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Option pricing formulas for generalized fuzzy stock model
College of Mathematics and Information Science, Hebei University, Baoding 071002, China |
Fuzzy stock model has been studied by many scholars in recent years, in which option pricing problem is the most important part. In this paper, we studied option pricing for a new generalized fuzzy stock model. Based on credibility theory, pricing formulas of European option and American option were obtained.
References:
[1] |
F. Black and M. Scholes,
The pricing of option and corporate liabilities, Journal of Political Economy, 81 (1973), 637-654.
doi: 10.1086/260062. |
[2] |
X. Chen and Z. Qin,
A new existence and uniqueness theorem for fuzzy differential equation, International Journal of Fuzzy Systems, 13 (2011), 148-151.
|
[3] |
W. Dai, Reflection principle of Liu process, 2007. Available from: http://orsc.edu.cn/process\/071110.pdf. Google Scholar |
[4] |
W. Dai, Lipschitz continuity of Liu process, 2008. Available from: http://orsc.edu.cn/process\/080831.pdf. Google Scholar |
[5] |
Z. Ding, M. Ma and A. Kandel,
Exsitence of the solutions of fuzzy differential equations with parameters, Information Sciences, 99 (1999), 205-217.
doi: 10.1016/S0020-0255(96)00279-4. |
[6] |
J. Gao and X. Gao, A new stock model for credibilistic option pricing, Journal of Uncertain Systems, 2 (2008), 243-247. Google Scholar |
[7] |
X. Gao and X. Chen, Option pricing formula for generalized stock models, 2008. Available from: http://orsc.edu.cn/process/080317.pdf. Google Scholar |
[8] |
H. Hu, Power option pricing model for stock price follow geometric fractional Liu process, Journal of Henan Normal University (Natural Science Edition), 41 (2013), 1-5. Google Scholar |
[9] |
O. Kaleva,
Fuzzy differential equations, Fuzzy Sets and Systems, 24 (1987), 301-317.
doi: 10.1016/0165-0114(87)90029-7. |
[10] |
B. Liu, Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems, 2 (2008), 3-16. Google Scholar |
[11] |
B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems, 10 (2002), 445-450. Google Scholar |
[12] |
R. Merton,
Theory of rational option pricing, Bell Journal of Economics and Management Science, 4 (1973), 141-183.
doi: 10.2307/3003143. |
[13] |
J. Peng, A general stock model for fuzzy markets, Journal of Uncertain Systems, 2 (2008), 248-254. Google Scholar |
[14] |
Z. Qin and X. Li, Option pricing formula for fuzzy financial market, Journal of Uncertain System, 2 (2008), 17-21. Google Scholar |
[15] |
Z. Qin and X. Li, Fuzzy calculus for finance, 2008. Available from: http://orsc.edu.cn/process\/fc.pdf. Google Scholar |
[16] |
C. You, H. Huo and W. Wang,
Multi-dimensional Liu process, differential and integral, East Asian Mathematical Journal, 29 (2013), 13-22.
doi: 10.7858/eamj.2013.002. |
[17] |
C. You, H. Ma and H. Huo,
A new kind of generalized fuzzy integrals, Journal of Nonlinear Science and Applications, 9 (2016), 1396-1401.
doi: 10.22436/jnsa.009.03.63. |
[18] |
C. You and G. Wang, Properties of a new kind of fuzzy integral, Journal of Hebei University (Natural Science Edition), 31 (2011), 337-340. Google Scholar |
[19] |
C. You, W. Wang and H. Huo, Existence and unqiueness theorems for fuzzy differential equation, Journal of Uncertain Systems, 7 (2013), 303-315. Google Scholar |
[20] |
L. Zadeh,
Fuzzy sets, Information and Control, 8 (1965), 338-353.
doi: 10.1016/S0019-9958(65)90241-X. |
show all references
References:
[1] |
F. Black and M. Scholes,
The pricing of option and corporate liabilities, Journal of Political Economy, 81 (1973), 637-654.
doi: 10.1086/260062. |
[2] |
X. Chen and Z. Qin,
A new existence and uniqueness theorem for fuzzy differential equation, International Journal of Fuzzy Systems, 13 (2011), 148-151.
|
[3] |
W. Dai, Reflection principle of Liu process, 2007. Available from: http://orsc.edu.cn/process\/071110.pdf. Google Scholar |
[4] |
W. Dai, Lipschitz continuity of Liu process, 2008. Available from: http://orsc.edu.cn/process\/080831.pdf. Google Scholar |
[5] |
Z. Ding, M. Ma and A. Kandel,
Exsitence of the solutions of fuzzy differential equations with parameters, Information Sciences, 99 (1999), 205-217.
doi: 10.1016/S0020-0255(96)00279-4. |
[6] |
J. Gao and X. Gao, A new stock model for credibilistic option pricing, Journal of Uncertain Systems, 2 (2008), 243-247. Google Scholar |
[7] |
X. Gao and X. Chen, Option pricing formula for generalized stock models, 2008. Available from: http://orsc.edu.cn/process/080317.pdf. Google Scholar |
[8] |
H. Hu, Power option pricing model for stock price follow geometric fractional Liu process, Journal of Henan Normal University (Natural Science Edition), 41 (2013), 1-5. Google Scholar |
[9] |
O. Kaleva,
Fuzzy differential equations, Fuzzy Sets and Systems, 24 (1987), 301-317.
doi: 10.1016/0165-0114(87)90029-7. |
[10] |
B. Liu, Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems, 2 (2008), 3-16. Google Scholar |
[11] |
B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems, 10 (2002), 445-450. Google Scholar |
[12] |
R. Merton,
Theory of rational option pricing, Bell Journal of Economics and Management Science, 4 (1973), 141-183.
doi: 10.2307/3003143. |
[13] |
J. Peng, A general stock model for fuzzy markets, Journal of Uncertain Systems, 2 (2008), 248-254. Google Scholar |
[14] |
Z. Qin and X. Li, Option pricing formula for fuzzy financial market, Journal of Uncertain System, 2 (2008), 17-21. Google Scholar |
[15] |
Z. Qin and X. Li, Fuzzy calculus for finance, 2008. Available from: http://orsc.edu.cn/process\/fc.pdf. Google Scholar |
[16] |
C. You, H. Huo and W. Wang,
Multi-dimensional Liu process, differential and integral, East Asian Mathematical Journal, 29 (2013), 13-22.
doi: 10.7858/eamj.2013.002. |
[17] |
C. You, H. Ma and H. Huo,
A new kind of generalized fuzzy integrals, Journal of Nonlinear Science and Applications, 9 (2016), 1396-1401.
doi: 10.22436/jnsa.009.03.63. |
[18] |
C. You and G. Wang, Properties of a new kind of fuzzy integral, Journal of Hebei University (Natural Science Edition), 31 (2011), 337-340. Google Scholar |
[19] |
C. You, W. Wang and H. Huo, Existence and unqiueness theorems for fuzzy differential equation, Journal of Uncertain Systems, 7 (2013), 303-315. Google Scholar |
[20] |
L. Zadeh,
Fuzzy sets, Information and Control, 8 (1965), 338-353.
doi: 10.1016/S0019-9958(65)90241-X. |
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