# Frequently Asked Questions in Quantitative Finance

Preface to the Second EditionPreface to the First EditionThe Quantitative Finance TimelineBrown Bachelier Einstein Richardson Wiener s Samuelson Its Markowitz Sharpe, Lintner and Mossin Fama s Sobol', Faure, Hammersley, Haselgrove and Halton... Thorp Black, Scholes and Merton Merton, again Boyle Vasicek Cox, Ross and Rubinstein -81 Harrison, Kreps and Pliska Ho and Lee Heath, Jarrow and Morton s Cheyette, Barrett, Moore and Wilmott Dupire, Rubinstein, Derman and Kani Avellaneda and Paras Brace, Gatarek and Musiela Li Hagan, Kumar, Lesniewski and Woodward August 2007 quantitative finance in disrepute And Now a Brief Unofficial History!References and Further ReadingFAQs 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 volatilityQuants' salariesWhat 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 equationThe backward equationOption pricesWhat is the Black—Scholes Equation?Which Numerical Method should I Use and When?Finite-difference methodsNumber of dimensions Functional form of coefficients Boundary/final conditions Decision features Linear or non-linear EfficiencyProgramme of studyMonte Carlo methodsNumber of dimensions Functional form of coefficients Boundary/final conditions Decision features Linear or non-linear EfficiencyProgramme of studyNumerical integrationEfficiencyProgramme of studySummaryWhat 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 membersHow 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?The Financial Modellers' ManifestoPrefaceManifestoEssaysScience in Finance: IntroductionScience in Finance I Revisited: Supply and Demand, and Spoon BendingScience in Finance II: '... ists'Science in Finance IV: The Feedback EffectScience in Finance VI: True Sensitivities, CDOs and CorrelationsScience in Finance VII: Risk Management — What is the Point?Science in Finance IX: In Defence of Black, Scholes and MertonMagicians and MathematiciansVolatility ArbitrageThe Same Old Same OldResults and Ideas: Two Classical PutdownsIt Is and It Isn'tThis is No Longer FunnyTHERE 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 FrustrationPonzi Schemes, Auditors, Regulators, Credit Ratings, and Other ScamsEconomics Makes My Brain HurtName and Shame in Our New Blame Game!The Commonest Mistakes in Quantitative Finance: A Dozen Basic Lessons in Commonsense for Quants and Risk Managers and the Traders Who Rely on ThemIntroductionQuizLesson 1: Lack of DiversificationLesson 2: Supply and DemandLesson 3:Jensen's Inequality ArbitrajeLesson 4: Sensitivity to ParametersLesson 5: CorrelationLesson 6: Reliance on Continuous Hedging (Arguments)Lesson 7: FeedbackLesson 8: Reliance on Closed-Form SolutionsLesson9: Valuation is Not LinearLesson 10: CalibrationWhy is calibration unstable?Lesson 11: Too Much PrecisionEquity, FX and commodity markets Fixed-income markets Correlation markets Credit markets Lesson 12: Too Much ComplexityBonus Lesson 13: The Binomial Method is RubbishSummaryThe 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 ExponentialTwelve Different Ways to Derive Black-ScholesHedging and the Partial Differential EquationMartingalesChange of NumeraireLocal TimeParameters as VariablesContinuous-Time Limit of the Binomial ModelCAPMUtility TheoryTaylor SeriesMellin TransformA Diffusion EquationBlack—Scholes for AccountantsOther DerivationsModels and EquationsEquity, Foreign Exchange and CommoditiesThe lognormal random walkMulti-dimensional lognormal random walksStochastic volatilityHull & White (1987) Square-root model/Heston (1993) /2 modelGARCH-diffusion Ornstein-Uhlenbeck process Asymptotic analysis Schonbucher's stochastic implied volatility Jump diffusionFixed IncomeThe yield to maturity (YTM) or internal rate of return (IRR) Duration Convexity The spot rate and forward rates Black 1976Bond options Caps and floors Swaptions Spot rate modelsVasicek Cox, Injersoll & Ross Ho & Lee Hull & White Black & Karasinski Two-factor modelsBrennan & Schwartz Fong & Vasicek Longstaff & Schwartz Hull & White The market price of risk as a random factor SABRHeath, Jarrow & MortonBrace, Gatarek & MusielaPrices as expectationsCreditStructural modelsReduced formThe Black-Scholes Formulae and the GreeksCommon ContractsThings to Look Out For in Exotic ContractsTime dependence Cash flows Path dependence Dimensionality The order of an option Embedded decisions ExamplesAccrual 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 optionRange note Ratchet Repo Reverse repo Straddle Strangle STRIPS Swap Swaption Total Return Swap (TRS) Ultras Variance swap Popular Quant BooksPaul Wilmott Introduces Quantitative Finance, Second Edition by Paul WilmottPaul Wilmott on Quantitative Finance, Second Edition by Paul WilmottAdvanced Modelling in finance Using Excel and VBA by Mary Jackson and Mike StauntonOption Valuation under Stochastic Volatility by Alan LewisThe Concepts and Practice of Mathematical Finance by Mark JoshiC++ Design Patterns and Derivatives Pricing by Mark JoshiHeard on the Street by Timothy CrackMonte Carlo Methods in Finance by Peter JackelCredit Derivatives Pricing Models by Philipp SchonbucherPrinciples of Financial Engineering by Salih NeftciOptions, Futures, and Other Derivatives by John HullThe Complete Guide to Option Pricing Formulas by Espen Gaarder HaugThe Most Popular Search Words and Phrases on Wilmott.comAmerican 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 EsotericaBrainteasersThe QuestionsRussian rouletteMatching 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 kgof 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 AnswersRussian rouletteMatching birthdaysAnother one about birthdaysBiased coinsTwo headsBalls in a bagSums of uniform random variablesMinimum and maximum correlationAirforce OneHit-and-run taxiAnnual returnsDice gamekg of berriesUrban planningCloser to the edge or the centre?SnowflakeThe doorsTwo thirds of the averageOnes and zerosBookwormCompensationEinftein'f brainteaserGender ratioCovering a chessboard with dominoesAircraft armourHanging a pictureAges of three childrenThe Monty Hall problemAnts on a circleFour switches and a lightbulbTurnoverMuddy facesThe Oracle at DelphiMiss MoneypennyPirate puzzlePaul & Dominic's Guide to Getting a Quant JobIntroductionMaking a difference Unberstanb the process What you need to proveKissing frogs Writing a CVRead 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 InterviewsBe prepared Be confident Be punctual Set traps Show you can do things Questions for the interviewerGetting the message across Find out more about the job AppearanceGood clothes Neatness is good Colours Jewellery Perfume and aftershave Make-up What People Get WrongZeroth 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