As an economic lever in financial market, interest rate option is not only the function of facilitating the bank to adjust the market fund supply and demand relation indirectly, but also provides the guarantee for investors to choose whether to exercise the right at the maturity date, thereby locking in the interest rate risk. This paper mainly studies the price of the interest rate ceiling as well as floor under the uncertain environment. Firstly, from the perspective of expert reliability, rather than relying on a large amount of historical financial data, to consider interest rate trends, and further assume that the dynamic change of the interest rate conforms to the uncertain process. Secondly, since uncertain fractional-order differential equations (UFDEs) have non-locality features to reflect memory and hereditary characteristics for the asset price changes, thus is more suitable to model the real financial market. We construct the mean-reverting interest rate model based on the UFDE in Caputo type. Then, the pricing formula of the interest rate ceiling and floor are provided separately. Finally, corresponding numerical examples and algorithms are given by using the predictor-corrector method, which support the validity of the proposed model.
MertonR.C., Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics3(1-2) (1976), 125–144.
2.
HoT.S.Y. and LeeS.B., Term structure movements and pricing interest rate contingent claims, Journal of Finance41(5) (1986), 1011–1029.
3.
HullJ.C. and WhiteA., Pricing interest-ratederivative securities, Review of Financial Studies3(4) (1990), 573–592.
4.
VasicekO.A., An equilibrium characterization of the term structure, Journal of Financial Economics5(2) (1977), 177–188.
5.
GuptaA. and SubrahmanyamM.G., Pricing and hedging interest rate options: Evidence from cap-floor markets, Journal of Banking and Finance29(3) (2005), 701–733.
6.
MollonaE. and MarcozziA., Firmnet: the scope of firms and the allocation of task in a knowledge-based economy, Computational and Mathematical Organization Theory15(2) (2009), 109–126.
7.
Suárez-TaboadaM. and VázquezC., Numerical solution of a pde model for a ratchet-cap pricing with bgm interest rate dynamics, Applied Mathematics and Computation218(9) (2012), 5217–5230.
8.
GaoS., ZhouM., WangY., ChengJ., YachiH. and WangJ., Dendritic neural model with effective learning algorithms for classification, approximation, and prediction, IEEE Transactions on Neural Networks and Learning Systems30(2) (2019), 601–604.
9.
GaoS., YuY., WangY., WangJ., ChengJ., ZhouM., Chaotic local search-based differential evolution algorithms for optimization, IEEE Transactions on Systems Man and Cybernetics: Systems (2019).
10.
DengW., XuJ., SongY. and ZhaoH., An effective improved co-evolution ant colony optimization algorithm with multi-strategies and its application, International Journal of Bio-Inspired Computation16(3) (2020), 158–70. DOI: 10.1504/IJBIC.2020.10033314
11.
DengW., XuJ., SongY., ZhaoH., Differential evolution algorithm with wavelet basis function and optimal mutation strategy for complex optimization problem, Applied Soft Computing (2020), 106724. DOI:10.1016/j.asoc.2020.106724
12.
LiuB., Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems2(1) (2008), 3–16.
13.
LiuB., Some research problems in uncertainy theory, Journal of Uncertain Systems3 (2009), 3–10. 01
14.
ChenX. and LiuB., Existence and uniqueness theorem for uncertain differential equations, Fuzzy Optimization and Decision Making9 (2010), 69–81. 03
15.
YaoK., GaoJ. and GaoY., Some stability theorems of uncertain differential equation, Fuzzy Optimization and Decision Making12(1) (2013), 3–13.
16.
YaoK. and ChenX., A numerical method for solving uncertain differential equations, Journal of Intelligent and Fuzzy Systems2501 (2013).
17.
CoxJ., IngersollJ. and RossS., A theory of the term structure of interest rates, Econometrica53 (1985), 385–407. 02
18.
TianM., YangX. and ZhangY., Barrier option pricing of mean-reverting stock model in uncertain environment, Mathematics and Computers in Simulation166 (2019), 126–143.
19.
YangX., ZhangZ. and GaoX., Asian-barrier option pricing formulas of uncertain financial market, Chaos, Solitons & Fractals123 (2019), 79–86.
20.
YaoK., LiuB., Parameter estimation in uncertain differential equations, Fuzzy Optimization and Decision Making (2020), 1–12.
21.
YangX., LiuY. and ParkG.K., Parameter estimation of uncertain differential equation with application to financial market, Chaos Solitons & Fractals139 (2020), 110026.
22.
LiuZ., Generalized moment estimation for uncertain differential equations, Applied Mathematics and Computation392 (2020), 125724.
23.
LiZ., ShengY., TengZ. and MiaoH., An uncertain differential equation for sis epidemic model, Journal of Intelligent & Fuzzy Systems33(4) (2017), 2317–2327.
24.
ZhangZ. and YangX., Uncertain population model, Soft Computing24(4) (2020), 2417–2423.
25.
ZhuY., Uncertain fractional differential equations and an interest rate model, Mathematical Methods in the Applied Sciences38(15) (2015), 3359–3368.
26.
ZhuY., Existence and uniqueness of the solution to uncertain fractional differential equation, Journal of Uncertainty Analysis and Applications3(1) (2015), 1–11.
27.
LuZ., YanH. and ZhuY., European option pricing model based on uncertain fractional differential equation, Fuzzy Optimization and Decision Making18(2) (2019), 199–217.
28.
LuZ. and ZhuY., Numerical approach for solution to an uncertain fractional differential equation, Applied Mathematics and Computation343 (2019), 137–148. 02
29.
JinT., SunY. and ZhuY., Extreme values for solution to uncertain fractional differential equation and application to american option pricing model, Physica A: Statistical Mechanics and its Applications534 (2019), 122357.
30.
JinT., SunY. and ZhuY., Time integral about solution of an uncertain fractional order differential equation and application to zero-coupon bond model, Applied Mathematics and Computation372 (2020), 124991.
31.
JinT. and ZhuY., First hitting time about solution for an uncertain fractional differential equation and application to an uncertain risk index model, Chaos Solitons & Fractals137 (2020), 109836.
32.
FordN.J. and SimpsonA.C., The numerical solution of fractional differential equations: speed versus accuracy, Numerical Algorithms26(4) (2001), 333–346.
33.
DiethelmK., FordN.J. and FreedA.D., A predictorcorrector approach for the numerical solution of fractional differential equations, Nonlinear Dynamics29(1-4) (2002), 3–22.
34.
ZhangZ., RalescuD., WeiqiL., Valuation of interest rate ceiling and floor in uncertain financial market, Fuzzy Optimization and Decision Making 07 (2015).
35.
ChenX. and GaoJ., Uncertain term structure model of interest rate, Soft Computing1704 (2013).
