Hi all, Does anyone know why to work out the equation below? I've looked at it for a long time and couldn't figure out how to get to the second line. It comes from the solution of Q3 (iii). dV(t) = d(e^rt*Ft) = re^rt*Ftdt + e^rt dFt = re^rt*Ftdt + e^rt *OtdSt + re^rt (Ft - Ot*Dt) dt = OtdSt + ψt dBt. Your help is much appreciated. Thanks.
This question's been posted a while ago but in case anyone's wondering the second line in the solution that mange refers to cannot be directly derived from the previous one (at least I cannot do so), but requires some intermediate steps as follows: dV(t) = d(e^rt*Ft) = r*e^rt*Ftdt + e^rt dFt = r*e^rt*Ftdt + e^rt Ot dDt .. from part (ii) and since Dt = e^-rt * St this becomes = r*e^rt*Ftdt + e^rt Ot (-r*e^-rt St dt + e^-rt dSt) cancelling out the exp's we get = r*e^rt*Ftdt + Ot dSt - r Ot St dt = Ot dSt + r*e^rt (Ft dt - Ot Dt dt) = Ot dSt + r*e^rt ψt dt = Ot dSt + ψt dBt. (apologies for the awkward notation)
