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A short course of lectures
«The mathematics of financial models»





Modeling Future Fund Value MovementsCommissionsADAPTATIONS OF THE OLACK-SCHOLES FORMULAESpread OptionsEarnings RiderROAD MAP OF THE BOOKStochastic Growth and Risk-Free RatesJoint MortalityPayoff Associated with the GuaranteesTransactions Costs, Continuous Trading, and DivisibilityTreasury NotesControl Variable TechniqueVARIANCE REDUCTION TECHNIQUESSimulating a QueueUsing Volatility Term StructureAPPLICATIONS OF SIMULATIONSStep 3: Calibrate to Obtain Zero Rates for First Two YearsReal OptionsSimulationsValuing Vanilla OptionsGetting the Implied Probabilities When i = 1Nonlinear Payoff OptionsValuing Exotic OptionsSurrenders and WithdrawalsUsing Historical Underlying ValuesParting ThoughtsPricing Options on Futures ContractsRandom SamplingM/M/2 QueueStochastic Volatility RatesIMPROVING MODELING ASSUMPTIONSUsing Historical Implied VolatilitiesPricing Options on Forward ContractsSwapsTESTING HEDGING STRATEGIESAcknowledgmentsStep 4: Calibrate to Obtain Zero Rates for First Five YearsInferring qt,TBuy High and Sell LowOn-Risk and Off-Risk AgeBinary OptionsInverse Transform MethodVALUING PATH-DEPENDENT, EUROPEAN-STYLE OPTIONS ON A SINGLE VARIABLEValuing the Guarantees Using More Frequent OptionsOTHER DETAILS ASSOCIATED WITH GMDB PRODUCTSAPPENDIXWHY IS THIS BOOK DIFFERENT?ADDING SERVERS IN A QUEUESplining over All Time IntervalsIncorporating Views into StrategiesHedging the Sale of a Vanilla European-Style Put Option on a Dividend-Paying StockNON-UNIFORM NUMBER GENERATIONCALIBRATION OF INTEREST RATE OPTION MODEL PARAMETERSUNIFORM NUMBER GENERATIONBLACK-SCHOLES FORMULAEHedging the Sale of a Vanilla European-Style Call Option on a Nondividend-Paying StockStock Price ProcessLatin Hypercube SamplingAveraging OptionsGMWBsBASIC GMDBExchange OptionsStep 2: Calibrate Zero Rates for First YearShort SellingHybrid of Economical and Noneconomic Rational BehaviorThe Effectiveness of Hedging StrategiesDELTA HEDGINGVALUING PATH-DEPENDENT, EUROPEAN-STYLE OPTIONS ON MULTIPLE VARIABLESModeling Economic Rational Behavior in a GMAB RiderContinued Investments ReallocationAPPLICATION IN CURRENCY RISK MANAGEMENTRachet RiderDEATH BENEFIT RIDERSLIMITATIONS OF THE BLACK-SCH0LES FORMULAEAveraging Spread OptionsValuing the Guarantees Using Annualized OptionsSplining over Four Time IntervalsFinding a Forward Bond YieldFeesM/M/fr QueueAntithetic Variable TechniqueAPPENDIX: FINDING SWAP RATES USING A FLOATING COUPON 00ND APPROACHPricing Options on Dividend-Paying StocksHedging the Sale of a Vanilla Eupopean-Style Call Option on a Dividend-Paying StockSplining over One Time intervalCALIBRATION OF PARAMETERS IN THE BLACK – SCHOLES MODELInvestment AllocationLINEAR INTERPOLATIONDividendsChanges in Volatility and Risk-Free RatesTreasury BillsASSUMPTIONS UNDERLYING DELTA HEDGINGMinimums and MaximumsArbitrage Opportunities and Constant Risk-Free RateRoll-Up RiderPrefaceValuing European-Style OptionsAdditional ConsiderationsModeling Noneconomic Rational BehaviorUSING VOLATILITY SURFACEVALUING PATH-INDEPENDENT, EUROPEAN-STYLE OPTIONS ON A SINGLE VARIABLESetting the StageRisk-Management Strategies – Pros and ConsGMABsStep 1: Convert Eurodollar Futures Prices to Forward RatesRelated Distribution MethodDelta HedgingEstimating Model ParametersGMIBsBEYOND DELTA HEDGINGStratified SamplingSTATISTICAL ESTIMATIONBuilding Zero CurvesLookback Basket OptionsANALYSIS ASSOCIATED WITH THE HEDGING OF A EUROPEAN-STYLE VANILLA PUT OPTIONTreasury BondsDelta/Vega HedgingCUBIC SPLIIMIIMGSURRENDERING A GMAB RIDEREurodollar FuturesRegulatory Requirements and ReturnSplining over Two Time IntervalsInferring σt,TMARKET INSTRUMENTSM/M/1 QueueEstimating PiUSING IMPLIED BLACK-SCHOLES VOLATILITY SURFACE AND ZERO RATE TERM STRUCTURE TO VALUE OPTIONSValuing Variable Annuity GuaranteesVALUING PATH-INDEPENDENT, EUROPEAN-STYLE OPTIONS ON TWO VARIADLESInstallment OptionsNumerical ExamplePay-Later OptionsLIVING BENEFIT RIDERS
 
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