A New Class of Local Correlation Models

36 Pages Posted: 22 Jun 2013

See all articles by Julien Guyon

Julien Guyon

Bloomberg L.P.; Columbia University - Department of Mathematics; New York University - Courant Institute of Mathematical Sciences

Date Written: June 21, 2013

Abstract

Allowing correlation to be local, i.e., state-dependent, in multi-asset models allows better hedging by incorporating correlation moves in the delta. When options on a basket, be it a stock index, a cross FX rate, or an interest rate spread, are liquidly traded, one may calibrate a local correlation to these option prices. In this article we introduce a new family of local correlation models from which one can pick a model that not only calibrates to the basket smile but also has extra desirable properties, like fitting a view on correlation skew, mimicking historical correlation, or matching prices of exotic options. The family is built using the particle method and the procedure is easily adapted to calibrate path-dependent volatility models, path-dependent correlation models, and to include stochastic rates, stochastic dividend yield, and stochastic volatility.

Keywords: local correlation, path-dependent volatility, path-dependent correlation, calibration, particle method, local stochastic volatility, stochastic interest rates, stochastic dividend yield

JEL Classification: G13

Suggested Citation

Guyon, Julien, A New Class of Local Correlation Models (June 21, 2013). Available at SSRN: https://ssrn.com/abstract=2283419 or http://dx.doi.org/10.2139/ssrn.2283419

Julien Guyon (Contact Author)

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States

Columbia University - Department of Mathematics ( email )

3022 Broadway
New York, NY 10027
United States

New York University - Courant Institute of Mathematical Sciences ( email )

New York University
New York, NY 10012
United States

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