Pricing Study on Two Kinds of Power Options in Jump-Diffusion Models with Fractional Brownian Motion and Stochastic Rate
Abstract: In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the reset option with a single reset date and the phenomena of delta of the reset jumps existing in the reset option during the reset date are discussed. The closed-form formulae of pricing for two kinds of power options are derived in the end.
Cite this paper: Li, J. , Xiang, K. and Luo, C. (2014) Pricing Study on Two Kinds of Power Options in Jump-Diffusion Models with Fractional Brownian Motion and Stochastic Rate. Applied Mathematics, 5, 2426-2441. doi: 10.4236/am.2014.516234.
References

[1]   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

[2]   Hu, Y. and Oksendal, B. (2000) Fractional White Noise Calculus and Application to Finance. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 6, 1-32.
http://dx.doi.org/10.1142/S0219025703001110

[3]   Elliott, R. and Hoek, J. (2003) A General Fractional White Noise Theory and Applications to Finance. Mathematical Finance, 13, 301-330.
http://dx.doi.org/10.1111/1467-9965.00018

[4]   Necula, C. (2002) Option Pricing in a Fractional Brownian Motion Environment. Pure Mathematics, 2, 63-68.

[5]   Liu, S.Y. and Yang, X.Q. (2004) Pricing of European Contingent Claim in Fractional Brownian Motion Environment. Chinese Journal of Applied Probability and Statistics, 20, 429-434.

[6]   Liu, S.Y. and Yang, X.Q. (2006) Pricing Compound Option in a Fractional Brownian Motion Environment. Chinese Journal of Engineering Mathematics, 23, 153-157.

[7]   Xue, H. and Wang, L.S. (2008) Pricing of Maximum Option in the Fractional Brownian Motion Environment. Chinese Journal of Engineering Mathematics, 25, 843-850.

[8]   Elliott, R.J. and Chan, L.L. (2004) Perpetual American Options with Fractional Brownian Motion. Quantative Finance, 4, 123-128.
http://dx.doi.org/10.1080/14697680400000016

[9]   Peng, D.H. (2007) Pricing of Perpetual American Put with Fractional O-U Process. Mathematica Acta Scienta, 27A, 1141-1147.

[10]   Deng, G.H. and Lin, H.Y. (2008) Pricing American Put Option in a Fractional Black-Scholes Model via Compound Option Approximation. Advance in Systems Science and Applications, 8, 447-456.

[11]   Deng, X.H. (2009) Option Pricing under Stochastic Rate in Fractional Brownian Motion. Chongqing University, Chongqing.

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