4 Measure change/state price 6_CAMP Let dS = Stdt + StdZt dX = xX+dt +xXdZt Let V(x) = BxA 5 The "physical" measure is P. Consider a measure change to Q, such that the St process has drift r under Q. 4.1 State the derivatives Vr, Vxx. [20 points] [20 points] 4.2 State the V process under the P measure using Ito's lemma. 4.3 State the X process under the Q measure. [Note: Unlike the sim- ilar tutorial problem, nothing has been stated about the Sharpe ratio for the X process.] [20 points] 4.4 Now make an additional assumption: that the Sharpe ratio for the Vt process is the same as the Sharpe ratio for the St process. [Note that this is different from the tutorial assignment.] Verify that e-rt V, is a martingale under the Q measure by applying Ito's lemma. [20 points] 4.5 Continuing with the Sharpe ratio assumption, find the of the Vt. [20 points]