Research Article
Pricing Options in a Delayed Market Driven by Le'vy Noise
- Al-Baha University, Saudi Arabia
Abstract
In this paper we studied stochastic delayed differential equations driven by Le'vy noise. The analogue of Ito formula is considered. The Black-Scholes formula analogue for Vanilla call option price formula is derived.
How to Cite
I. H. Elsanousi, Pricing Options in a Delayed Market Driven by Le'vy Noise, Int. J. Anal. Appl. 19 (2021), 494–502. https://doi.org/10.28924/2291-8639-19-2021-494
BibTeX
@article{Elsanousi2021,
author = {Elsanousi, Ismail Hamed},
title = {Pricing Options in a Delayed Market Driven by Le'vy Noise},
journal = {Int. J. Anal. Appl.},
volume = {19},
year = {2021},
pages = {494--502},
doi = {10.28924/2291-8639-19-2021-494}
}References
- [1] A. Chojnowska-Michalik, Representation theorem for general stochastic delay equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 26 (1978), 635-642.
- [2] G. Da Prato, J. Zabczyk, Stochastic equations in infinite dimensions, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge (UK), 1992.
- [3] I. Elsanousi, B. Pksendal, A. Sulem, Some solvable stochastic control problems with delay, Stoch. Stoch. Rep. 71 (2000), 69-89.
- [4] J.C. Hull, A. White, The pricing of options on assets with stochastic valatilities, J. Finance, 42 (1987), 281-300.
- [5] S.-E.A. Mohammed, Stochastic Differential Systems With Memory: Theory, Examples and Applications, in: L. Decreusefond, B. Øksendal, J. Gjerde, A.S. Ust ¨unel (Eds.), Stochastic Analysis and Related Topics VI, Birkh ¨auser Boston, Boston, ¨ MA, 1998: pp. 1-77.
- [6] F. Black, M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973), 637-654.
- [7] B. Oksendal, A. Sulem, Applied stochastic control of jump diffusions, Springer, Berlin, 2005.
- [8] M. Arriojas, Y. Hu, S.-E. Mohammed, G. Pap, A delayed black and scholes formula, Stoch. Anal. Appl. 25 (2007), 471-492.
- [9] D. Applebanm, Le'vy process and stochastic calculus, Cambridge Studies in Advanced Mathematics Vol. 116, Cambridge University Press, Cambridge, 2009.
- [10] P.E. Protter, Stochastic integration and differential equations, Springer, Berlin, 2005.
- [11] M. Reiß, M. Riedle, O. van Gaans, Delay differential equations driven by L ´evy processes: Stationarity and Feller properties, Stoch. Proc. Appl. 116 (2006), 1409-1432.
- [12] Y. Kazmerchuk, A. Swishchuk, J. Wu, The pricing of options for securities markets with delayed response, Math. Computers Simul. 75 (2007), 69-79.
- [13] S. Federico, B.K. Øksendal, Optimal Stopping of Stochastic Differential Equations with Delay Driven by L ´evy Noise, Potential Anal. 34 (2011), 181-198.