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





CALIBRATION OF PARAMETERS IN THE BLACK – SCHOLES MODELAcknowledgmentsLookback Basket OptionsTreasury BondsRegulatory Requirements and ReturnRisk-Management Strategies – Pros and ConsRelated Distribution MethodBASIC GMDBChanges in Volatility and Risk-Free RatesHedging the Sale of a Vanilla European-Style Put Option on a Dividend-Paying StockVALUING PATH-DEPENDENT, EUROPEAN-STYLE OPTIONS ON MULTIPLE VARIABLESThe Effectiveness of Hedging StrategiesJoint MortalityBinary OptionsNonlinear Payoff OptionsAveraging OptionsRandom SamplingAdditional ConsiderationsEstimating PiTransactions Costs, Continuous Trading, and DivisibilityM/M/2 QueueSTATISTICAL ESTIMATIONStochastic Growth and Risk-Free RatesPricing Options on Forward ContractsVALUING PATH-INDEPENDENT, EUROPEAN-STYLE OPTIONS ON A SINGLE VARIABLEValuing Exotic OptionsMARKET INSTRUMENTSReal OptionsValuing European-Style OptionsAveraging Spread OptionsAPPENDIX: FINDING SWAP RATES USING A FLOATING COUPON 00ND APPROACHInferring qt,TBLACK-SCHOLES FORMULAEGMABsBuy High and Sell LowPay-Later OptionsCUBIC SPLIIMIIMGParting ThoughtsShort SellingM/M/1 QueueStep 1: Convert Eurodollar Futures Prices to Forward RatesM/M/fr QueueDelta HedgingStock Price ProcessAPPENDIXValuing the Guarantees Using Annualized OptionsTreasury BillsContinued Investments ReallocationHedging the Sale of a Vanilla Eupopean-Style Call Option on a Dividend-Paying StockPricing Options on Futures ContractsPrefaceDEATH BENEFIT RIDERSGMIBsDividendsIMPROVING MODELING ASSUMPTIONSModeling Future Fund Value MovementsGMWBsNumerical ExampleVALUING PATH-INDEPENDENT, EUROPEAN-STYLE OPTIONS ON TWO VARIADLESIncorporating Views into StrategiesInverse Transform MethodASSUMPTIONS UNDERLYING DELTA HEDGINGFinding a Forward Bond YieldHedging the Sale of a Vanilla European-Style Call Option on a Nondividend-Paying StockOn-Risk and Off-Risk AgeWHY IS THIS BOOK DIFFERENT?ANALYSIS ASSOCIATED WITH THE HEDGING OF A EUROPEAN-STYLE VANILLA PUT OPTIONStep 2: Calibrate Zero Rates for First YearADDING SERVERS IN A QUEUEDELTA HEDGINGHybrid of Economical and Noneconomic Rational BehaviorControl Variable TechniqueUNIFORM NUMBER GENERATIONValuing the Guarantees Using More Frequent OptionsSimulationsEstimating Model ParametersSplining over Two Time IntervalsDelta/Vega HedgingInvestment AllocationModeling Noneconomic Rational BehaviorLIVING BENEFIT RIDERSSurrenders and WithdrawalsGetting the Implied Probabilities When i = 1CALIBRATION OF INTEREST RATE OPTION MODEL PARAMETERSStep 3: Calibrate to Obtain Zero Rates for First Two YearsNON-UNIFORM NUMBER GENERATIONModeling Economic Rational Behavior in a GMAB RiderSetting the StageLINEAR INTERPOLATIONInstallment OptionsOTHER DETAILS ASSOCIATED WITH GMDB PRODUCTSLIMITATIONS OF THE BLACK-SCH0LES FORMULAELatin Hypercube SamplingVARIANCE REDUCTION TECHNIQUESSURRENDERING A GMAB RIDERUSING IMPLIED BLACK-SCHOLES VOLATILITY SURFACE AND ZERO RATE TERM STRUCTURE TO VALUE OPTIONSBuilding Zero CurvesUsing Historical Implied VolatilitiesArbitrage Opportunities and Constant Risk-Free RateAPPLICATION IN CURRENCY RISK MANAGEMENTSplining over One Time intervalMinimums and MaximumsValuing Vanilla OptionsInferring σt,TEarnings RiderTESTING HEDGING STRATEGIESRoll-Up RiderCommissionsSpread OptionsUSING VOLATILITY SURFACEAPPLICATIONS OF SIMULATIONSSplining over All Time IntervalsTreasury NotesSimulating a QueueADAPTATIONS OF THE OLACK-SCHOLES FORMULAEStep 4: Calibrate to Obtain Zero Rates for First Five YearsStratified SamplingStochastic Volatility RatesROAD MAP OF THE BOOKPayoff Associated with the GuaranteesPricing Options on Dividend-Paying StocksExchange OptionsAntithetic Variable TechniqueBEYOND DELTA HEDGINGVALUING PATH-DEPENDENT, EUROPEAN-STYLE OPTIONS ON A SINGLE VARIABLESplining over Four Time IntervalsFeesValuing Variable Annuity GuaranteesUsing Historical Underlying ValuesRachet RiderEurodollar FuturesUsing Volatility Term StructureSwaps
 
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