ABSTRACT
In this article, we find empirical evidence of a new smirk factor, obtained from the jump structure of the risk neutral distribution of the underlying Lévy process. As an application we show how to price a barrier style contract.
Acknowledgements
I would like to thank an anonymous referee for his very useful comments. Also, I would like to thank Bruno Dupire, Liuren Wu, Roger Lee, and Ernst Eberlein for very useful comments and Fernando Mendo Lopez for research assistance. I also thank the comments of seminar participants at Stevanovich center University of Chicago. PIMSV–Universitat Bern. IMUB-Universitat de Barcelona. Universität Freiburg. CRM-Universitat Autonoma de Barcelona. V LubraFin. 7th Bachelier Finance Society Meeting and 10th World Congress of The Econometric Society for comments. Finally, I thank CNPq from Brazil for financial support. The usual disclaimer applies.
Disclosure statement
No potential conflict of interest was reported by the author.
Notes
1 could be defined as 0. Here we follow Cont and Tankov (Citation2004).
2 Henceforth FW.
3 The intuition for this name came from the fact that when we plot implied volatility versus moneyness and , we can obtain a figure with a torsion, as in , build using Brazilian asset Petróbras (PETR4).
4 Taken from http://www.cboe.com/data/mktstat.aspx
5 It is also important to mention that this choice of allow us to guarantee
for the sample set of moneyness.
6 Here we need the law of be absolutely continuous. The absolute continuity holds in all Lévy models of interest, see Theorem 27.4 in Sato (Citation1999).
7 We simulate realizations of a NIG distribution with the estimated parameters.
8 see 5.2 in Cont and Tankov (Citation2004).