Abstract
Uncertain finance is an application to the finance of the uncertainty theory which provides an alternative analysis method from the probability theory under the circumstance that few samples are available. Under the research paradigm of uncertain finance, some financial assets are investigated and modeled with various tools in order to describe the price fluctuation accurately. This paper models the prices of stocks under uncertain finance based on the exponential Ornstein–Uhlenbeck model with periodic dividends. Through the \(\alpha \)-path method, the pricing formulas are derived for European call and put options whose underlying assets follow the proposed stock model. In addition, some numerical algorithms to calculate the option prices are designed.
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References
Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81(3):637–654
Chen X (2011) American option pricing formula for uncertain financial market. Int J Oper Res 8(2):32–37
Chen X, Liu B (2010) Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optim Decis Mak 9(1):69–81
Chen X, Liu Y, Ralescu DA (2013) Uncertain stock model with periodic dividends. Fuzzy Optim Decis Mak 12(1):111–123
Dai L, Fu Z, Huang Z (2017) Option pricing formulas for uncertain financial market based on the exponential Ornstein–Uhlenbeck model. J Intell Manuf 28(3):597–604
Gao R, Liu K, Li Z, Lv R (2019) American barrier option pricing formulas for stock model in uncertain environment. IEEE Access 7:97846–97856
Howatt B, Zuber RA, Gandar JM, Lamb RP (2009) Dividends, earnings volatility and information. Appl Financ Econ 19(7):551–562
Hussainey K, Oscar Mgbame C, Chijoke-Mgbame AM (2016) Dividend policy and share price volatility: UK evidence. J Risk Finance 12(1):57–68
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10
Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin
Liu Y, Ha M (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186
Liu J, Zhang Y (2020) The stability analysis for uncertain heat equations based on \(p\)-th moment. Soft Comput 24(4):2833–2839
Lu Z, Yan H, Zhu Y (2019) European option pricing model based on uncertain fractional differential equation. Fuzzy Optim Decis Mak 18(2):199–217
Merton R (1973) Theory of rational option pricing. Bell J Econ Manag Sci 4(1):141–183
Sheng Y, Kar S (2015) Some results of moments of uncertain variable through inverse uncertainty distribution. Fuzzy Optim Decis Mak 14(1):57–76
Sun J, Chen X (2015) Asian option pricing formula for uncertain financial market. J Uncertain Anal Appl 3(1), Article 11
Tao N, Zhu Y (2016) Stability and attractivity in optimistic value for dynamical systems with uncertainty. Int J Gen Syst 45(4):418–433
Tian M, Yang XF, Kar S (2019) Equity warrants pricing problem of mean-reverting model in uncertain environment. Phys A Stat Mech Appl 531, Article 121593
Wang W, Chen P (2020) Valuation of stock loan under uncertain stock model with floating interest rate. Soft Comput 24(3):1803–1814
Yang X, Ni Y, Zhang Y (2017) Stability in inverse distribution for uncertain differential equations. J Intell Fuzzy Syst 32:2051–2059
Yang X, Zhang Z, Gao X (2019) Asian-barrier option pricing formulas of uncertain financial market. Chaos Solitons Fractals 123:79–86
Yao K (2015) A formula to calculate the variance of uncertain variable. Soft Comput 19(10):2947–2953
Yao K, Chen X (2013) A numerical method for solving uncertain differential equations. J Intell Fuzzy Syst 25(3):825–832
Yao K, Gao J, Gao Y (2013) Some stability theorems of uncertain differential equation. Fuzzy Optim Decis Mak 12(1):3–13
Yu S, Ning Y (2019) An interest-rate model with jumps for uncertain financial markets. Phys A Stat Mech Appl 527, Article 121424
Zhang Z, Ke H, Liu W (2019) Lookback options pricing for uncertain financial market. Soft Comput 23(14):5537–5546
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 61403360) and the University of Chinese Academy of Sciences.
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Liu, Y., Yao, K. Option pricing formulas for uncertain exponential Ornstein–Uhlenbeck model with dividends. Soft Comput 25, 673–681 (2021). https://doi.org/10.1007/s00500-020-05177-z
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DOI: https://doi.org/10.1007/s00500-020-05177-z