Evaluation of Geometric Asian Power Options under Fractional Brownian Motion

Show more

References

[1] B. Rosenow, “Fluctuations and Market Friction in Financial Trading,” International Journal of Modern Physics, Vol. 13, No. 3, 2002, p. 419. http://dx.doi.org/10.1142/S012918310200322X

[2] R. P. Feynman, “Space-Time Approach to Non-Relativistic Quantum Mechanics,” Reviews of Modern Physics, Vol. 20, No. 2, 1948, pp. 367-387. http://dx.doi.org/10.1103/RevModPhys.20.367

[3] N. Wiener, “The Average of an Analytical Functional,” Proceedings of the National Academy of Sciences, Vol. 7, No. 9, 1921, pp. 253-260. http://dx.doi.org/10.1073/pnas.7.9.253

[4] R. Feynman and H. Kleinert, “Effective Classical Partition Functions,” Physical Review, Vol. 34, 1986, pp. 5080-5084.

[5] A. Kemna and A. Vorst, “A Pricing Method for Options Based on Average Values,” Journal of Banking and Finance, Vol. 14, No. 1, 1990, pp. 113-129. http://dx.doi.org/10.1016/0378-4266(90)90039-5

[6] L. C. G. Rogers and Z. Shi, “The Value of an Asian Option,” JAP, Vol. 32, 1995, pp. 1077-1088.

[7] L. Bachelier, “Theory of Speculation: The Origins of Modern Finance,” Princeton University Press, Princeton, 1900.

[8] F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3, 1973, pp. 637-654.

[9] M. Li and M. Wang, “Comparison of Black-Scholes Formula with Fractional Black-Scholes Formula in the Foreign Exchange Option Market with Changing Volatility,” APFM, Vol.17, 2010, pp. 99-111.

[10] A. M. Yaglom, “Correlation Theory of Processes with Random Stationary nth Increments,” AMS Translation, Vol. 2, No. 8, 1958, pp. 87-141.

[11] C. Necula, “Option Pricing in a Fracitonal Brownian Motion Environment,” Bucharest University of Economics, Bucharest, 2008.

[12] B. Mandelbrot and H. Taylor, “On the Distribution of Stock Price Differences,” Operations Research, Vol. 15, No. 6, 1967, pp. 1057-1062. http://dx.doi.org/10.1287/opre.15.6.1057

[13] E. E. Peters, “Fractal Structure in the Capital Markets,” FAJ, Vol. 45, No. 4, 1989, pp. 32-37.

[14] Y. Hu and B. Oksendal, “Fractional White Noise Calculus and Applications to Finance,” Infinite Dimensional Analysis, Vol. 6, No. 1, 2003, pp. 1-32.

[15] F. Biagini, Y. Hu, B. Oksendal and T. Zhang, “Stochastic Calculus for Fractional Brownian motion and Applications,” Springer, Berlin, 2008. http://dx.doi.org/10.1007/978-1-84628-797-8

[16] G. Fusai and A. Meucci, “Pricing Discretely Monitored Asian Options under Levy Processes,” Journal of Bank Finance, Vol. 32, No. 10, 2008, pp. 2076-2088.

http://dx.doi.org/10.1016/j.jbankfin.2007.12.027

[17] T. E. Duncan, B. Maslowski and B. P. Duncan, “Adaptive Control for Semi-Linear Stochastic Systems,” Journal on Control and Optimization, Vol. 38, No. 6, 2000, pp. 1683-1706.

http://dx.doi.org/10.1137/S0363012999351826

[18] Y. J. Wang and S. W. Zhou, “The Pricing of European Power Options,” Journal of Gansu Science, Vol. 17, No. 2, 2005, pp. 21-23.

[19] Y. Xiao and J. Zhou, “Observed Information Based Option Pricing Model in Fractional B-S Market,” Mathematics in Economics, Vol. 25, No. 2, 2008, pp. 171-174.

[20] Y. J. Wang, Y. Zhang and S. Fan, “Pricing of Power-Asian Options,” Journal of Xuzhou Institute of Architectural Technology, Vol. 6, Vol. 2, 2006, pp. 39-41.

[21] D. Zhao, “The Pricing of European Power Options Based on FBM,” Mathematics in Economics, Vol. 24, No.1, 2007, pp. 22-26.

[22] Sh. Zhou and H. Liu, “Power Option Pricing under FBM,” College Mathematics, Vol. 25, No. 5, 2009, pp. 69-72.