Closed Form Option Pricing Under Generalized Hermite Expansions
15 Pages Posted: 5 Nov 2013 Last revised: 21 Mar 2018
Date Written: October 5, 2013
In this article, we generalize the classical Edgeworth series expansion used in the option pricing literature. We obtain a closed-form pricing formula for European options by employing a generalized Hermite expansion for the risk-neutral density. The main advantage of the generalized expansion is that it can be applied to heavy-tailed return distributions, a case for which the standard Edgeworth expansions are not suitable. We also show how the expansion coefficients can be inferred directly from market option prices.
Keywords: European options, generalized Hermite series expansion, calibration
JEL Classification: C63, G13
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