Filling the Gaps

Risk Magazine, October 2011, 66-71

22 Pages Posted: 23 Sep 2012

See all articles by Alex Lipton

Alex Lipton

Hebrew University of Jerusalem; Massachusetts Institute of Technology (MIT)

Artur Sepp

Sygnum Bank's Asset Management

Date Written: October 1, 2011

Abstract

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

Lipton, Alex and Sepp, Artur, Filling the Gaps (October 1, 2011). Risk Magazine, October 2011, 66-71, Available at SSRN: https://ssrn.com/abstract=2150646

Alex Lipton

Hebrew University of Jerusalem ( email )

Mount Scopus
Jerusalem, Jerusalem 91905
Israel

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Artur Sepp (Contact Author)

Sygnum Bank's Asset Management ( email )

Uetlibergstrasse 134a
Zurich, 8045
Switzerland

HOME PAGE: http://artursepp.com

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
515
Abstract Views
2,273
rank
68,762
PlumX Metrics