ExamplesSuppose that a U.S. firm has an asset in Britainwhose local currency price is random. For simplicitylet us assume that there are three possible states ofthe world,with each state equally likely to occur. Thefuture local currency priceof this British asset as wellas the future exchange rate will be determined,depending on the realized state of the world
Suppose that a U.S. firm has an asset in Britain whose local currency price is random. For simplicity , let us assume that there are three possible states of the world,with each state equally likely to occur. The future local currency price of this British asset as well as the future exchange rate will be determined, depending on the realized state of the world. Examples
Case 1The local currency price of the asset (P*)and the dollar ofthe pound (S)are posititively correlatedp*sProbabilityParametersP (=SP*)11/3980$1.40$1,372Cov (P, S)=34/3Var(s)=0.02/3b=1,70021/3$1.501,000$1,50031/31,070$1.60$1,712$1.50$1,528Mean
Case 1 Text in here Text in here Text in here Probability P* S P（=SP*） Parameters 1 1/3 £980 $1.40 $1,372 Cov（P，S)=34/3 Var(s)=0.02/3 2 1/3 £1,000 $1.50 $1,500 b=£1,700 3 1/3 £1,070 $1.60 $1,712 Mean $1.50 $1,528 The local currency price of the asset (P*) and the dollar of the pound (S) are posititively correlated
Case1:ComputationsofRegressionParameters1.ComputationofMeans1P=Zq,P,=1372×+1500×+17211528333iS=Zq,S,=1.40×+1.50×-+1.60×-1.503332.Computationof Varianceand CovarianceVar(S)=Zq,(S, S) =[(1.40 1.50) +(1.50-1.50)2 +(1.60 1.50)]/3 = 0.02 /3Cov(PS)= Eq;(P, - P)(S, - S)1=[(1372-1528)(1.40-1.50)+(1500-1528)(1.50-1.50)+(1712-1528)(1.60-1.50))/3=34/33.ComputationoftheExposureCoefficientb=Cov(P，S)/Var (S)=(34/3)/(0.02/3)-1700
Case 1：Computations of Regression Parameters 222 1.Computation of Means 1 1 1 1372 +1500 +1721 =1528 3 3 3 111 S 1.40 +1.50 +1.60 =1.50 333 2.Computation of Variance and Covariance Var(S)= ( ) [(1.40 1.50) (1.50 1.50) (1.60 1.50) ] / 3 i i i i i i i i i P q P q S q S S − − − = = = = − = − + − + − = 0.02 / 3 ( ) ( )( ) [(1372 1528)(1.40 1.50) (1500 1528)(1.50 1.50) (1712 1528)(1.60 1.50)] / 3 34 / 3 3.Computation of the Exposure Coefficient b=Cov P S)/Var S = 34/3 / 0.02/3 =1700 i i i i i Cov PS q P P S S − − = − − = − − + − − + − − = （ ， （ ）（ ）（ ）