Uncertainty of volatility estimates from Heston Greeks

  • Volatility is a widely recognized measure of market risk. As volatility is not observed it has to be estimated from market prices, i.e., as the implied volatility from option prices. The volatility index VIX making volatility a tradeable asset in its own right is computed from 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. In the present paper we quantify the information content of the constituents of the VIX about the volatility of the S&P 500 in terms of the Fisher information matrix. Assuming that observed option prices are centered on the theoretical price provided by Heston's model perturbed by additive Gaussian noise we relate their Fisher information matrix to the Greeks in the Heston model. We find that the prices of options contained in the VIX basket allow for reliable estimates of the volatility of the S&P 500 with negligible uncertainty as long as volatility is large enough. Interestingly, if volatility drops below a critical value of roughly 3%, inferences from option prices become imprecise because Vega, the derivative of a European option w.r.t. volatility, and thereby the Fisher information nearly vanishes.

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Metadaten
Author:Oliver Pfante, Nils Bertschinger
URN:urn:nbn:de:hebis:30:3-514976
DOI:https://doi.org/10.3389/fams.2017.00027
Parent Title (English):Frontiers in applied mathematics and statistics
Publisher:Frontiers Research Foundation
Place of publication:Lausanne
Document Type:Article
Language:English
Year of Completion:2018
Date of first Publication:2018/01/10
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2019/10/24
Tag:Fisher information; Greeks; Heston model; fractional Fourier transform; option pricing; stochastic volatility
Volume:3
Issue:article 27
Page Number:12
HeBIS-PPN:455689733
Institutes:Wissenschaftliche Zentren und koordinierte Programme / Frankfurt Institute for Advanced Studies (FIAS)
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Sammlungen:Universit├Ątspublikationen
Licence (German):License LogoCreative Commons - Namensnennung 4.0