3contingentclaimsmarkets(編輯修改稿)
2025-02-06 01:10 本頁面
【文章內(nèi)容簡介】 ? Coupled with p = E(mx), we obtain the consumptionbased model again. ( ( ) )( ) ( )()( ) ( ( ) )()( ) ( )u c spc s sucpc s u c smss u c???????????marginal rates of substitution ? The investor’s first order conditions say that marginal rates of substitution between states tomorrow equals the relevant price ratio, 邊際替代率 相對價(jià)格比（經(jīng)概率調(diào)整） 1122( ) ( ( ) )( ) ( ( ) )m s u c sm s u c s???Economics behind this approach to asset pricing (figure ) Risk Sharing ? In plete markets, the prices are the same for all investors. 如果信息是透明的，每個人都知道客觀概率，則 marginal utility growth should be the same for all investors ? If investors have the same homothetic utility function (for example, power utility), then consumption itself should move in lockstep. 11( ) ( )( ) ( )ijijttijttu c u cu c u c?? ???????11ijttijttcccc???? It means that shocks to consumption are perfectly correlated across individuals. ? It doesn’t say that expected consumption growth should be equal。 it says that consumption growth should be equal ex post. ? In a plete contingent claims market, all investors share all risks, so when any shock hits, it hits us all equally (after insurance payments). Paretooptimal risk sharing. ? Suppose a social planner wished to maximize everyone’s utility given the available resources. For example, with two investors i and j, he would maximize m a x ( ) ( )..t i t ji t j ttti j at t tE u c E u cs t c c c? ? ? ?????? first order condition ? This simple fact has profound implications: It shows you why only aggregate shocks should matter for risk prices. Any idiosyncratic ine risk will be equally shared, and so 1/N of it bees an aggregate shock. Then the stochastic discount factors m that determine asset prices are no lo
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