j******n
发帖数: 91 | 1 Suppose we have a contract with maturity T. It pays the maximum of two Europ
ean call options (C1 & C2) expiring at T, with the underlying stocks S1 & S2
, ( dS/S=rdt + sigma dW) S1 and S2 are correlated. How to get the analytical
form of the price of this contract? |
r**a
发帖数: 536 | 2 log(S^1_T) follows normal, log(S^2_T) follows normal. Once you know the
correlation between these two RM, then you can find the joint distribution.
Then you can price any option of S^1 and S^2.
Europ
S2
analytical
【在 j******n 的大作中提到】
: Suppose we have a contract with maturity T. It pays the maximum of two Europ
: ean call options (C1 & C2) expiring at T, with the underlying stocks S1 & S2
: , ( dS/S=rdt + sigma dW) S1 and S2 are correlated. How to get the analytical
: form of the price of this contract?
|
j******n
发帖数: 91 | 3 Assuming the two stocks are linearly correlated, with correlation
coefficient rho. So the problem would be: what is the distribution of S^3_T,
where S^3_T = max[S^1_T, S^2_T]?
.
【在 r**a 的大作中提到】
: log(S^1_T) follows normal, log(S^2_T) follows normal. Once you know the
: correlation between these two RM, then you can find the joint distribution.
: Then you can price any option of S^1 and S^2.
:
: Europ
: S2
: analytical
|
j******n
发帖数: 91 | 4 I found a paper discussing about the expression of the exact distribution of
max(X_1, X_2) with \rho, it seems a little bit complicated. I do not think
the interviewer is expecting interviewee to write out that formula |
j******n
发帖数: 91 | 5 However, it seems that S^3_T is no longer log-normal...so pricing the
corresponding option is a problem...any idea? |
r**a
发帖数: 536 | 6 i am not sure if you should expect S^3_T is log-normal or not, since I did
not do the calculation by myself. But, as long as u have the full joint
distribution log(S^1_T) and log(S^2_T), u can price any European path
independent option related to S^1 and S^2.
【在 j******n 的大作中提到】
: However, it seems that S^3_T is no longer log-normal...so pricing the
: corresponding option is a problem...any idea?
|
j******n
发帖数: 91 | 7 大牛，再多说点呗？
【在 r**a 的大作中提到】
: i am not sure if you should expect S^3_T is log-normal or not, since I did
: not do the calculation by myself. But, as long as u have the full joint
: distribution log(S^1_T) and log(S^2_T), u can price any European path
: independent option related to S^1 and S^2.
|
r**a
发帖数: 536 | 8 这个还有啥说的呀？该说的我都说了。也告诉你咋算了。你动动手呗。光听别人说学不
到东西的。
【在 j******n 的大作中提到】
: 大牛，再多说点呗？
|
x******a
发帖数: 6336 | 9 similar to chooser option |
r**a
发帖数: 536 | 10 equity的chooser用啥做？local vol?
FX里面TARN Chooser很烦的。
【在 x******a 的大作中提到】
: similar to chooser option
|
