Uncertainty Estimates in the Heston Model via Fisher Information
Abstract
We address the information content of European option prices about volatility in terms of the Fisher information matrix. We assume that observed option prices are centred on the theoretical price provided by Heston's model disturbed by additive Gaussian noise. We fit the likelihood function on the components of the VIX, i.e., near- and next-term put and call options on the S&P 500 with more than 23 days and less than 37 days to expiration and non-vanishing bid, and compute their Fisher information matrices from the Greeks in the Heston model. We find that option prices allow reliable estimates of volatility with negligible uncertainty as long as volatility is large enough. Interestingly, if volatility drops below a critical value, inferences from option prices become impossible because Vega, the derivative of a European option w.r.t. volatility, nearly vanishes.
Keywords
Cite
@article{arxiv.1610.04760,
title = {Uncertainty Estimates in the Heston Model via Fisher Information},
author = {Oliver Pfante and Nils Bertschinger},
journal= {arXiv preprint arXiv:1610.04760},
year = {2016}
}
Comments
29 pages, 11 figures. The text overlap of the first version with arXiv:1609.02108 by other authors has been removed. It occurred in the introduction (page 2 line 22-37) of the first version. A part of the introduction of arXiv:1609.02108 was incidentally adopted. The issue is removed in the second version: the introduction is independent and arXiv:1609.02108 is cited properly