Collocating Local Volatility: A Competitive Alternative to Stochastic Local Volatility Models
31 Pages Posted: 9 Oct 2018
Date Written: September 11, 2018
We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Local Volatility (CLV) model, introduced in Grzelak (2016). The CLV 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 CLV 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-CLV, CIR-CLV and Heston-CLV 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
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