Fin 501: Asset Pricing 16:22 Lecture 09Multi-period Model Lecture 09: Multi-period Model Prof. Markus K. Brunnermeier

Fin 501: Asset Pricing 16:22 Lecture 09Multi-period Model many one period models how to model information?

Fin 501: Asset Pricing 16:22 Lecture 09Multi-period Model F1F1 F2F2  ; [[ Events A i,t States s

Fin 501: Asset Pricing 16:22 Lecture 09Multi-period Model from static to dynamic… asset holdingsDynamic strategy (adapted process) asset payoff xNext period’s payoff x t+1 + p t+1 Payoff of a strategy span of assetsMarketed subspace of strategies Market completenessa) Static completeness (Debreu) b) Dynamic completeness (Arrow) No arbitrage w.r.t. holdingsNo arbitrage w.r.t strategies State prices q(s)Event prices q t (A t (s))

Fin 501: Asset Pricing 16:22 Lecture 09Multi-period Model …from static to dynamic State prices q(s)Event prices q t (A(s)) Risk free rate rRisk free rate r t varies over time Discount factor from t to 0  t (s) Risk neutral prob.  * (s) = q(s) / r Risk neutral prob.  * (A t (s)) = q t (A t (s)) /  t (A t ) Pricing kernel p j = E[k q x j ] 1 = E[k q ] r Pricing kernel k t p t j = E t [k t+1 (p j t+1 + x j t+1 )] k t = r t+1 E t [k t+1 ] __ _ _ _

Fin 501: Asset Pricing 16:22 Lecture 09Multi-period Model Add LaTex-slides