An efficient algorithm to compute correlation Greeks

Antoine Vandendorpe

Save this article

Need to know

We develop a new algorithm to compute couple correlation sensitivities in a Monte-Carlo framework, by only modifying one Brownian trajectory when shifting one correlation pair.
For a correlation matrix of dimension n, the memory needs and computational complexity are O>n² smaller than the classical bump and reprice algorithm.
The approach can also be used in the framework of Algorithmic differentiation, resulting in a faster, simpler and more robust way to estimate correlation sensitivities.
The new algorithm is illustrated on a numerical example and proved to significantly improve the estimation of correlation risk for large exotic equity correlation books.

Abstract

We develop a new algorithm that allows us to compute pairwise-correlation sensitivities in a Monte Carlo framework by modifying only one trajectory at a time, resulting in a significant decrease in Brownian noise, computing time and memory requirements. We apply this algorithm to the case of the risk management of a large portfolio of options on baskets of equities, but the same algorithm can be used for computing correlation sensitivities in any Monte Carlo framework. We show how this idea can also simplify the computation of correlation Greeks in the framework of adjoint algorithmic differentiation.

As outlined in our terms and conditions, https://www.infopro-digital.com/terms-and-conditions/subscriptions/ (point 2.4), printing is limited to a single copy.

If you would like to purchase additional rights please email info@risk.net

You may share this content using our article tools. As outlined in our terms and conditions, https://www.infopro-digital.com/terms-and-conditions/subscriptions/ (clause 2.4), an Authorised User may only make one copy of the materials for their own personal use. You must also comply with the restrictions in clause 2.5.

If you would like to purchase additional rights please email info@risk.net