eye contact
Apply for the right job
Barbarians
Read your CV
Mobile phone interviews
Focus
Asking questions
Buzzwords
Show some market insight
Brainteasers
Be polite
Be true to yourself
Do not sound as if you work for Accenture
Interview overlap
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