Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market

Nomikos, N. & Soldatos, O. A. (2010). Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market. Energy Economics, 32(2), pp. 302-312. doi: 10.1016/j.eneco.2009.10.011

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Abstract

In this paper we examine the importance of mean reversion and spikes in the stochastic behaviour of the underlying asset when pricing options on power. We propose a model that is flexible in its formulation and captures the stylized features of power prices in a parsimonious way. The main feature of the model is that it incorporates two different speeds of mean reversion to capture the differences in price behaviour between normal and spiky periods. We derive semi-closed form solutions for European option prices using transform analysis and then examine the properties of the implied volatilities that the model generates. We find that the presence of jumps generates prominent volatility skews which depend on the sign of the mean jump size. We also show that mean reversion reduces the volatility smile as time to maturity increases. In addition, mean reversion induces volatility skews particularly for ITM options, even in the absence of jumps. Finally, jump size volatility and jump intensity mainly affect the kurtosis and thus the curvature of the smile with the former having a more important role in making the volatility smile more pronounced and thus increasing the kurtosis of the underlying price distribution.

Item Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Energy Economics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Energy Economics, Volume 32, Issue 2, March 2010, Pages 302–312, http://dx.doi.org/10.1016/j.eneco.2009.10.011.
Uncontrolled Keywords: Affine jump diffusion models, Electricity derivatives, Implied volatility, Risk management, Volatility skew
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
Divisions: Cass Business School > Faculty of Finance
URI: http://openaccess.city.ac.uk/id/eprint/7527

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