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The mathematics of financial models





PrefaceAcknowledgmentsSetting the StageWHY IS THIS BOOK DIFFERENT?ROAD MAP OF THE BOOKBuilding Zero CurvesMARKET INSTRUMENTSTreasury BillsTreasury NotesTreasury BondsEurodollar FuturesSwapsLINEAR INTERPOLATIONStep 1: Convert Eurodollar Futures Prices to Forward RatesStep 2: Calibrate Zero Rates for First YearStep 3: Calibrate to Obtain Zero Rates for First Two YearsStep 4: Calibrate to Obtain Zero Rates for First Five YearsCUBIC SPLIIMIIMGSplining over One Time intervalSplining over Two Time IntervalsSplining over Four Time IntervalsSplining over All Time IntervalsAPPENDIX: FINDING SWAP RATES USING A FLOATING COUPON 00ND APPROACHValuing Vanilla OptionsBLACK-SCHOLES FORMULAEADAPTATIONS OF THE OLACK-SCHOLES FORMULAEPricing Options on Dividend-Paying StocksPricing Options on Futures ContractsPricing Options on Forward ContractsLIMITATIONS OF THE BLACK-SCH0LES FORMULAEAPPLICATION IN CURRENCY RISK MANAGEMENTRisk-Management Strategies – Pros and ConsIncorporating Views into StrategiesAPPENDIXFinding a Forward Bond YieldSimulationsUNIFORM NUMBER GENERATIONRandom SamplingStratified SamplingLatin Hypercube SamplingNON-UNIFORM NUMBER GENERATIONInverse Transform MethodRelated Distribution MethodAPPLICATIONS OF SIMULATIONSValuing European-Style OptionsSimulating a QueueEstimating PiVARIANCE REDUCTION TECHNIQUESAntithetic Variable TechniqueControl Variable TechniqueValuing Exotic OptionsVALUING PATH-INDEPENDENT, EUROPEAN-STYLE OPTIONS ON A SINGLE VARIABLEBinary OptionsPay-Later OptionsNonlinear Payoff OptionsVALUING PATH-DEPENDENT, EUROPEAN-STYLE OPTIONS ON A SINGLE VARIABLEAveraging OptionsInstallment OptionsVALUING PATH-INDEPENDENT, EUROPEAN-STYLE OPTIONS ON TWO VARIADLESExchange OptionsSpread OptionsVALUING PATH-DEPENDENT, EUROPEAN-STYLE OPTIONS ON MULTIPLE VARIABLESAveraging Spread OptionsLookback Basket OptionsEstimating Model ParametersCALIBRATION OF PARAMETERS IN THE BLACK – SCHOLES MODELInferring qt,TInferring σt,TUSING IMPLIED BLACK-SCHOLES VOLATILITY SURFACE AND ZERO RATE TERM STRUCTURE TO VALUE OPTIONSUsing Volatility Term StructureUSING VOLATILITY SURFACEGetting the Implied Probabilities When i = 1CALIBRATION OF INTEREST RATE OPTION MODEL PARAMETERSSTATISTICAL ESTIMATIONUsing Historical Implied VolatilitiesUsing Historical Underlying ValuesThe Effectiveness of Hedging StrategiesDELTA HEDGINGHedging the Sale of a Vanilla European-Style Call Option on a Nondividend-Paying StockHedging the Sale of a Vanilla Eupopean-Style Call Option on a Dividend-Paying StockHedging the Sale of a Vanilla European-Style Put Option on a Dividend-Paying StockASSUMPTIONS UNDERLYING DELTA HEDGINGStock Price ProcessShort SellingTransactions Costs, Continuous Trading, and DivisibilityDividendsArbitrage Opportunities and Constant Risk-Free RateBEYOND DELTA HEDGINGBuy High and Sell LowChanges in Volatility and Risk-Free RatesTESTING HEDGING STRATEGIESANALYSIS ASSOCIATED WITH THE HEDGING OF A EUROPEAN-STYLE VANILLA PUT OPTIONDelta HedgingDelta/Vega HedgingAdditional ConsiderationsValuing Variable Annuity GuaranteesBASIC GMDBModeling Future Fund Value MovementsPayoff Associated with the GuaranteesValuing the Guarantees Using Annualized OptionsValuing the Guarantees Using More Frequent OptionsDEATH BENEFIT RIDERSRoll-Up RiderRachet RiderEarnings RiderOTHER DETAILS ASSOCIATED WITH GMDB PRODUCTSFeesCommissionsOn-Risk and Off-Risk AgeInvestment AllocationContinued Investments ReallocationSurrenders and WithdrawalsMinimums and MaximumsJoint MortalityRegulatory Requirements and ReturnIMPROVING MODELING ASSUMPTIONSStochastic Growth and Risk-Free RatesStochastic Volatility RatesLIVING BENEFIT RIDERSGMABsGMIBsGMWBsReal OptionsSURRENDERING A GMAB RIDERModeling Economic Rational Behavior in a GMAB RiderModeling Noneconomic Rational BehaviorHybrid of Economical and Noneconomic Rational BehaviorADDING SERVERS IN A QUEUEM/M/1 QueueM/M/2 QueueM/M/fr QueueNumerical ExampleParting Thoughts
 
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