Journal of Computational Finance

A simple local correlation model

Frank Koster

  • We introduce a new version of the “local-in-index” model.
  • The model can be fit to implied volatility smiles of medium sized equity indices using the particle method.
  • The number of model parameters can be small without losing fit quality.
  • The model allows the computation of prices and Greeks of basket products as fast as with constant correlation models.

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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