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If S1 follows a Geometric Brownian Motion and S2 also follows a Geometric Brownian Motion. then how will S1 * S2 be distributed. will it be normally distributed or lognormally distributed? Note that in this S1 and S2 will be lognormally distributed.waiting for replymanish

Lognormally distributed. Use Ito on S1*S2.Sri

supernaut20,thanks a lot for the answer. i have a few things to discuss with. can we discuss them offline. can i email you. or you can mail me at manishs@kesdee.com

You can send me a pvt message thru this forum.

Sounds like a currency pair. S1*S2 will be lognormally distributed with vol(s1*s2)=sqrt(vol(s1)^2+vol(s2)^2+2*rho(s1,s2)*vol(s1)*vol(s2)) where rho(s1,s2) is the correlation between ln(s1) and ln(s2).

Alternatively, write Z = X*Y where X, Y are lognormally distributed. Take the log of the eqn. to get ln(Z) = ln(X) + ln(Y). Since ln(X) & ln(Y) are normally distributed we have a case of sum of normal distributed RV's, and ln(Z) is normally distributed. Therefore Z is lognormal. (Uncorrelated case though....)