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A New Stock Model for Option Pricing in Uncertain Environment | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 3، دوره 11، شماره 3، شهریور 2014، صفحه 27-41 اصل مقاله (425.76 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2014.1568 | ||
نویسندگان | ||
Jin Peng* 1؛ Shengguo Li2 | ||
1Institute of Uncertain Systems, Huanggang Normal University, Hubei 438000, China | ||
2School of Mathematics and Statistics, Huazhong Normal University, Hubei 430079, China | ||
چکیده | ||
The option-pricing problem is always an important part in modern finance. Assuming that the stock diffusion is a constant, some literature has introduced many stock models and given corresponding option pricing formulas within the framework of the uncertainty theory. In this paper, we propose a new stock model with uncertain stock diffusion for uncertain markets. Some option pricing formulas on the proposed uncertain stock model are derived and a numerical calculation is illustrated. | ||
کلیدواژهها | ||
Uncertainty theory؛ Uncertain process؛ Stock model؛ Option pricing | ||
مراجع | ||
\bibitem{Ba:Tdls} L. Bachelier, {\it Theorie de la speculation}, Paris Doctoral Dissertation in Mathematics, 1900. %\bibitem{BaXi:Paojd} E. Bayraktar and H. Xing, {\it Pricing asian options for jump diffusion}, Mathematical Finance, {\bf 21}\textbf{(1)}(2011), 117--143. %\bibitem{BlKa:Bopwstral} F. Black and P. Karasinski, {\it Bond and option pricing when short-term rates are lognormal}, Financial Analysts Journal, {\bf 47}\textbf{(4)}(1991), 52--59. \bibitem{BlSc:Tpocl} F. Black and M. Scholes, {\it The pricing of options and corporate liabilities}, Journal of Political Economy, {\bf 81}\textbf{(3)} (1973), 637--654. %\bibitem{BuEs:Psoufs} J. J. Buckley and E. Eslamt, {\it Pricing stock options using fuzzy sets}, Iranian Journal of Fuzzy Systems, {\bf 4}\textbf{(2)}(2007), 1--14. %\bibitem{CaRb:Afarov} C. Carlssona and F. Robert, {\it A fuzzy approach to real option valuation}, Fuzzy Sets and Systems, {\bf 139}\textbf{(2)}(2003), 297--312. \bibitem{Ch:Aopfufm} X. Chen, {\it American option pricing formula for uncertain financial market}, International Journal of Operations Research, {\bf 8}\textbf{(2)} (2011), 32--37. \bibitem{ChDa:Mepuv} X. Chen and W. Dai, {\it Maximum entropy principle for uncertain variables}, International Journal of Fuzzy Systems, {\bf 13}\textbf{(3)} (2011), 232--236. \bibitem{ChLi:Eutude} X. Chen and B. Liu, {\it Existence and uniqueness theorem for uncertain differential equations}, Fuzzy Optimization and Decision Making, {\bf 9}\textbf{(1)} (2010), 69--81. \bibitem{CoRoRu:Opasa} C. Cox, A. Ross and M. Rubinstein, {\it Option pricing: a simplified approach}, Journal of Financial Economics, {\bf 7}\textbf{(3)} (1979), 229--263. \bibitem{Ga:Spcum} X. Gao, {\it Some properties of continuous uncertain measure}, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, {\bf 17}\textbf{(3)} (2009), 419--426. \bibitem{GaGa:Ansmcop} J. Gao and X. Gao, {\it A new stock model for credibilistic option pricing}, Journal of Uncertain Systems, {\bf 2}\textbf{(4)} (2008), 243--247. %\bibitem{He:Acfsosvabco} L. Heston, {\it A closed-form solution for options with stochastic volatility with applications to bond and currency options}, The Review of Financial Studies, {\bf 6}\textbf{(2)}(1993), 327--343. \bibitem{HuWh:Tpoasv} J. Hull and A. White, {\it The pricing of options on assets with stochastic volatility}, Journal of Finance, {\bf 42}\textbf{(2)} (1987), 281--300. %\bibitem{LeTzWa:Anafstbsopm} C. Lee, G. Tzeng and S. Wang, {\it A new application of fuzzy set theory to the Black-Scholes option pricing model}, Expert Systems with Applications, {\bf 29}\textbf{(2)}(2005), 330--342. %\bibitem{LiRaTa:Ftecmma} X. Li, D. Ralescu and T. Tang, {\it Fuzzy train energy consumption minimization model and algorithm}, Iranian Journal of Fuzzy Systems, {\bf 8}\textbf{(4)}(2011), 77--91. \bibitem{Li:Ut} B. Liu, {\it Uncertainty theory}, Springer-Verlag, Berlin, 2004. \bibitem{Li:Ut2} B. Liu, {\it Uncertainty theory}, 2nd ed., Springer-Verlag, Berlin, 2007. \bibitem{Li:Fphpup} B. Liu, {\it Fuzzy process, hybrid process and uncertain process}, Journal of Uncertain Systems, {\bf 2}\textbf{(1)} (2008), 3--16. \bibitem{Li:Srput} B. Liu, {\it Some research problems in uncertainty theory}, Journal of Uncertain Systems, {\bf 3}\textbf{(1)} (2009), 3--10. \bibitem{Li:Tpup} B. Liu, {\it Theory and practice of uncertain programming}, 2nd ed., Springer-Verlag, Berlin, 2009. \bibitem{Li:Utabmmhu} B. Liu, {\it Uncertainty theory: a branch of mathematics for modeling human uncertainty}, Springer-Verlag, Berlin, 2010. \bibitem{Li:Evtupairm} B. Liu, {\it Extreme value theorems of uncertain process with application to insurance risk model}, Soft Computing, {\bf 17}\textbf{(4)} (2013), 549--556. \bibitem{LiHa:Evfuv} Y. Liu and M. Ha, {\it Expected value of function of uncertain variables}, Journal of Uncertain Systems, {\bf 4}\textbf{(3)} (2010), 181--186. \bibitem{Me:Trop} R. Merton, {\it Theory of rational option pricing}, The Bell Journal of Economics and Management Science, {\bf 4}\textbf{(1)} (1973), 141--183. \bibitem{Me:Opwusrad} R. Merton, {\it Option pricing when underlying stock returns are discontinuous}, Journal of Financial Economics, {\bf 3}\textbf{(1-2)} (1976), 125--154. \bibitem{Pe:Agsmfm} J. Peng, {\it A general stock model for fuzzy markets}, Journal of Uncertain Systems, {\bf 2}\textbf{(4)} (2008), 248--254. \bibitem{PeYa:Anopmsum} J. Peng and K. Yao, {\it A new option pricing model for stocks in uncertainty markets}, International Journal of Operations Research, {\bf 8}\textbf{(2)} (2011), 18--26. \bibitem{QiLi:Opfffm} Z. Qin and X. Li, {\it Option pricing formula for fuzzy financial market}, Journal of Uncertain Systems, {\bf 2}\textbf{(1)} (2008), 17--21. %\bibitem{QiLi:Eptsieoffm} Z. Qin and X. Li, {\it Expected payoff of trading strategies involving European options for fuzzy financial market}, Iranian Journal of Fuzzy Systems, {\bf 8}\textbf{(3)}(2011), 81--94. \bibitem{StSt:Spdsvaaa} E. M. Stein and J. C. Stein, {\it Stock price distributions with stochastic volatility: an analytic approach}, Review of Financial Studies, {\bf 4}\textbf{(4)} (1991), 727--752. \bibitem{Yo:Sctus} C. You, {\it Some convergence theorems of uncertain sequences}, Mathematical and Computer Modelling, {\bf 49}\textbf{(3-4)} (2009), 482--487. \bibitem{Za:Fs} L. A. Zadeh, {\it Fuzzy sets}, Information and Control, {\bf 8}\textbf{(3)} (1965), 338--353. | ||
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