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





Splining over All Time IntervalsSimulationsInverse Transform MethodSplining over Four Time IntervalsLINEAR INTERPOLATIONInferring qt,TPayoff Associated with the GuaranteesTreasury BondsOn-Risk and Off-Risk AgeStock Price ProcessStep 3: Calibrate to Obtain Zero Rates for First Two YearsGMABsReal OptionsSTATISTICAL ESTIMATIONModeling Future Fund Value MovementsRoll-Up RiderContinued Investments ReallocationVALUING PATH-DEPENDENT, EUROPEAN-STYLE OPTIONS ON MULTIPLE VARIABLESSpread OptionsTransactions Costs, Continuous Trading, and DivisibilityUsing Historical Implied VolatilitiesUsing Historical Underlying ValuesDelta HedgingUNIFORM NUMBER GENERATIONSetting the StageValuing the Guarantees Using More Frequent OptionsModeling Noneconomic Rational BehaviorInstallment OptionsHedging the Sale of a Vanilla European-Style Put Option on a Dividend-Paying StockFinding a Forward Bond YieldM/M/1 QueueAPPENDIXADDING SERVERS IN A QUEUESwapsVALUING PATH-INDEPENDENT, EUROPEAN-STYLE OPTIONS ON A SINGLE VARIABLELIMITATIONS OF THE BLACK-SCH0LES FORMULAEDividendsValuing European-Style OptionsTreasury NotesRisk-Management Strategies – Pros and ConsANALYSIS ASSOCIATED WITH THE HEDGING OF A EUROPEAN-STYLE VANILLA PUT OPTIONDELTA HEDGINGValuing Exotic OptionsAntithetic Variable TechniqueRelated Distribution MethodValuing Vanilla OptionsSurrenders and WithdrawalsHedging the Sale of a Vanilla European-Style Call Option on a Nondividend-Paying StockFeesValuing the Guarantees Using Annualized OptionsBuilding Zero CurvesIncorporating Views into StrategiesHedging the Sale of a Vanilla Eupopean-Style Call Option on a Dividend-Paying StockNonlinear Payoff OptionsROAD MAP OF THE BOOKBLACK-SCHOLES FORMULAEAveraging OptionsSplining over One Time intervalVALUING PATH-DEPENDENT, EUROPEAN-STYLE OPTIONS ON A SINGLE VARIABLEControl Variable TechniquePrefaceADAPTATIONS OF THE OLACK-SCHOLES FORMULAEShort SellingBEYOND DELTA HEDGINGAPPLICATION IN CURRENCY RISK MANAGEMENTBinary OptionsModeling Economic Rational Behavior in a GMAB RiderUSING IMPLIED BLACK-SCHOLES VOLATILITY SURFACE AND ZERO RATE TERM STRUCTURE TO VALUE OPTIONSDEATH BENEFIT RIDERSAveraging Spread OptionsStochastic Volatility RatesInferring σt,TLIVING BENEFIT RIDERSEstimating PiDelta/Vega HedgingGMWBsPricing Options on Forward ContractsStep 1: Convert Eurodollar Futures Prices to Forward RatesUSING VOLATILITY SURFACELatin Hypercube SamplingTESTING HEDGING STRATEGIESAcknowledgmentsM/M/2 QueuePricing Options on Dividend-Paying StocksTreasury BillsCALIBRATION OF PARAMETERS IN THE BLACK – SCHOLES MODELParting ThoughtsNumerical ExampleEarnings RiderVARIANCE REDUCTION TECHNIQUESRandom SamplingGetting the Implied Probabilities When i = 1Arbitrage Opportunities and Constant Risk-Free RateVALUING PATH-INDEPENDENT, EUROPEAN-STYLE OPTIONS ON TWO VARIADLESExchange OptionsNON-UNIFORM NUMBER GENERATIONGMIBsUsing Volatility Term StructureStratified SamplingEurodollar FuturesStochastic Growth and Risk-Free RatesHybrid of Economical and Noneconomic Rational BehaviorStep 4: Calibrate to Obtain Zero Rates for First Five YearsAPPLICATIONS OF SIMULATIONSPricing Options on Futures ContractsEstimating Model ParametersMARKET INSTRUMENTSRegulatory Requirements and ReturnThe Effectiveness of Hedging StrategiesValuing Variable Annuity GuaranteesMinimums and MaximumsCUBIC SPLIIMIIMGOTHER DETAILS ASSOCIATED WITH GMDB PRODUCTSChanges in Volatility and Risk-Free RatesAdditional ConsiderationsCommissionsPay-Later OptionsJoint MortalityBuy High and Sell LowM/M/fr QueueCALIBRATION OF INTEREST RATE OPTION MODEL PARAMETERSBASIC GMDBSplining over Two Time IntervalsLookback Basket OptionsInvestment AllocationIMPROVING MODELING ASSUMPTIONSWHY IS THIS BOOK DIFFERENT?ASSUMPTIONS UNDERLYING DELTA HEDGINGAPPENDIX: FINDING SWAP RATES USING A FLOATING COUPON 00ND APPROACHSimulating a QueueSURRENDERING A GMAB RIDERStep 2: Calibrate Zero Rates for First YearRachet Rider
 
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