This paper introduces and analyzes specications of the Lévy Market Model originally proposed by Eberlein and Özkan (2005). An investigation of the term structure of option implied moments rules out the Brownian motion and homogeneous Lévy processes as suitable modeling devices, and consequently a variety of more appropriate models is proposed. Besides a diffusive component the models have jump structures with low or high frequency combined with constant or stochastic volatility. The models are subjected to an empirical analysis using a time series of data for Euribor caps. The results of the estimation show that pricing performances are improved when a high frequency jump component is incorporated. Specifically, excellent results are achieved with the 4 parameter Sato-Variance Gamma model, which is able to fit an entire surface of caps with an average absolute percentage pricing error of less than 3%.
Main Research Area:
19th Annual Derivatives Securities and Risk Management Conference, 2009