Stochastic Local Volatility Calibrator | SciComp Inc.

Stochastic Local Volatility Calibrator

The Stochastic Local Volatility Calibrator is based on the work of Ren, Madan and Qian [Risk, Sept 2007], Lipton [Risk, Feb 2002], Jex, Henderson and Wang [J.P.Morgan, 1999], and the Bloomberg paper "Stochastic Local Volatility" by Tataru & Fisher.

The Stochastic Local Volatility Calibrator takes any calibrated LV surface that matches vanillas. Then, using a non-linear Fokker-Planck equation, one adds a SV component and for any given set of SV parameters computes a new "leveraged local volatility surface" that still matches the vanillas, while accommodating SV. The Stochastic Local Volatility Calibrator then applies to this PDE solution a Levenberg-Marquardt optimizer and finds the (time bucketed) SV parameters that yield a maximally flat leveraged local volatility surface.

At this point you have the pure LV model (the original LV surface) and the pure SV model (the SV parameters that yield a nearly flat leveraged LV surface). Both models fit the vanillas. The Stochastic Local Volatility Calibrator then solves for a mixing fraction then mixes the two models together either by a) calibrating to selected exotics, or b) using historical data.

Test Drive the Stochastic Local Volatility Calibrator.

Stochastic Local Volatility Calibrator