Abstracts

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 want to calibrate a local correlation to these option prices. Only two particular solutions have been suggested so far in the literature. Both solutions impose a particular dependency of the correlation matrix on the asset values that one has no reason to undergo.
By combining the particle method presented in [Being Particular About Calibration, Guyon and Henry-Labordere, 2012] with a new simple idea, we build whole families of calibrated local correlation models, which include the two existing models as special cases. For the first time, one can now design a calibrated local correlation in order to fit a view on the correlation skew, or reproduce historical correlation, or match some exotic option prices, thus improving the pricing, hedging, and risk-management of multi-asset derivatives. We also show how to generalize this technique to calibrate (i) models that combine stochastic interest rates, stochastic dividend yield, local stochastic volatility, and local correlation; and (ii) single-asset path-dependent volatility models.
Numerical results show the wide variety of calibrated local correlations and give insight on a difficult (still unsolved) problem: find lower bounds/upper bounds on general multi-asset option prices given the whole surfaces of implied volatilities of a basket and its constituents.
This research will be published in the February 2014 issue of Risk Magazine. It is available online at http://dx.doi.org/10.2139/ssrn.2283419