A Pairwise Local Correlation Model

25 Pages Posted: 17 Jan 2019

Date Written: January 17, 2019


We develop a local correlation model that uses a given correlation matrix and a generic function g.t ; mi ; mj / to compute the local correlation between any asset–asset pair .i; j / of a basket of underlyings. The arguments mi , mj are spot moneynesses. The generic function is calibrated to fit the implied volatilities of an equity index such as the DAX or EURO STOXX 50. The advantage of this approach is that we do not need to simulate the complete index basket when pricing options on a (usually small) subset of this index. The approach does not suffer from the so-called chewing gum effect of correlation models, where the local correlation depends on just the index value. We first show how to calibrate the generic function for each time step with constraints on the positive definiteness of the resulting correlation matrixes and the smoothness of g to allow for stable evaluation. We then present numerical experiments that show the impact on prices and deltas for synthetic autocallable instruments.

Keywords: local correlation, Monte Carlo, Gyongy’s theorem, pairwise correlation, local in index correlation, Markovian projection.

Suggested Citation

Koster, Frank and Oeltz, Daniel, A Pairwise Local Correlation Model (January 17, 2019). Journal of Computational Finance, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3317654

Frank Koster (Contact Author)

DGZ-DekaBank ( email )

Mainzer Landstr. 16
D-60325 Frankfurt

Daniel Oeltz

RIVACON ( email )

Im Apfelgrund 4
Friedrichsdorf, 61381

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