Quanto Like Question :- IAI - Nov 2010 Q9

[Oxymoron]

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

 

[manish.rex]

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 !!!

 

[manish.rex]

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

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.

 

[manish.rex]

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.

Havent used the matrix oberation on it as I find solving the equations easier for me.