no. 6
Pricing rainbow option for uncertain financial market
RAIRO. Operations Research, Tome 56 (2022) no. 6, pp. 3973-3989

Rainbow option refers to the option whose payoff depends on at least two underlying risky assets, which is justifiably one of the most significant tool to hedge risk brought by the uncertainty from financial market. Hence, option pricing problem is always an issue with great attention. In this paper, we assume that the multiple dynamic stock prices obey uncertain differential equations without sharing dividends in the framework of uncertainty theory. Then we discuss the rainbow option pricing problem for multiple stocks in a financial market with uncertain information, give the concepts and derive pricing formulas for five scenarios including maximum call, minimum call, maximum put, minimum put, and put on 2 and call on 1. Moreover, some corresponding examples are respectively taken to illustrate the pricing formulas in five cases.

Reçu le :
Accepté le :
Première publication :
Publié le :
DOI : 10.1051/ro/2022195
Classification : 91G80
Keywords: Rainbow option, uncertain process, stock model 
@article{RO_2022__56_6_3973_0,
     author = {Gao, Rong and Wu, Xiaoli},
     title = {Pricing rainbow option for uncertain financial market},
     journal = {RAIRO. Operations Research},
     pages = {3973--3989},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {56},
     number = {6},
     doi = {10.1051/ro/2022195},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2022195/}
}
TY  - JOUR
AU  - Gao, Rong
AU  - Wu, Xiaoli
TI  - Pricing rainbow option for uncertain financial market
JO  - RAIRO. Operations Research
PY  - 2022
SP  - 3973
EP  - 3989
VL  - 56
IS  - 6
PB  - EDP-Sciences
UR  - https://www.numdam.org/articles/10.1051/ro/2022195/
DO  - 10.1051/ro/2022195
LA  - en
ID  - RO_2022__56_6_3973_0
ER  - 
%0 Journal Article
%A Gao, Rong
%A Wu, Xiaoli
%T Pricing rainbow option for uncertain financial market
%J RAIRO. Operations Research
%D 2022
%P 3973-3989
%V 56
%N 6
%I EDP-Sciences
%U https://www.numdam.org/articles/10.1051/ro/2022195/
%R 10.1051/ro/2022195
%G en
%F RO_2022__56_6_3973_0
Gao, Rong; Wu, Xiaoli. Pricing rainbow option for uncertain financial market. RAIRO. Operations Research, Tome 56 (2022) no. 6, pp. 3973-3989. doi: 10.1051/ro/2022195

[1] X. W. Chen, American option pricing formula for uncertain financial market. Int. J. Oper. Res. 8 (2011) 32–37.

[2] X. W. Chen and J. Gao, Uncertain term structure model of interest rate. Soft Comput. 17 (2013) 597–604.

[3] Z. C. Gao, X. S. Wang and M. H. Ha, Multi-asset option pricing in an uncertain financial market with jump risk. J. Uncertain. Anal. Appl. 4 (2016).

[4] R. Gao, K. X. Liu, Z. G. Li and R. J. Lv, American barrier option pricing formulas for stock model in uncertain environment. IEEE Access 7 (2019) 97846–97856.

[5] R. Gao, W. Wu, C. Lang and L. Y. Lang, Geometric Asian barrier option pricing formulas of uncertain stock model. Chaos Solit. Fractals 140 (2020) 110178.

[6] R. Gao, W. Wu and J. Liu, Asian rainbow option pricing formulas of uncertain stock model. Soft Comput. 25 (2021) 8849–8873.

[7] R. Gao, K. X. Liu, Z. G. Li and L. Y. Lang, American barrier option pricing formulas for currency model in uncertain environment. J. Syst. Sci. Complex. 35 (2022) 283–312.

[8] D. Y. Jiao and K. Yao, An interest rate model in uncertain environment. Soft Comput. 19 (2015) 775–780.

[9] B. Liu, Uncertainty Theory, 2nd edition. Springer-Verlag, Berlin (2007).

[10] B. Liu, Fuzzy process, hybrid process and uncertain process. J. Uncertain Syst. 2 (2008) 3–16.

[11] B. Liu, Some research problems in uncertainty theory. J. Uncertain Syst. 3 (2009) 3–10.

[12] B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Springer-Verlag, Berlin (2010).

[13] B. Liu, Uncertainty distribution and independence of uncertain processes. Fuzzy Optim. Decis. Mak. 13 (2014) 259–271.

[14] Y. H. Liu, X. W. Chen and D. A. Ralescu, Uncertain currency model and currency option pricing. Int. J. Intell. Syst. 31 (2015) 40–51.

[15] Z. Lu, H. Yan and Y. Zhu, European option pricing model based on uncertain fractional differential equation. Fuzzy Optim. Decis. Mak. 18 (2019) 199–217.

[16] W. Margrabe, The value of an option to exchange one asset for another. J. Finance 23 (1978) 177–186.

[17] M. Rubinstein, Somewhere over the rainbow. Risk 4 (1991) 63–66.

[18] R. M. Stulz, Options on the maximum of two risky assets. J. Financ. Econ. 10 (1982) 161–185.

[19] J. J. Sun and X. W. Chen, Asian option pricing formula for uncertain financial market. J. Uncertain. Anal. Appl. 3 (2015) 11.

[20] M. Tian, X. Yang and Y. Zhang, Barrier option pricing of mean-reverting stock model in uncertain environment. Math. Comput. Simul. 166 (2019) 126–143.

[21] X. Wang and Y. F. Ning, An uncertain currency model with floating interest rates. Soft Comput. 21 (2017) 6739–6754.

[22] X. Yang, Z. Zhang and X. Gao, Asian-barrier option pricing formulas of uncertain financial market. Chaos Solit. Fractals 123 (2019) 79–86.

[23] Z. Q. Zhang, D. A. Ralescu and W. Q. Liu, Valuation of interest rate ceiling and floor in uncertain financial market. Fuzzy Optim. Decis. Mak. 15 (2016) 139–154.

Cité par Sources :