甘小艇^1,2

1. 楚雄师范学院 数学与计算机科学学院, 楚雄 675000;
2. 电子科技大学 数学科学学院, 成都 611731

收稿日期:2019-08-16出版日期:2021-08-15发布日期:2021-08-20


基金资助:国家自然科学基金（61463002），云南省地方本科高校（部分）基础研究联合专项面上项目（2019FH001-079）和云南省教育厅科学基金项目（2019J0369）资助.

FITTED FINITE VOLUME METHOD FOR PRICING EUROPEAN OPTIONS UNDER REGIME-SWITHCHING MERTON'S JUMP-DIFFUSION PROCESSES

Gan Xiaoting^1,2

1. School of Mathematics and Computer Science, Chuxiong Normal University, Chuxiong 675000, China;
2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

Received:2019-08-16Online:2021-08-15Published:2021-08-20







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本文主要研究状态转换下欧式Merton跳扩散期权定价模型的拟合有限体积方法.针对该定价模型中的偏积分-微分方程，空间方向采用拟合有限体积方法离散，时间方向构造Crank-Nicolson格式.理论证明了数值格式的一致性、稳定性和单调性，因此收敛至原连续问题的解.数值实验验证了新方法的稳健性，有效性和收敛性.
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[1] Black F, Scholes M. The pricing of options and corporate liabilities[J]. Journal of Political Economy, 1973, 81(3):637-657 [2] 张凯. 美式期权定价————基于罚方法的金融计算[M]. 北京:经济科学出版社, 2012. [3] Gao Y, Song H M,Wang X S and Zhang K. Primal-dual active set method for pricing American better-of option on two assets[J]. Communications in Nonlinear Science and Numerical Simulation, 2020, 80:104976. [4] Yang H. A numerical analysis of American options with regime switching[J]. Journal of Scientific Computing, 2010, 44(1):69-91. [5] Florescu I, Liu R, Mariani M C and Sewell G. Numerical schemes for option pricing in regimeswitching jump diffusion models[J]. International Journal of Theoretical and Applied Finance, 2013, 16(8):1-25. [6] Bastani A F, Ahmadi Z, Damircheli D. A radial basis collocation method for prcing American options under regime-switching jump-diffusion models[J]. Applied Numerical Mathematics, 2013, 65(2):79-90. [7] Lee Y. Financial options pricing with regime-switching jump-diffusions[J]. Computers and Mathematics with Applications, 2014, 68(3):392-404. [8] Rambeerich N, Pantelous A A. A high order finite element scheme for pricing options under regime switching jump diffusion processes[J]. Journal of Computational and Applied Mathematics, 2016, 300:83-96. [9] Heidari S, Azari H. A front-fixing finite element method for pricing American options under regime-switching jump-diffusion models[J]. Computers and Mathematics with Applications, 2018, 37(3):3691-3707. [10] Kazmi K Khaliq A Q M, Alrabeei S. Solving complex PIDE systems for pricing American option under multi-state regime switching jump-diffusion model[J]. Computers and Mathematics with Applications, 2018, 75(8):2989-3001. [11] Kazmi K. An IMEX predictor-corrector method for pricing options under regime-switching jumpdiffusion models[J]. International Journal of Computer Mathematics, 2019, 96(6):1137-1157. [12] Zhang K, Teo K L, Swartz M. A robust numerical scheme for pricing American options under regime switching based on penalty method[J]. Computational Economics, 2014, 43(4):463-483. [13] Zhang K, Yang X Q. Power penalty approach to American options pricing under regime switching[J]. Journal of Optimization Theory and Applications, 2018, 179(1):311-331. [14] Wang S. A novel fitted finite volume method for the Black-Scholes equation governing option pricing[J]. IMA Journal of Numerical Analysis, 2004, 24(4):699-720. [15] Zhang K, Wang S. Pricing options under jump diffusion processes with fitted finite volume method[J]. Applied Mathematics and Computation, 2008, 201(1):398-431. [16] Zhang K, Teo K L. A penalty-based method from reconstructing smooth local volatility surfacf from American options[J]. Journal of Industrial and Management Optimization, 2015, 11(2):631-644. [17] Chernogorova T, Valkov R. Analysis of a finite volume element method for a degenerate parabolic equation in the zero-coupon bond pricing[J]. Computers and Mathematics with Applications, 2015, 34(2):619-646. [18] Zhang K, Yang X Q. Pricing European options on zero-coupon bonds with a fitted finite volume method[J]. International Journal of Numerical Analysis and Modeling, 2017, 14(3):405-418. [19] Zhang S H, Wang X Y and Li H. Modeling and computation of water management by real options[J]. Journal of Industrial and Management Optimization, 2018, 14(1):81-103. [20] Salmi S, Toivanen J. An iterative method for pricing American options under jump-diffusion model[J]. Applied Numerical Mathematics, 2011, 61(7):821-831. [21] Gan X T, Yin J F, Guo Y X. Finite volume method for pricing European and American options under jump-diffusion models[J]. East Asian Journal on Applied Mathematics, 2017, 7(2):227-247.

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