Valuation of European option under uncertain volatility model
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Valuation of an option plays an important role in modern finance. As the financial market for derivatives continues to grow, the progress and the power of option pricing models at predicting the value of option premium are under investigations. In this paper, we assume that the volatility of the stock price follows an uncertain differential equation and propose an uncertain counterpart of the Heston model. This study also focuses on deriving a numerical method for pricing a European option under uncertain volatility model, and some numerical experiments are presented. Numerical experiments confirm that the developed methods are very efficient.
KeywordsUncertainty theory Uncertain finance Uncertain volatility model European option pricing
The authors would like to thank the editor and two anonymous referees for helpful comments on an earlier version of this paper. The authors would like to thank Iran National Science Foundation (INSF) for supporting this research under project number 95843696.
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Conflict of interest
The authors declare that they have no conflict of interest.
- Chen X, Ralescu D (2013) Liu process and uncertain calculus. J Uncertain Anal Appl 1:3Google Scholar
- Dunn R, Hauser P, Seibold T, Gong H (2014) Estimating option prices with Heston’s stochastic volatility model. http://www.valpo.edu/ mathematics-statistics/files/2015/07/Estimating-Option-Prices-wi th-Heston%E2%80%99s-Stochastic-Volatility-Model.pdf
- Liu B (2008) Fuzzy process. Hybrid process and uncertain process. J Uncertain Syst 2(1):2–16Google Scholar
- Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10Google Scholar
- Liu B (2015) Uncertainty Theory, 5th edn. Uncertainty Theory Laboratory,Google Scholar
- Liu Y (2012) An analytic method for solving uncertian differential equation. J Uncrtain Syst 6(4):244–249Google Scholar
- Liu Y, Ha M (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186Google Scholar
- Sun Y, Su T (2016) Mean-reverting stock model with floating interest rate in uncertain environment. Fuzzy Optim Decis Mak. doi: 10.1007/s10700-016-9247-7
- Wang Z (2012) Analytic solution for a general type of uncertain differential equation. Int Inf Inst 15(12):153–159Google Scholar