Collocating Volatility: A Competitive Alternative to Stochastic Local Volatility Models
International Journal of Theoretical and Applied Finance, Vol. 23, No. 6 (September 2020)
33 Pages Posted: 9 Oct 2018 Last revised: 4 Sep 2020
Date Written: September 11, 2018
Abstract
We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) model, introduced in Grzelak (2016). The CV model consists of two elements, a 'kernel process' that can be efficiently evaluated and a local volatility function. The latter, based on stochastic collocation – e.g. Babuska et al. (2007), Witteveen et al. (2012) – connects the kernel process to the market and allows the CV model to be perfectly calibrated to European-type options. In this article we consider three different kernel process choices: the Ornstein-Uhlenbeck (OU) and Cox-Ingersoll-Ross (CIR) processes and the Heston model. The kernel process controls the forward smile and allows for an accurate and efficient calibration to exotic options, while the perfect calibration to liquid market quotes is preserved. We confirm this by numerical experiments, in which we calibrate the OU-CV, CIR-CV and Heston-CV models to FX barrier options.
Keywords: Collocating Local Volatility, stochastic local volatility, Monte Carlo, stochastic collocation, calibration, forward volatility, barrier options
JEL Classification: C63, G12, G13
Suggested Citation: Suggested Citation