Closed Form Option Pricing Under Generalized Hermite Expansions
42 Pages Posted: 5 Nov 2013 Last revised: 8 Jan 2018
Date Written: January 7, 2018
In this article we generalize the classical Edgeworth series expansion, the Gram- Charlier Type A expansion and the Gauss-Hermite expansion used in the option pricing literature. We obtain a closed-form pricing formula for European options by employing the 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. The expansion coefficients can be inferred directly from market option prices. We calibrate the model to European options on the S&P 500 index, and the results indicate that the option price data can be explained well by a risk-neutral density, whose tails are heavier than of normal distribution, but are not fat.
Keywords: European options, generalized Hermite series expansion, calibration
JEL Classification: C63, G13
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