No country for old distributions? On the comparison of implied option parameters between the Brownian motion and variance gamma process

Markus Ulze, Johannes Stadler and Andreas W. Rathgeber

The Quarterly Review of Economics and Finance, 2021, vol. 82, issue C, 163-184

Abstract: Advanced stochastic approaches are often suggested as a solution to real-world derivative pricing inconsistencies like the non-linearity of the implied volatility smile. Using a novel high-frequency data set with over one million option trades and corresponding order books from the German market, we compare the normal distribution approach with a variance gamma process, which is – as a pure jump process – especially suitable for tick-by-tick data. We are able to report a flattened implied volatility smile with the variance gamma process. Other low-frequency results like time, information, and underlying moment dependencies for both stochastic processes are unchanged. All in-sample residuals of the normal distribution have a smaller variance below the 1% significance level compared to the variance gamma process. Additionally, we reveal a mean-reversion process. We show that the normal distribution is superior to the variance gamma process in an out-of-sample context and conclude that – even in a high-frequency environment – it is still “a country for old distributions”.

Keywords: Implied volatility smile; Implied volatility determinants; Lévy process; Variance gamma process; Buyer-/seller-motivated trades (search for similar items in EconPapers)
JEL-codes: G10 G12 G14 G17 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:quaeco:v:82:y:2021:i:c:p:163-184

DOI: 10.1016/j.qref.2021.08.004

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