Efficient Adjoint methods for computing financial derivative Greeks
Stochastic Processes and Financial Mathematics
PhD Competion talk
by Chao Yang
Abstract: We introduce a new methodology for computing Hessians from algorithms for function evaluation, using backwards methods.
We show that the complexity of the Hessian calculation is a linear function of the number of state variables times the complexity of the original algorithm. We apply our results to computing the Gamma matrix of multi-dimensional financial derivatives including Asian Baskets, cancellable swaps and multi-name credit derivatives.
In particular, our algorithm for computing Gammas of Bermudan cancellable swaps is order $O(n^2)$ per step in the number of rates.
We present numerical results demonstrating that the computing all $n(n+1)/2$ Gammas in the LMM takes roughly $n/3$ times as long as computing the price.
For More Information: contact: Prof Daniel Dufresne at email@example.com OR Dr Aihua Xia at firstname.lastname@example.org