BSM for path dependent derivative

kindlyMe · May 30th, 2011, 5:35 am

Dear all, I am aware of the BSM equation that must be followed by any derivative. My question is if the derivative is path-dependent then also that equation is valid? I am asking because, I understood that, on the derivation of that equation, derivative is assumed to dependent of St only (and of course on t), but not St, St-1, ... etc.Is there any BSM like equation that cover all families of path dependent derivatives?Thanks,

frolloos · May 30th, 2011, 12:05 pm

yes the model can be applied to path dependent derivatives. don't confuse the BSM differential equation with the BSM formula though. The differential equation governs all derivatives (with the correct boundary conditions), the BSM formula is specifically for vanillas.

kindlyMe · May 30th, 2011, 12:27 pm

Thanks frolloos