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OPTION PRICING FOR PROCESSES DRIVEN BY MIXED FRACTIONAL BROWNIAN MOTION WITH SUPERIMPOSED JUMPS

Published online by Cambridge University Press:  15 July 2015

B.L.S. Prakasa Rao
B.L.S. Prakasa Rao*
Affiliation:
C R Rao Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad 500046, India E-mail: blsprao@crraoaimscs.res.in; blsprao@gmail.com
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Abstract

We propose a geometric mixed fractional Brownian motion model for the stock price process with possible jumps superimposed by an independent Poisson process. Option price of the European call option is computed for such a model. Some special cases are studied in detail.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 4 , October 2015 , pp. 589 - 596
Copyright
Copyright © Cambridge University Press 2015 

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References

1. Cheridito, P. (2000). Regularizing fractional Brownian motion with a view toward stock price modeling. PhD Dissertation, ETH, Zurich.Google Scholar
2. Cheridito, P. (2001) Mixed fractional Brownian motion, Bernoulli 7: 913–934.Google Scholar
3. Foad, S. and Adem, K. (2014) Pricing currency option in a mixed fractional Brownian motion with jumps environment, Mathematical Problems in Engineering Vol. 2014, pp. 13, Article ID 858210, http://dx.doi.org/10.1155/2014/858210 Google Scholar
4. Kuznetsov, Yu. (1999). The absence of arbitrage in a model with fractal Brownian motion. Russian Mathematical Surveys 54: 847–848.Google Scholar
5. Mishura, Y. (2008). Stochastic Calculus for Fractional Brownian Motion and Related Processes, Lecture Notes in Mathematics No. 1929, Berlin: Springer.Google Scholar
6. Mishura, Y. and Valkeila, E. (2002). The absence of arbitrage in a mixed Brownian-fractional Brownian model. Proceedings of the Steklov Institute of Mathematics 237: 224–233.Google Scholar
7. Prakasa Rao, B.L.S. (2010). Statistical Inference for Fractional Diffusion Processes, Chichester, UK: Wiley.Google Scholar
8. Ross, S.M. (2003). An Elementary Introduction to Mathematical Finance, 2nd edn., Cambridge, UK: Cambridge University Press.Google Scholar
9. Sun, L. (2013). Pricing currency options in the mixed fractional Brownian motion. Physica A 392(16): 3441–3458.Google Scholar
10. Sun, X. and Yan, L. (2012). Mixed-fractional models to credit risk pricing, Journal of Statistical and Econometric Methods 1: 79–96.Google Scholar
11. Xiao, W.-L., Zhang, W,-G., Zhang, X.-L., and Wang, Y.-L. (2010). Pricing currency options in a fractional Brownian motion with jumps, Economic Modelling 27: 935–942.Google Scholar
12. Yu, Z. and Yan, L. (2008). European call option pricing under a mixed fractional Brownian motion environment, Journal of University of Science and Technology of Suzhou 25: 4–10 (in Chinese).Google Scholar
13. Zili, M. (2006). On the mixed fractional Brownian motion, Journal of Applied Mathematics and Stochastic Analysis, DOI 10.1155/JAMSA/2006/32435.Google Scholar