OJAppS  Vol.5 No.5 , May 2015
Option Pricing with Markov Switching in Uncertainty Markets
In this paper, we present a stock model with Markov switching in the uncertainty markets, where the parameters of drift and volatility change according to the states of a Markov process. To price the option, we firstly establish a risk-neutral probability based on the uncertain measure given by Liu. Then a closed form of the European option pricing formula is obtained by applying the Laplace transforms and the inverse Laplace transforms.

Cite this paper
Wang, G. and Zhao, D. (2015) Option Pricing with Markov Switching in Uncertainty Markets. Open Journal of Applied Sciences, 5, 191-198. doi: 10.4236/ojapps.2015.55019.
[1]   Bachelier, L. (1900) Theorie de la Speculation. Gauthier-Villars, Paris.

[2]   Samuelson, P.A. (1965) Proof That Properly Anticipated Prices Fluctuate Randomly. Industrial Management Review, 6, 41-49.

[3]   Black, F. and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, 637-654. http://dx.doi.org/10.1086/260062

[4]   Liu, B. (2010) Uncertainty Theory. 3rd Edition, Springer-Verlag, Berlin.

[5]   Liu, B. (2008) Fuzzy Process, Hybrid Process and Uncertain Process. Journal of Uncertain Systems, 2, 3-16.

[6]   Liu, B. (2009) Some Research Problems in Uncertainty Theory. Journal of Uncertain Systems, 3, 3-10.

[7]   Chen, X. (2011) American Option Pricing Formula for Uncertain Financial Market. International Journal of Operations Research, 8, 32-37.

[8]   Hamilton, J. (1989) A New Approach to the Economics Analysis of Non-Stationary Time Series and the Business Cycle. Econometrica, 57, 357-384.

[9]   Masi, G., Kabanov, Y. and Runggaldier, W. (1994) Mean-Variance Hedging of Options on Stocks with Markov Volatility. Theory of Probability and Its Applications, 39, 173-181.

[10]   Guo, X. (2001) Information and Option Pricings. Quantitative Finance, 1, 38-44.

[11]   Cheng, D.F., Ho, K.W.R., Hu, I. and Wang, R.H. (2012) Option Pricing with Markov Switching. Journal of Data Science, 10, 483-509.

[12]   Mamon, R.S. and Rodrigo, M.R. (2005) Explicit Solutions to European Options in a Regime-Switching Economy. Operations Research Letters, 33, 581-586.

[13]   Liu, B. (2014) Uncertainty Theory. 5th Edition. http://orsc.edu.cn/liu/ut.pdf

[14]   Yao, K. (2010) Expected Value of Lognormal Uncertain Variable. Proceedings of the First International Conference on Uncertainty Theory, Urumchi, 11-19 August 2010, 241-243.