Hermite Polynomial based Expansion of European Option Prices
University of Chicago - Booth School of Business
December 28, 2012
Chicago Booth Research Paper No. 11-40
We seek a closed-form series approximation of European option prices under a variety of diffusion models. The proposed convergent series are derived using the Hermite polynomial approach. Departing from the usual option pricing routine in the literature, our model assumptions have no requirements for affine dynamics or explicit characteristic functions. Moreover, convergent expansions provide a distinct insight into how and on which order the model parameters affect option prices, in contrast with small-time asymptotic expansions in the literature. With closed-form expansions, we explicitly translate model features into option prices, such as mean-reverting drift and self-exciting or skewed jumps. Numerical examples illustrate the accuracy of this approach and its advantage over alternative expansion methods. Empirically, we calibrate VIX derivatives using the Hawkes self-exciting jump diffusion model.
Number of Pages in PDF File: 52
Keywords: Option Valuation, Closed-Form Expansion, Mean-Reversion, Self-Exciting Jumps, Double Exponential Jumps
JEL Classification: G12, C51working papers series
Date posted: November 8, 2010 ; Last revised: January 3, 2013
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