http://www.actuariesindia.org/downloads/exampapers/Nov 2010/QP/ST6_IAI_QP_1110.pdf In Q9, when using the (inverse of variance-covariance matrix)*(drift - r matrix) approach explained in Baxter and Rennie for quantos, the value of the drift coefficient does not converge to just r, but rather forms a complicated function of beta, sigma and p. Both mu and alpha will converge to r, if and only if sigma = p. Can someone please confirm this? I see they've conveniently removed the answer for ST6 alone in this diet http://www.actuariesindia.org/subMenu.aspx?id=121&val=Paper_for_Nov_2010
Looks like they didnt knew the answers themselves or failed to receive the answer scripts for publication !!!
Do the following: 1. Use Ito's lemma on d(LogS1(t)), get the SDE for LogS1(t). 2. Recognize that d(LogS1(t)) is the SDE of the instantenous return process. 3. take the drift term in this SDE. The drift must equal MPR(1)xp + MPR(2)xsigma + R 4. Repeat the steps 1-3 for the second process S2(t). get a second equation for MPR(1)*b + r. 5. Use the fact that dW under Q = dW under P + MPRxdt. 6. Do the substitutions in the process of dS1(t) and dS2(t). 7. You will get extra terms in the drift: 1/2(p^2+sigma^2). 6. If you again take the process for dLog(S1(t), these will disappear. This is the desired result.
