De-Arbitraging with a Weak Smile: Application to Skew Risk

Wilmott Magazine, p. 40, 2013

10 Pages Posted: 25 Apr 2014 Last revised: 21 May 2014

See all articles by Babak Mahdavi-Damghani

Babak Mahdavi-Damghani

University of Oxford - Oxford-Man Institute of Quantitative Finance

Andrew Kos

Credit Suisse AG

Date Written: July 26, 2013

Abstract

The aim of this article is to address the methodology behind de-arbitraging a realistic volatility surface and stressing it without adding arbitrages. We derive from basic principles the constraints which the changes on the strike and the tenor axis must satisfy in order to make a volatility surface arbitrage-free. The two most influential parameterized versions of the volatility surface will then be discussed, along with their origin and their limitations. Furthermore, this review will address the issues of finding the closest arbitrage-free volatility surface through the gSVI method, a more realistic parameterized version of the volatility surface applicable to the FX, commodities, and equities markets. Finally, using examples, the methodology behind coherently stressing this arbitrage-free volatility surface will be looked at, in order to capture and isolate the risk associated with higher-order Greeks like the Vanna or the Vomma.

Keywords: arbitrage-free volatility surface; Dupire local volatility; Fokker-Planck equation; Kolmogorov forward equation; constraint optimization; search algorithm; butterfly spread; calendar spread; arbitrage frontier; SVI; gSVI; skew risk; Vanna

Suggested Citation

Mahdavi-Damghani, Babak and Kos, Andrew, De-Arbitraging with a Weak Smile: Application to Skew Risk (July 26, 2013). Wilmott Magazine, p. 40, 2013. Available at SSRN: https://ssrn.com/abstract=2428532

Babak Mahdavi-Damghani (Contact Author)

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

United Kingdom

Andrew Kos

Credit Suisse AG

Giessh├╝belstrasse 40
Zurich, 8002
Switzerland

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