Option pricing and hedging performance under stochastic volatility and stochastic interest rates

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1、Chapter37OptionPricingandHedgingPerformanceUnderStochasticVolatilityandStochasticInterestRatesGurdipBakshi,CharlesCao,andZhiwuChenAbstractRecentstudieshaveextendedtheBlack–Scholes37.1Introductionmodeltoincorporateeitherstochasticinterestratesorstochasticvolatility.B

2、ut,thereisnotyetanycomprehensiveOptionpricinghas,inthelasttwodecades,witnessedanempiricalstudydemonstratingwhetherandbyhowmuchexplosionofnewmodelsthateachrelaxsomeofthere-eachgeneralizedfeaturewillimproveoptionpricingandstrictiveassumptionsunderlyingtheseminalBlack–

3、Scholeshedgingperformance.Thispaperfillsthisgapbyfirstde-(1973)model.Indoingso,mostofthefocushasbeenonvelopinganimplementableoptionmodelinclosed-formthatthecounterfactualconstant-volatilityandconstant-interest-admitsbothstochasticvolatilityandstochasticinterestratesra

4、tesassumptions.Forexample,Merton’s(1973)optionpric-andthatisparsimoniousinthenumberofparameters.Theingmodelallowsinterestratestobestochasticbutkeepsmodelincludesmanyknownonesasspecialcases.Basedaconstantvolatilityfortheunderlyingasset,whileAminonthemodel,bothdelta-n

5、eutralandsingle-instrumentmin-andJarrow(1992)developasimilarmodelwhere,unlikeinimum-variancehedgingstrategiesarederivedanalytically.Merton’s,interestrateriskisalsopriced.AsecondclassofUsingS&P500optionprices,wethencomparethepricingoptionmodelsadmitsstochasticconditi

6、onalvolatilityfortheandhedgingperformanceofthismodelwiththatofthreeunderlyingasset,butmaintainstheconstant-interest-ratesas-existingonesthatrespectivelyallowfor(i)constantvolatil-sumption.TheseincludetheCoxandRoss(1976)constant-ityandconstantinterestrates(theBlack–S

7、choles),(ii)con-elasticity-of-variancemodelandthestochasticvolatilitystantvolatilitybutstochasticinterestrates,and(iii)stochasticmodelsofBaileyandStulz(1989),Bates(1996b,2000),volatilitybutconstantinterestrates.Overall,incorporatingHeston(1993),HullandWhite(1987a),S

8、cott(1987),SteinstochasticvolatilityandstochasticinterestratesproducestheandStein(1991),andWiggins(1987).Recently,Bakshiandbestperformance