book

Practical Methods of Financial Engineering and Risk Management

by Rupak Chatterjee

August 2014

Intermediate to advanced

388 pages

9h 44m

English

Apress

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Bloomberg Market Data ScreensCash InstrumentsFed FundsEurodollar DepositsUS Treasury Bills, Notes, and BondsRepo and Reverse RepoEquity IndicesCommercial PaperLIBORSpot ForexKey RatesGoldFutures and SwapsCrude OilFed Funds Futures90-Day Eurodollar Futures10-Year Treasury Note FuturesSwapsSwap ValuationSwap SpreadsSwap FuturesDerivatives and Structured ProductsDynamic Hedging and ReplicationImplied VolatilityCaps and FloorsMarket Implied Volatility Quotes for Caps and FloorsSwaptionsMortgage-Backed SecuritiesAppendix: Daycount ConventionsProblemsFurther Reading
Overview of Yield Curve ConstructionCash LIBOR Rates90D Eurodollar FuturesSwapsGeneric Discount FactorsProblemsProblem 2.1: Build a Simple Yield CurveFurther Reading
Tools in Probability TheoryMoments of a DistributionCreating Random Variables and DistributionsThe Inverse Transform MethodCreating a Density Function: Histograms and FrequenciesMixture of Gaussians: Creating a Distribution with High KurtosisSkew Normal Distribution: Creating a Distribution with SkewnessCalibrating Distributions through Moment MatchingCalibrating a Mixed Gaussian Distribution to Equity ReturnsCalibrating a Generalized Student’s-t Distribution to Equity ReturnsCalibrating a Beta Distribution to Recovery Rates of Defaulted BondsBasic Risk MeasuresCalculating VaR and CVaR from Financial Return DataThe Term Structure of StatisticsThe Term Structure of the MeanThe Term Structure of SkewThe Term Structure of KurtosisThe Term Structure of VolatilityThe Term Structure of “Up” VolatilityThe Term Structure of “Down” VolatilityAutocorrelationDynamic Portfolio AllocationModern Portfolio TheoryGeneric Rules to Dynamic Portfolio Allocation with Volatility TargetsAppendix. Joint Distributions and CorrelationJoint Distribution FunctionJoint Density FunctionMarginal Distribution FunctionIndependenceCovariance and CorrelationCauchy-Schwarz InequalityConditional Distribution and Density FunctionsConditional ExpectationConvolutionProblemsProblem 3-1. Create a Gaussian Random Number Generator in ExcelProblem 3-2. Create a Mixture of Gaussians in ExcelProblem 3-3. Calibrate S&P 500 Returns to a Mixed Normal in ExcelProblem 3-4. Calibrate SX5E Returns to a Student’s-t distribution in ExcelProblem 3-5. Create a Skew Normal Distribution in ExcelProblem 3-6. VaR and CVaRProblem 3-7. Term Structure of StatisticsReferences
Stochastic CalculusWiener Stochastic ProcessQuadratic VariationStochastic IntegralsGeometric Brownian Motion and Monte Carlo SimulationsCreating Random Stock Paths in ExcelGARCH Process for Stock ReturnsGARCH(1,1)The GARCH(1,1) Model for the “Traditional” Term Structure of VolatilityStatistical Modeling of Trading StrategiesPairs TradingModels for Residuals: Mean Reverting Ornstein-Uhlenbeck ProcessEquilibrium StatisticsETF Factor-Neutral Calibration and Trading StrategyIncluding the Drift TermHints for Constructing Market-Neutral PortfoliosThe Rolling NAV EquationAppendix A. Black-Scholes with HolesAppendix B. Moment Matching and Binomial TreesProblemsProblem 4-1. Create a Brownian Motion Process for Stock Returns Using Monte Carlo Simulations in ExcelProblem 4-2. Ito’s LemmaProblem 4-3. Calibrate a GARCH(1,1) Process for SX5EProblem 4-4. Create a GARCH(1,1) Simulator in ExcelProblem 4-5. Volume Adjustment for Pairs Trading for MCD versus XLYReferences
Dynamic Hedging and ReplicationWealth Change Equations: Spot, Forwards, and OptionsForward ContractsEuropean OptionsThe OHMC Optimization Problem and Solution MethodologyThe OHMC Optimization ProblemThe OHMC TechniqueBasis Function Expansions and the Lagrange Multiplier TechniqueRisk CapitalThe OHMC ExamplesHedge Fund Index: GARCH Calibration to Daily ReturnsOption Pricing: Hedge Fund Index: 1.20Yr 110% Strike Call, 2 Day LiquidityOption Pricing: Hedge Fund Index: 1.20Yr 99% Strike Put, 2 Day LiquidityDynamic Portfolio Allocation Index: GARCH Calibration to Daily ReturnsOption Pricing: Dynamic Portfolio Allocation: 2.00Yr 110% Strike Call, 5 Day LiquidityOption Pricing: Dynamic Portfolio Allocation: 2.00Yr 95% Strike Put, 5 Day LiquidityHedge Fund Index: GARCH Calibration to Monthly ReturnsOption Pricing: Hedge Fund Index: 3.00Yr 100% Strike Put, 3-Month LiquidityOption Pricing: Hedge Fund Index: 3.00-Yr 110% Strike Call, 3-Month LiquidityCliquet ContractsKnockout Cliquet Sellers Wealth Change EquationProblemsProblem 5-1. Linear Basis Function ExpansionProblem 5-2. Hermite Cubic Basis Function ExpansionProblem 5-3. One-Time-Step OHMC ProblemReferences and Further Reading
The CDS Contract: OverviewThe CDS Contract: PricingIntensity-Based Reduced-Form Default ModelsBootstrapping a Survival Curve with Piecewise Constant Hazard RatesCredit TriangleQuotation Conventions for Standard ContractsPar Asset SwapsCollateralizationCDO2Standard CDS Indices and TranchesCorrelation and CopulasDensity MethodVariable MethodFactor ModelsCopulasLarge Homogeneous Portfolio ApproximationOne-Factor Gaussian ModelImplied Compound and Base CorrelationsStochastic Hazard RatesCase 1: Risky Zero Coupon Discount Bond B(t) Maturing at T with No RecoveryCase 2: Continuous Coupon Payment Ct until DefaultCase 3: Recovery Payment Rt at DefaultOHMC and the Static Hedging of a Risky Bond with a CDSOHMC and CDS SwaptionsAppendix. Bloomberg FunctionalityProblemsProblem 6-1. Calculate Hazard Rates from Par CDS SpreadsProblem 6-2. Standard Convention Upfront PaymentProblem 6-3. Generating Correlated Bivariate Normal VariablesReferences
Risk TypesMarket RiskCredit RiskOperational RiskLiquidity RiskSystemic RiskCoherent Risk MeasuresRegulation and Its EffectsAccounting Credit Valuation Adjustment (CVA)Wrong-Way RiskBasel IBasel IICCR RWAMarket Risk RWAOperational Risk RWABasel IIICapital Requirements under Basel IIIEAD and EPE ProfilesPortfolio CCR Aggregation, Netting Sets, and Collateral MarginInitial MarginVariation MarginMargin Period of RiskMargin ThresholdMinimum Transfer AmountOIS DiscountingCalculating “Adjusted” Forward LIBOR Rates from OIS Curves and Basis SwapsReferences
Power Laws and ScalingMomentsExtrapolationPower-Law Monte Carlo SimulationMaximum Likelihood CalibrationExtreme Value TheoryMaximum Likelihood Calibration for the GPDThe Power-Law Equivalence of the GPDVaR and CVaRProblemsProblem 8-1. Power-Law MC Simulation in ExcelProblem 8-2. The Power-Law Nature of the GPDReferences
Overview of Hedge Fund StylesReplicating MethodologiesA Heuristic ExampleReplication through Kalman FilteringProcess ModelMeasurement ModelKalman FilterTime Update with an Initial PredictionMeasurement (Observation) Update with Kalman Filter CorrectionReferences

Content preview from Practical Methods of Financial Engineering and Risk Management

CHAPTER 4

Stochastic Processes

In the previous chapter, distributions were calibrated to historical data, and risk measures such as VaR and CVaR were calculated. Yet the valuation of financial products and the associated risk measures all deal with events in the future. Bonds, stocks, options, and so forth all have potential cash flows in the future, and therefore one needs a method to generate distributions at arbitrary times in the future, as indicated in Figure 4-1. This is the purpose of a stochastic (or random) process, which represents the evolution of a random variable in time.

Figure 4-1. Distributions moving forward in time

Stochastic ...

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Quantitative Financial Risk Management: Theory and Practice

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Practical Methods of Financial Engineering and Risk Management

by Rupak Chatterjee

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Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.