Abstract
We describe a (B, S,X )-incomplete market of securities with jumps as a jump random evolution process that is a combination of an ltô process in random Markov medium and a geometric compound Poisson process. For this model, we derive the Black-Scholes equation and formula, which describe the pricing of the European call option under conditions of (B,S,X)-mcomplete market.
This is a preview of subscription content, log in via an institution to check access.
References
R. Griego and A. A. Swishchuk, “Black-Scholes formula for a market in a random environment,” Stochast. Proc. Their Appl. (1998) (to appear).
F. Black and M. Scholes, “The pricing of options and cooperate liabilities,” J. Polit. Economy, No. 3, 637–659 (1973).
A. V. Svishchuk, “Hedging of options under mean-square criterion and semi-Markov volatility,” Ukr. Mat. Zh., 47, No. 7, 976–983 (1995).
A. V. Svishchuk and D. G. Zhuravitskii, “Application of discontinuous evolution systems in financial mathematics,” Dopov. Akad. Nauk Ukr., No. 7, 50–56 (1997).
K. K. Aase, “Contingent claims valuation when the security price is a combination of a Ito process and random point process,” Stochast. Proc. Their Appl, 28, 185–220 (1998).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Svishchuk, A.V., Zhuravitskii, D.G. & Kalemanova, A.V. Analog of the black-scholes formula for option pricing under conditions of (b, s, x)-incomplete market of securities with jumps. Ukr Math J 52, 489–497 (2000). https://doi.org/10.1007/BF02513144
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02513144