Multivariate Variance Gamma and Gaussian dependence: a study with copulas 203- ObtainNrealisations(xn 1 ,x 2 n)ofX( 1 )by means of the relations
xn 1 =μ 1 g 1 n+σ 1 M 1 (n)xn 2 =μ 2 g 2 n+σ 2 M 2 (n).Acknowledgement.We thank Claudio Patrucco for having provided the marginal calibra-
tions and Ksenia Rulik for computational assistance. Financial support from MIUR (grant
20061327131) is gratefully acknowledged.
References
- Cherubini, U., Luciano, E., Vecchiato W.: Copula Methods in Finance, John Wiley, Chich-
ester (2004) - Chourdakis, K.: Option pricing using the fractional FFT. J. Comput. Finan. 8, 1–18 (2005)
- Cont, R., Tankov, P.: Financial modelling with jump processes. Chapman and Hall-CRC
financial mathematics series (2004) - Embrechts, P., McNeil, A.J., Straumann, D.: Correlation and dependency in risk man-
agement: properties and pitfalls. In: Dempster, M.A.H. (ed.) Value at Risk and Beyond.
Cambridge University Press (2002) - Fiorani, F., Luciano, E., Semeraro, P.: Single and joint default in a structural model with
purely discontinuous assets prices. Quant. Finan. (2009) - Luciano, E., Schoutens, W.: A multivariate Jump-Driven Financial Asset Model. Quant.
Finan. 6, 385–402 (2005) - Luciano, E., Semeraro, P.: Extending Time-Changed Levy Asset Models Through Mu ́ lti-
variate Subordinators, working paper, Collegio Carlo Alberto (2007) - Madan, D.B., Seneta, E.: The VG model for share market returns. J. Busin. 63, 511–524
(1990) - Nelsen, R.B.: An introduction to copulas. Lecture Notes in Statistics 139, Springer (1999)
- Sato, K.I.: Levy processes and infinitely divisible distributions. Studies in Advanced Math- ́
ematics. Cambridge University Press (2003) - Semeraro, P.: A multivariate variance gamma model for financial application. J. Theoret.
Appl. Finan. 11, 1–18 (2006) - Sklar A.: Fonctions de repartition`andimensions et leurs marges. Publication Inst. Statist.
Univ. Paris 8, 229–231 (1959)