6.6 The Price of the Market Portfolio
The price of the market portfolio at date t, St ,is
St = £ exp(rf (t - s))E[DsΦt,s∖Dt) + exp(-rf h)E(dpDt+ eΦt,t+h∖Dt)
s=t
= A £ exp(r, (t - s)) £ Dtв
exp[(1 - δtV(s - t)){μ1D - δiβσD,/2)]
N
+A exp(-rf h) £ Dt(1 -δi)βi dp1 -δi
exp[(1 - δi)dh{μD - [(1 - δi)d - 1]⅛/2)]
with
A-1 ≡ Y D-δitBt,t
Bis ≡ βi dp-δiexp[-δzd(t + h - s){μD - [δzd + 1]σD/2)]
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