Title: Flexible Bayesian modelling of implied volatility surfaces

Authors: Björn Uhl

Addresses: 154 East India Dock Road, E14 0BP London, UK

Abstract: In their Bayesian approach to non-parametric bivariate regression, Smith and Kohn (1997) propose a regressor selection algorithm to fit a smooth surface to data. In this paper, we demonstrate how this methodology can be applied to estimate implied volatility surfaces and why it should be considered an alternative to classical estimators. In addition to mere volatility fitting, we also consider the fit with respect to option prices, which is particularly relevant in practice. For the empirical illustration, European style options on the S&P 500 index are used. The time series of inclusion probabilities gives evidence that parsimonious regression models exclude some relevant regressors but can also be regarded as the highest posterior estimate of the model. Moreover, we illustrate how model risk can be estimated using the BMA spline model.

Keywords: implied volatility surfaces; Bayesian model averaging; model risk; value at risk; VAR; S&P 500; flexible Bayesian modelling; volatility fitting; option prices.

DOI: 10.1504/IJFERM.2014.065650

International Journal of Financial Engineering and Risk Management, 2014 Vol.1 No.4, pp.355 - 374

Received: 07 Nov 2012
Accepted: 02 Dec 2013
Published online: 30 Apr 2015 *

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