An exact and explicit implied volatility inversion formula

Yuxuan Xia () and Zhenyu Cui
Additional contact information
Yuxuan Xia: School of Business, Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07310, USA
Zhenyu Cui: School of Business, Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07310, USA

International Journal of Financial Engineering (IJFE), 2018, vol. 05, issue 03, 1-29

Abstract: In this paper, we develop an exact and explicit (model-independent) Taylor series representation of the implied volatility based on the novel applications of an extended Faà di Bruno formula under the operator calculus setting, and the Lagrange inversion theorem. We rigorously establish that our formula converges to the true implied volatility as the truncation order increases. Numerical examples illustrate the remarkable accuracy and efficiency of the formula. The formula distinguishes from previous literature as it converges to the true exact implied volatility, is a closed-form formula whose coefficients are explicitly determined and do not involve numerical iterations.

Keywords: Implied volatility; Taylor series; arbitrary greeks; Lagrange inversion theorem; operator calculus (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S2424786318500329
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:wsi:ijfexx:v:05:y:2018:i:03:n:s2424786318500329

Ordering information: This journal article can be ordered from

DOI: 10.1142/S2424786318500329

Access Statistics for this article

International Journal of Financial Engineering (IJFE) is currently edited by George Yuan

More articles in International Journal of Financial Engineering (IJFE) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().