Covariance i.e. Cov(S(t),S(T))

This has only come up when the lognormal model is being used. A formula that I have for this is:



Cov(S(t),S(T)) = X(0)^2 * exp{(alpha-delta)(t+T)} * (exp(t*sigma^2) – 1)



I am wondering. What happens when you are looking for Cov(S(T),S(t)) ? Shouldn’t it be the same?



However look at the formula and see how you have (exp(t*sigma^2) – 1) in the third term (independent of T). Let me know If I'm not being clear enough...



I picked up this formula from the free Mahler exam. Is it correct?



Thanks

Covariance i.e. Cov(S(t),S(T))