Option pricing in the multidimensional case, i.e. when the contingent claim paid at maturity depends on a number of risky assets, is considered. It is assumed that the prices of the risky assets are in discrete time subject to binomial disturbances. Two approaches to option pricing are studied: geometric and analytic. A numerical example is also given.
@article{bwmeta1.element.bwnjournal-article-zmv25i1p55bwm,
author = {Micha\l\ Motoczy\'nski and \L ukasz Stettner},
title = {On option pricing in the multidimensional Cox-Ross-Rubinstein model},
journal = {Applicationes Mathematicae},
volume = {25},
year = {1998},
pages = {55-72},
zbl = {0895.90016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv25i1p55bwm}
}
Motoczyński, Michał; Stettner, Łukasz. On option pricing in the multidimensional Cox-Ross-Rubinstein model. Applicationes Mathematicae, Tome 25 (1998) pp. 55-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv25i1p55bwm/
[000] [1] J. C. Cox, S. A. Ross and M. Rubinstein, Option pricing: A simplified approach, J. Financial Econom. 7 (1979), 229-263 | Zbl 1131.91333
[001] [2] I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer, New York, 1991. | Zbl 0734.60060
[002] [3] A. N. Shiryaev, Yu. M. Kabanov, D. O. Kramkov and A. V. Melnikov, On the theory of pricing of European and American options. I. Discrete time, Teor. Veroyatnost. i Primenen. 39 (1994), 23-79 (in Russian). | Zbl 0833.60064
[003] [4] G. Tessitore and J. Zabczyk, Pricing options for multinomial models, Bull. Polish Acad. Sci. Math. 44 (1996), 363-380. | Zbl 0868.90010