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Lookback option pricing problem of uncertain exponential Ornstein–Uhlenbeck model

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Abstract

A lookback option is an exotic option that allows investors to “look back” at the underlying prices occurring over the life of the option, and exercises the right at asset’s optimal point. This paper mainly investigates the lookback call and put option pricing formulas based on the uncertain exponential Ornstein–Uhlenbeck model and designs the algorithms to calculate those prices numerically. Several numerical examples are given to illustrate the effectiveness of the proposed model.

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References

  • Chen X (2011) American option pricing formula for uncertain financial market. Int J Op Res 8(2):27–32

    MathSciNet  Google Scholar 

  • Chen X, Liu YH, Ralescu DA (2013) Uncertain stock model with periodic dividends. Fuzzy Optim Decis Mak 12(1):111–123

  • Conze A, Viswanathan (1991) Path dependent options: the case of lookback options. J Financ 46(5):1893–1907

  • Dai LR, Fu ZF, Huang ZY (2017) Option pricing formulas for uncertain financial market based on the exponential Ornstein–Uhlenbeck model. J Intell Manuf 28(3):597–604

    Article  Google Scholar 

  • Goldman MB, Sosin HB, Gatto MA (1979) Path dependent options: “Buy at the low, sell at the high”. J Financ 34(5):1111–1127

    Google Scholar 

  • Ji XY, Zhou J (2015) Option pricing for an uncertain stock model with jumps. Soft Comput 19(11):3323–3329

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Liu B (2008) Fuzzy process, hybrid process and uncertain process. J Uncertain Syst 2(1):3–16

    Google Scholar 

  • Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10

    Google Scholar 

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

    Google Scholar 

  • Liu B (2013) Toward uncertain finance theory. J Uncertain Anal Appl 1:1

    Article  Google Scholar 

  • Peng J, Yao K (2011) A new option pricing model for stocks in uncertainty markets. Int J Op Res 8(2):18–26

    MathSciNet  Google Scholar 

  • Stef-Praun T, Rego V, Houstis E (2006) Option stream—an automated system for tracking derivative effects on equity prices. Expert Syst Appl 30(2):168–178

    Article  Google Scholar 

  • Sun YY, Yao K, Fu ZF (2016) Interest rate model in uncertain environment based on exponential Ornstein–Uhlenbeck equation. Soft Comput. doi:10.1007/s00500-016-2337-1

  • Yang X, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertain Anal Appl 1:17

    Article  Google Scholar 

  • Yang X, Gao J (2016) Linear–quadratic uncertain differential games with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819–826

    Article  Google Scholar 

  • Yang X, Yao K (2016) Uncertain partial differential equation with application to heat conduction. Fuzzy Optim Decis Mak. doi:10.1007/s10700-016-9253-9

  • Yao K (2012) No-arbitrage determinant theorems on mean-reverting stock model in uncertain market. Knowl Based Syst 35:259–263

    Article  Google Scholar 

  • Yao K (2013) Extreme values and integral of solution of uncertain differential equation. J Uncertain Anal Appl 1:2

    Article  Google Scholar 

  • Yao K (2015a) Uncertain contour process and its application in stock model with floating interest rate. Fuzzy Optim Decis Mak 14(4):399–424

  • Yao K (2015b) A no-arbitrage theorem for uncertain stock model. Fuzzy Optim Decis Mak 14(2):227–242

  • Yao K (2016) Uncertain differential equations. Springer, New York

    Book  MATH  Google Scholar 

  • Yao K, Chen X (2013) A numerical method for solving uncertain differential equations. J Intell Fuzzy Syst 25(3):825–832

  • Zhang ZQ, Liu WQ (2014) Geometric average asian option pricing for uncertain financial market. J Uncertain Syst 8(4):317–320

    Google Scholar 

  • Zhang ZQ, Liu WQ, Sheng YH (2016) Valuation of power option for uncertain financial market. Appl Math Comput 286:257–264

    MathSciNet  Google Scholar 

  • Zhu Y (2010) Uncertain optimal control with application to a portfolio selection model. Cybern Syst 41(7):535–547

    Article  MATH  Google Scholar 

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Acknowledgements

The author gratefully acknowledges the financial support provided by National Natural Science Foundation of China (Grant No. 61374082).

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Authors and Affiliations

  1. School of Information, Renmin University of China, Beijing, 100872, China

    Yin Gao & Zongfei Fu

  2. School of Information Technology & Management, University of International Business & Economics, Beijing, 100029, China

    Xiangfeng Yang

Authors
  1. Yin Gao
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  2. Xiangfeng Yang
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  3. Zongfei Fu
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Correspondence to Xiangfeng Yang.

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The authors declare that they have no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by Y. Ni.

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Gao, Y., Yang, X. & Fu, Z. Lookback option pricing problem of uncertain exponential Ornstein–Uhlenbeck model. Soft Comput 22, 5647–5654 (2018). https://doi.org/10.1007/s00500-017-2558-y

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  • DOI: https://doi.org/10.1007/s00500-017-2558-y

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