PowerPoint PresentationSlide 2Slide 3from static to dynamic……from static to dynamicAdd LaTex-slides23:0223:02 Lecture 09 Lecture 09 Multi-period ModelMulti-period ModelFin 501: Asset PricingFin 501: Asset PricingLecture 09: Multi-period ModelLecture 09: Multi-period ModelProf. Markus K. Brunnermeier23:0223:02 Lecture 09 Lecture 09 Multi-period ModelMulti-period ModelFin 501: Asset PricingFin 501: Asset Pricing0 123many one period modelshow to model information?23:0223:02 Lecture 09 Lecture 09 Multi-period ModelMulti-period ModelFin 501: Asset PricingFin 501: Asset Pricing0 123 0 1 2 3F1F2;[ [Events Ai,tStates s23:0223:02 Lecture 09 Lecture 09 Multi-period ModelMulti-period ModelFin 501: Asset PricingFin 501: Asset Pricingfrom static to dynamic…from static to dynamic…asset holdings Dynamic strategy (adapted process)asset payoff x Next period’s payoff xt+1+ pt+1Payoff of a strategyspan of assets Marketed subspace of strategiesMarket completeness a) Static completeness (Debreu)b) Dynamic completeness (Arrow)No arbitrage w.r.t. holdings No arbitrage w.r.t strategiesState prices q(s) Event prices qt(At(s))23:0223:02 Lecture 09 Lecture 09 Multi-period ModelMulti-period ModelFin 501: Asset PricingFin 501: Asset Pricing……from static to dynamicfrom static to dynamicState prices q(s) Event prices qt(A(s))Risk free rate r Risk free rate rt varies over timeDiscount factor from t to 0 t(s)Risk neutral prob.*(s) = q(s) / rRisk neutral prob.*(At(s)) = qt(At(s)) / t (At)Pricing kernelpj = E[kq xj]1 = E[kq] rPricing kernelkt ptj = Et[kt+1(pjt+1+ xjt+1)]kt = rt+1 Et[kt+1]_ ____23:0223:02 Lecture 09 Lecture 09 Multi-period ModelMulti-period ModelFin 501: Asset PricingFin 501: Asset PricingAdd LaTex-slidesAdd
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