16 Pages Posted: 16 Mar 2016
Date Written: March 14, 2016
It is a market practice to price exotic derivatives, like callable basket options, with the local volatility model (B. Dupire, 1994, E. Derman & I. Kani, 1994) which can, contrary to stochastic volatility frameworks, handle multi-dimensionality easily. On the other hand a well-known limitation of the nonparametric local volatility model is the necessity of a short-stepping simulation, which, in high dimensions, is computationally expensive. In this article we propose a new local volatility framework called the Collocating Local Volatility (CLV) model which allows for large Monte Carlo steps and therefore it is computationally efficient. The CLV model is by its construction guaranteed to be almost perfectly calibrated to implied volatility smiles/skews at a given set of expiries. Additionally, the framework allows to control forward volatilities without affecting the fit to plain vanillas. The model requires only a fraction of a second for complete calibration to simple vanilla products and, finally, it allows for calculation of the Greeks without re-simulating of the Monte Carlo paths. We will apply the CLV model for pricing FX barrier options and also show that under this new framework we can easily price Bermudan options on 100-dimensional baskets of correlated underlyings within just a few seconds. Illustrative examples will be also presented.
Keywords: Parametric Local Volatility, Stochastic Collocation Method, SCMC sampler, Monte Carlo, Basket Options, Efficient Pricing
JEL Classification: G12, G13, C63
Suggested Citation: Suggested Citation
Grzelak, Lech A., The CLV Framework - A Fresh Look at Efficient Pricing with Smile (March 14, 2016). Available at SSRN: https://ssrn.com/abstract=2747541