Heston随机波动率模型的Multilevel Monte Carlo方法

Heston随机波动率模型的Multilevel Monte Carlo方法Title: Multilevel Monte Carlo Simulation of Heston Stochastic

HestonMultilevelMonteCarlo 随机波动率模型的 方法 Title:MultilevelMonteCarloSimulationofHestonStochastic VolatilityModel Abstract: TheHestonstochasticvolatilitymodeliswidelyusedinthe fieldoffinancialmathematicstocapturethedynamicbehaviorof assetpricesandthecorrespondingimpliedvolatilities.Its complexitystemsfromtheincorporationofastochasticvolatility processthatisgovernedbyavariancemean-reverting mechanism.Inthispaper,weproposeaMultilevelMonteCarlo (MLMC)simulationapproachtoefficientlyestimatetheoption pricesandhedgingparameterswithintheHestonframework.The MLMCmethodutilizesahierarchyofdiscretizationlevelsto reducecomputationalcostswhilemaintainingaccuracy.We demonstratetheeffectivenessofthisapproachthroughnumerical experimentsandcompareitsperformancewithtraditionalMonte Carlomethods. 1.Introduction TheHestonstochasticvolatilitymodel,introducedbySteven Hestonin1993,hasbecomeapopularmodelforpricingand hedgingoptionsinthefinancialindustry.Itprovidesmorerealistic dynamicsforassetpricesbyincorporatingavolatilityprocessthat exhibitsmean-revertingbehavior.However,pricingoptionsunder theHestonmodelpresentssignificantcomputationalchallenges duetoitscomplexnature.TraditionalMonteCarlomethodsare oftentime-consuming,requiringlargesamplesizesforaccurate estimations.Therefore,moreefficientnumericaltechniquesare desiredtoestimateoptionpricesandhedgingparameters accurately. 2.HestonStochasticVolatilityModel WepresentabriefoverviewoftheHestonmodel,including thestochasticdifferentialequationsthatgovernassetprice dynamicsandtheassociatedvolatilityprocess.Additionally,we discusstheFouriertransformapproachforpricingoptionsunder theHestonmodel.