Filling the Gaps
Risk Magazine, October 2011, 66-71
22 Pages Posted: 23 Sep 2012
Date Written: October 1, 2011
The calibration of local volatility models to market data is one of the most fundamental problems of financial engineering. Under the restrictive assumption that the entire implied volatility surface is known, this problem can be solved by virtue of the so-called Dupire equation. In reality, however, the number of available data points is very limited and construction of a non-arbitrageable implied volatility surface is difficult, if not impossible, since it requires both interpolation and extrapolation of the market data. Thus, it is more natural to build the local volatility surface directly. In this article we present a generic semi-analytical approach to calibrating a parametric local volatility surface to the market data in the realistic case when this data is sparse. This approach also allows one to build a non-arbitrageable implied volatility surface. The power of the method is illustrated by considering layered local volatility and generating local and implied volatility surfaces for options on SX5E.
Keywords: local volatility, diffusion with tiled volatility
JEL Classification: C00
Suggested Citation: Suggested Citation