Oh, a challenge to describe this in FAQ/easy terms....Malliavin calculus is sometime refered to as a variational calculus for stochastic calculus.The idea is that you form shifts on Weiner spaces. The family of shifts, y, form a Cameron-Martin space. From this you can form the Malliavin derivative D (wrt e) of (x + ey). Let e go to zero. Since the derivative is defined, one can continue to define the calculus......The two papers for learning this are Oksendals' and Peter Fritz (sp?) PS - really it is just a caculus of functions on Wiener spaces. One of the powers of it is that, via integration by parts that naturally falls out of the calculus, when computing various greek sensitivities, you can move the derivative off the payoff functional. The payoff functional is a function of X_t's, given by the usual BS SDE, and its expectation defines the contigent claim on the security. Since this this SUCKS so bad, it can be 1) impossible or 2) computationally expensive to take derivatives. The Malliavsin integration by parts takes the derivative off the functional. This way Greeks can be computed. It extends to other, more, exotic things involving S.
Last edited by chiral3
on June 8th, 2004, 10:00 pm, edited 1 time in total.