# Efficient Adjoint methods for computing financial derivative Greeks

Stochastic Processes and Financial Mathematics
PhD Competion talk

#### by Chao Yang

Institution: The Centre for Actuarial Studies, The University of Melbourne
Date: Thu 19th May 2011
Time: 1:15 PM
Location: Alice Hoy-316, The University of Melbourne

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 dufresne@unimelb.edu.au OR Dr Aihua Xia at xia@ms.unimelb.edu.au