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Uncertain strike lookback options pricing with floating interest rate

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Abstract

Considering the floating interest rate and the uncertainty of the strike price, we derive the pricing formulas of lookback options including lookback call option and lookback put option. Furthermore, we give the numerical algorithms to illustrate our results and analyze the relationships between the price of lookback options and all the parameters.

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References

  • Chen, X. (2011). American option pricing formula for uncertain financial market. International Journal of Operations Research, 8(2), 32–37.

    Google Scholar 

  • Dai, L., Fu, Z., & Huang, Z. (2017). Option pricing formulas for uncertain financial market based on the exponential Ornstein–Uhlenbeck model. Journal of Intelligent Manufacturing, 28(3), 597–604.

    Article  Google Scholar 

  • Gao, J. (2013). Uncertain bimatrix game with applications. Fuzzy Optimization and Decision Making, 12(1), 65–78.

    Article  Google Scholar 

  • Gao, R., Liu, K., Li, Z., et al. (2019). American barrier option pricing formulas for stock model in uncertain environment. IEEE Access, 7, 97846–97856.

    Article  Google Scholar 

  • Gao, Y., Yang, X., & Fu, Z. (2018). Lookback option pricing problem of uncertain exponential Ornstein–Uhlenbeck model. Soft Computing, 22(17), 5647–5654.

    Article  Google Scholar 

  • Jiao, D., & Yao, K. (2015). An interest rate model in uncertain environment. Soft Computing, 19(3), 775–780.

    Article  Google Scholar 

  • Kahneman, D., & Tversky, A. (1979). Prospect theory: Analysis of decision under risk. Econometrica, 47(2), 263–291.

    Article  Google Scholar 

  • Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.

    Google Scholar 

  • Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain systems, 2(1), 3–16.

    Google Scholar 

  • Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain systems, 3(1), 3–10.

    Google Scholar 

  • Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.

    Book  Google Scholar 

  • Liu, B. (2013a). A new definition of independence of uncertain sets. Fuzzy Optimization and Decision Making, 12(4), 451–461.

    Article  Google Scholar 

  • Liu, B. (2013b). Toward uncertain finance theory. Journal of Uncertainty, Analysis and Applications., 1(1), 1.

    Article  Google Scholar 

  • Liu, B. (2014). Uncertain random graph and uncertain random network. Journal of Uncertain systems, 8(1), 3–12.

    Google Scholar 

  • Liu, B. (2015). Uncertainty theory. Berlin: Springer.

    Google Scholar 

  • Peng, J., & Yao, K. (2011). A new option pricing model for stocks in uncertainty markets. International Journal of Operations Research, 8(2), 18–26.

    Google Scholar 

  • Sun, J., & Chen, X. (2015). Asian option pricing formula for uncertain financial market. Journal of Uncertainty Analysis and Applications, 3(1), 11.

    Article  Google Scholar 

  • Sun, Y., Yao, K., & Fu, Z. (2018). Interest rate model in uncertain environment based on exponential Ornstein–Uhlenbeck equation. Soft Computing, 22(2), 465–475.

    Article  Google Scholar 

  • Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323.

    Article  Google Scholar 

  • Yao, K. (2013). Extreme values and integral of solution of uncertain differential equation. Journal of Uncertainty Analysis and Applications, 1(1), 1–21.

    Article  Google Scholar 

  • Yao, K., & Chen, X. (2013). A numerical method for solving uncertain differential equations. Journal of Intelligent and Fuzzy Systems, 25(3), 825–832.

    Article  Google Scholar 

  • Yu, X. (2012). A stock model with jumps for uncertain markets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 20(3), 421–432.

    Article  Google Scholar 

  • Zhang, L., & Sun, Y. (2020). Power options pricing in uncertain environment. Acta Scientiarum Naturalium Universitatis Nankaiensis, 53(2), 1–6.

    Google Scholar 

  • Zhang, L., Sun, Y., & Meng, X. (2020). European spread option pricing with the floating interest rate for uncertain financial market. Mathematical Problems in Engineering, 2020, 1–8.

    Google Scholar 

  • Zhang, Z., & Liu, W. (2014). Geometric average asian option pricing for uncertain financial market. Journal of Uncertain Systems, 8(4), 317–320.

    Google Scholar 

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Acknowledgements

The authors would like to thank the anonymous referee and the editor for their helpful comments and valuable suggestions that led to several important improvements.

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Correspondence to Lidong Zhang.

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This research was supported in part by The Youth Project of Humanities and Social Sciences of Ministry of Education (Grant No. 19YJCZH251) and in part by The Scientific Research Program of Tianjin Education Commission (Grant No. 2018KJ113).

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Zhang, L., Sun, Y., Du, Z. et al. Uncertain strike lookback options pricing with floating interest rate. Rev Deriv Res 24, 79–94 (2021). https://doi.org/10.1007/s11147-020-09170-4

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  • DOI: https://doi.org/10.1007/s11147-020-09170-4

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