Asymptotic extrapolation of model-free implied variance: exploring structural underestimation in the VIX Index

Philip Stahl ()
Additional contact information
Philip Stahl: Technische Universität Darmstadt

Review of Derivatives Research, 2022, vol. 25, issue 3, No 4, 315-339

Abstract: Abstract We show that the VIX Index structurally underestimates model-free implied volatility because its implementation omits extrapolation of the volatility smile in the tails. We use the asymptotic behavior of the volatility surface to construct a correction term that is model-independent and only requires option prices at the two outermost strikes. We show how to apply this correction to the VIX Index ex-post as well as how to modify its implementation accordingly. Furthermore, we show that the degree of underestimation varies over time. For the S&P 500 Index and the DJIA Index the error is larger in periods of sustained low volatility. This cannot be observed for the Volatility-of-VIX Index.

Keywords: Model-free implied volatility; Volatility smile; VIX index; Variance swaps (search for similar items in EconPapers)
JEL-codes: G10 G12 G13 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11147-022-09190-2 Abstract (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:revdev:v:25:y:2022:i:3:d:10.1007_s11147-022-09190-2

Ordering information: This journal article can be ordered from
http://www.springer. ... 29/journal/11147/PS2

DOI: 10.1007/s11147-022-09190-2

Access Statistics for this article

Review of Derivatives Research is currently edited by Gurdip Bakshi and Dilip Madan

More articles in Review of Derivatives Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().