From arbitrage to arbitrage-free implied volatilities

Cornelis W. Oosterlee and Lech A. Grzelak

Journal of Computational Finance

Abstract: ABSTRACT We propose a method for determining an arbitrage-free density implied by the Hagan;formula. (We use the wording "Hagan formula" as an abbreviation of the Hagan-Kumar-Le´sniewski-Woodward model.) Our method is based on the stochastic collocation;method. The principle is to determine a few collocation points on the implied;survival distribution function and project them onto the polynomial of an arbitrage free;variable for which we choose the Gaussian variable. In this way, we have equality;in probability at the collocation points while the generated density is arbitrage free.;Analytic European option prices are available, and the implied volatilities stay very;close to those initially obtained by the Hagan formula. The proposed method is very;fast and straightforward to implement, as it only involves one-dimensional Lagrange;interpolation and the inversion of a linear system of equations. The method is generic;and may be applied to other variants or other models that generate arbitrage.

References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.risk.net/journal-computational-finance ... implied-volatilities (text/html)

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:rsk:journ0:2463775

Access Statistics for this article

More articles in Journal of Computational Finance from Journal of Computational Finance
Bibliographic data for series maintained by Thomas Paine ().