March 12th, 2005, 8:40 pm
QuoteOriginally posted by: CuchulainnAlan,As you can see I do not know so much about this. Is there some way to average a basket into a single Canonical option and then 1-factor PDE? Well, I don't know about it much either but am mostly guessing how it would go.If the expansion I am suggesting for index option payoffs works, itis probably equivalent to manipulations with the PDE. For example, suppose youhave the BS-type PDE with N spatial variables S_1, S_2, ..., S_N. You could makea transformation to a new set of variables X_n, where X_1 = w_1 S_1 + w_2 S_2 + ... + w_N S_N is the "index" variable and the X_i (i > 1) are some other convenient variables (don't ask me what, since I haven't done it).Then, because the expansion "works", the PDE spatial operator reducesto the BS operator in X_1 plus terms (including cross-terms) in the other X_i. The drift and variance terms associated with X_1 would be the ones that arecomputed from the individual S_i and their covariances (see Fermion's comments earlier)But all those other terms are a perturbation and generate the other terms of my series.Having said all that, I would suspect that while you 'could' manipulate thePDE this way, it's probably more convenient to work with the integral form ofthe solution that I talked about earlier.