Barrier style contracts under Lévy processes once again
In this paper we present new pricing formulas for some Barrier style contracts of European type when the underlying process is driven by an important class of Lévy processes, which includes CGMY model, generalized hyperbolic Model and Meixner Model, when no symmetry properties are assumed, complementing in this way previous findings in Fajardo (J Bank Financ 53:179–187, 2015). Also, we show how to implement our new formulas.
KeywordsSkewness Lévy processes Absence of symmetry Barrier contracts
JEL ClassificationC52 G12
I would like to thank the comments of an anonymous referee who helps to improve the present version of the paper. Also, I would like to thank seminar participants at EMAp/FGV, SBFin 2015, SAET 2016 and Barcelona Workshop on Mathematical Finance. Financial support from CNPq of Brazil is also acknowledge.
- Bates, D.: The skewness premium: Option pricing under asymmetric processes. Adv Futur Options Res 9, 51–82 (1997)Google Scholar
- Cont, R., Tankov, P.: Financial Modelling with Jump Processes. Chapman and Hall /CRC Financial Mathematics Series, London (2004)Google Scholar
- Eberlein, E., Glau, K., Papapantoleon, A.: Analyticity of the wiener-hopf factors and valuation of exotic options in Lévy models. In: Nunno, G.D., Øksendal, B. (eds.) Advanced Mathematical Methods for Finance. Springer, Berlin (2011)Google Scholar
- Eberlein, E., Prause, K.: The generalized hyperbolic model: Financial derivatives and risk measures. In: Geman, S.P.T.V.H., Madan, D. (eds.) Mathematical Finance-Bachelier Congress 2000. Springer, Berlin (2002)Google Scholar
- Fajardo, J., Farias, A.: Generalized hyperbolic distributions and Brazilian data. Braz Rev Econ 24(2), 249–271 (2004)Google Scholar
- Lewis, A.L.: A simple option formula for general jump-diffusion and other exponential Lévy processes. Working paper. Envision Financial Systems and OptionCity.net Newport Beach, California, USA. http://www.optioncity.net (2001)
- Sato, K.-I.: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999)Google Scholar
- Schoutens, W., Cariboni, J.: Lévy Processes in Credit Risk. Wiley, New York (2009)Google Scholar