A simple local correlation model

Frank Koster

Journal of Computational Finance

Abstract: In this paper we introduce a simple version of the “local-in-index†correlation model in which the correlation function does not depend on the index but on a synthetic index computed solely from the Brownian motion driving the multivariate equity process. The model fits the index smile as well as the respective local-in-index model, but the price of instruments on a small subset of index constituents can be computed with nearly the same work count as for the constant correlation model. Moreover, computing Greeks such as Delta and Vega is significantly easier due to the reduced implicit dependencies on market data.

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