3contingentclaimsmarkets(存儲版)
【正文】 perpendicular to pc have the same projection onto pc, they must have the same price. ( ) ( ) ( ) ( | )sp x pc s x s pc x pc proj x pc? ? ? ? ??x? Planes of constant price move out linearly, and the origin x = 0 must have a price of zero. ? If payoff y = 2x, then its price is twice the price of x, p(y) =∑pc(s) y(s) = ∑pc(s) 2x(s) = 2p(x) ? We can think of p(x) as a pricing function, a map from the state space or payoff space in which x lies (Rs in this case) to the real line. We have just deduced from the definition () that p(x) is a linear function, . that p(ax＋ by) =a p(x)+b p(y) ? The constant price lines in Figure 7 are of course exactly what one expects from a linear function from Rs to R. ? Figure 7 also includes the payoffs to a contingent claim to individual states. ? The plane of price = 1 payoffs is the plane of asset returns。在上圖中，pc(1)pc(2),所以 pc線較陡。 ? From (),we have ( ) ( )fpttdp D d dpE dt r dt E dtp p p??????? ? ? ? ??— — 超 額 收 益可 見 是 風 險 價 格 。 Investors’ choice ? The investor starts with a pile of initial wealth y and a statecontingent ine y(s). He purchases contingent claims to each possible state in the second period. His problem is then ? ?? ?, ( )( ) ( ) [ ].( ) ( ) ( ) ( )c c s sssM ax u c s u c sstc pc s c s y pc s y s???? ? ????? Eliminating the Lagrange multiplier λ , ? the plane of price = 0 payoffs is the plane of excess returns. ? A riskfree unit payoff (the payoff to a riskfree pure discount bond) lies on the (1， 1) point。投資者越愛好（經(jīng)概率調整）某種狀態(tài)的PAYOFF，該狀態(tài)的 PC就越高。 they just need enough other securities to span or synthesize all contingent claims. ? （有幾種狀態(tài)，就有幾種相互無法復制的證券，就是完全市場） ? x(s) denote an asset’s payoff in state of nature s ? Since the asset is a bundle of contingent claims , its price must then equal the total value of
外語相關推薦
鄂ICP備17016276號-1