Title: Pricing Options in a Delayed Market Driven by Le’vy Noise
Author(s): Ismail Hamed Elsanousi
Pages: 494-502
Cite as:
Ismail Hamed Elsanousi, Pricing Options in a Delayed Market Driven by Le’vy Noise, Int. J. Anal. Appl., 19 (4) (2021), 494-502.

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.

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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. Google Scholar

  2. G. Da Prato, J. Zabczyk, Stochastic equations in infinite dimensions, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge (UK), 1992. Google Scholar

  3. I. Elsanousi, B. Pksendal, A. Sulem, Some solvable stochastic control problems with delay, Stoch. Stoch. Rep. 71 (2000), 69-89. Google Scholar

  4. J.C. Hull, A. White, The pricing of options on assets with stochastic valatilities, J. Finance, 42 (1987), 281-300. Google Scholar

  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. Google Scholar

  6. F. Black, M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973), 637-654. Google Scholar

  7. B. Oksendal, A. Sulem, Applied stochastic control of jump diffusions, Springer, Berlin, 2005. Google Scholar

  8. M. Arriojas, Y. Hu, S.-E. Mohammed, G. Pap, A delayed black and scholes formula, Stoch. Anal. Appl. 25 (2007), 471–492. Google Scholar

  9. D. Applebanm, Le’vy process and stochastic calculus, Cambridge Studies in Advanced Mathematics Vol. 116, Cambridge University Press, Cambridge, 2009. Google Scholar

  10. P.E. Protter, Stochastic integration and differential equations, Springer, Berlin, 2005. Google Scholar

  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. Google Scholar

  12. Y. Kazmerchuk, A. Swishchuk, J. Wu, The pricing of options for securities markets with delayed response, Math. Computers Simul. 75 (2007), 69–79. Google Scholar

  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. Google Scholar


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