Risk Minimization in Stochastic Volatility Models: Model Risk and Empirical Performance

23 Pages Posted: 23 Feb 2007 Last revised: 4 Dec 2007

See all articles by Rolf Poulsen

Rolf Poulsen

University of Copenhagen - Department of Statistics and Operations Research

Klaus Reiner Schenk-Hoppé

University of Manchester - Department of Economics; Norwegian School of Economics (NHH) - Department of Finance

Christian-Oliver Ewald

University of Glasgow; Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance

Date Written: September 2007

Abstract

In this paper the performance of locally risk-minimizing hedge strategies for European options in stochastic volatility models is studied from an experimental as well as from an empirical perspective. These hedge strategies are derived for a large class of diffusion-type stochastic volatility models, and they are as easy to implement as usual delta hedges. Our simulation results on model risk show that the locally risk-minimizing hedges are robust with respect to uncertainty and even misconceptions about the underlying data generating process. The empirical study indicates that locally risk-minimizing hedge strategies consistently produce lower standard deviations of profit-and-loss-ratios than delta hedges (over different time periods as well as in different markets). The more skewed the market and the more out-of-the-money the option, the higher the benefit.

Keywords: Locally risk-minimizing hedge, delta hedge, stochastic volatility,

JEL Classification: C90, G13

Suggested Citation

Poulsen, Rolf and Schenk-Hoppé, Klaus Reiner and Ewald, Christian-Oliver, Risk Minimization in Stochastic Volatility Models: Model Risk and Empirical Performance (September 2007). FINRISK Working Paper No. 361; Swiss Finance Institute Research Paper No. 07-10. Available at SSRN: https://ssrn.com/abstract=964739 or http://dx.doi.org/10.2139/ssrn.964739

Rolf Poulsen (Contact Author)

University of Copenhagen - Department of Statistics and Operations Research ( email )

Universitetsparken 5
DK-2100
Denmark
+45 (353) 20685 (Phone)

Klaus Reiner Schenk-Hoppé

University of Manchester - Department of Economics ( email )

Arthur Lewis Building
Oxford Road
Manchester, M13 9PL
United Kingdom

Norwegian School of Economics (NHH) - Department of Finance ( email )

Helleveien 30
N-5045 Bergen
Norway

Christian-Oliver Ewald

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance ( email )

Castlecliffe
The Scores
St. Andrews, Fife KY16 9AL
United Kingdom
+44(0)1334 462435 (Phone)

HOME PAGE: http://www.maths.usyd.edu.au/u/ewald/

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