02Lecture_a.ppt - Fin 501 Asset Pricing Lecture 02 One...

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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing Lecture 02: One Period Model Lecture 02: One Period Model Prof. Markus K. Brunnermeier
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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing Overview Overview 1. 1. Securities Structure Securities Structure Arrow-Debreu securities structure Arrow-Debreu securities structure Redundant securities Redundant securities Market completeness Market completeness Completing markets with options Completing markets with options 2. Pricing (no arbitrage, state prices, SDF, EMM …) 3. Optimization and Representative Agent (Pareto efficiency, Welfare Theorems, …)
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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing The Economy The Economy State space (Evolution of states) Two dates: t=0,1 S states of the world at time t=1 Preferences U ( c 0 , c 1 , …,c S ) (slope of indifference curve) Security structure Arrow-Debreu economy General security structure 0 s=1 s=2 s=S
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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing Security Structure Security Structure Security j is represented by a payoff vector Security structure is represented by payoff matrix NB. Most other books use the inverse of X as payoff matrix.
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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing One A-D asset e 1 = ( 1,0 ) Payoff Space < X > This payoff cannot be replicated! Arrow-Debreu Security Structure in Arrow-Debreu Security Structure in R R 2 2 ) Markets are incomplete incomplete c 1 c 2
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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing Add second second A-D asset e 2 = ( 0,1 ) to e 1 = ( 1,0 ) Arrow-Debreu Security Structure in Arrow-Debreu Security Structure in R R 2 2 c 1 c 2
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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing Arrow-Debreu Security Structure in Arrow-Debreu Security Structure in R R 2 2 Payoff space < X > Any payoff can be replicated with two A-D securities c 1 c 2 Add second second A-D asset e 2 = ( 0,1 ) to e 1 = ( 1,0 )
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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing Arrow-Debreu Security Structure in Arrow-Debreu Security Structure in R R 2 2 Payoff space < X > New asset is redundant redundant – it does not enlarge the payoff space c 1 c 2 Add second second asset ( 1,2 ) to
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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing Arrow-Debreu Security Structure Arrow-Debreu Security Structure S Arrow-Debreu securities each state s can be insured individually All payoffs are linearly independent Rank of X = S Markets are complete
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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing General Security Structure General Security Structure Only bond Payoff space < X > c 1 c 2
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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing General Security Structure General Security Structure Only bond x bond = (1,1) Payoff space < X > can’t be reached c 1 c 2
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08:44 Lecture 02 One Period Model Fin 501: Asset Pricing Fin 501: Asset Pricing Add security ( 2 , 1 ) to bond ( 1 , 1 ) General Security Structure General Security Structure c 1 c 2
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  • Spring '15
  • Michael Parzen

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