×

Generalized finite integration method with Volterra operator for pricing multi-asset barrier option. (English) Zbl 1537.91357

MSC:

91G60 Numerical methods (including Monte Carlo methods)
65R20 Numerical methods for integral equations
91G20 Derivative securities (option pricing, hedging, etc.)
Full Text: DOI

References:

[1] Hull, J. C., Options, futures, and other derivatives, 1-9 (2012), Pearson Education, Inc.
[2] Guardasoni, C.; Rodrigo, M. R.; Sanfelici, S., A Mellin transform approach to barrier option pricing, IMA J Manag Math, 31, 1, 49-67 (2020) · Zbl 07254127
[3] Elliott, R. J.; Siu, T. K.; Chan, L. L., On pricing barrier options with regime switching, J Comput Appl Math, 256, 196-210 (2014) · Zbl 1350.91016
[4] Tangman, D. Y.; Gopaul, A.; Bhuruth, M., Exponential time integration and Chebychev discretisation schemes for fast pricing of options, Appl Numer Math, 58, 9, 1309-1319 (2008) · Zbl 1151.91546
[5] Feng, L.; Linetsky, V., Pricing options in jump-diffusion models: An extrapolation approach, Oper Res, 56, 2, 304-325 (2008) · Zbl 1167.91367
[6] Park, S. H.; Kim, J. H., Asymptotic option pricing under the CEV diffusion, J Math Anal Appl, 375, 2, 490-501 (2011) · Zbl 1202.91324
[7] Tian, M.; Yang, X. F.; Zhang, Y., Barrier option pricing of mean-reverting stock model in uncertain environment, Math Comput Simulation, 166, 126-143 (2019) · Zbl 1540.91076
[8] De Staelen, R. H.; Hendy, A. S., Numerically pricing double barrier options in a time-fractional Black-Scholes model, Comput Math Appl, 74, 6, 1166-1175 (2017) · Zbl 1415.91315
[9] Chan, L. L.; Zhu, S. P., An explicit analytic formula for pricing barrier options with regime switching, Math Financial Econ, 9, 1, 29-37 (2015) · Zbl 1308.91158
[10] Jeon, J.; Choi, S. Y.; Yoon, J. H., Analytic valuation of European continuous-installment barrier options, J Comput Appl Math, 363, 392-412 (2020) · Zbl 1422.91704
[11] Ballestra, L. V.; Pacelli, G., A boundary element method to price time-dependent double barrier options, Appl Math Comput, 218, 8, 4192-4210 (2011) · Zbl 1239.91158
[12] Guardasoni, C.; Sanfelici, S., A boundary element approach to barrier option pricing in Black-Scholes framework, Int J Comput Math, 93, 4, 696-722 (2016) · Zbl 1338.65226
[13] Rosalino, E.; da Silva, A. J.; Baczynski, J.; Leão, D., Pricing and hedging barrier options, Appl Stoch Models Bus Ind, 34, 4, 499-512 (2018) · Zbl 1396.91806
[14] Goto, Y.; Fei, Z.; Kan, S.; Kita, E., Options valuation by using radial basis function approximation, Eng Anal Bound Elem, 31, 10, 836-843 (2007) · Zbl 1195.91047
[15] Kim, Y. S.; Bae, H. O.; Koo, H. K., Option pricing and Greeks via a moving least square meshfree method, Quant Finance, 14, 10, 1753-1764 (2014) · Zbl 1402.91793
[16] Rad, J. A.; Höök, J.; Larsson, E.; von Sydow, L., Forward deterministic pricing of options using Gaussian radial basis functions, J Comput Sci, 24, 209-217 (2018)
[17] Rashidinia, J.; Jamalzadeh, S., Collocation method based on modified cubic B-spline for option pricing models, Math Commun, 22, 1, 89-102 (2017) · Zbl 1467.91214
[18] Abdi-Mazraeh, S.; Khani, A., An efficient computational algorithm for pricing European, barrier and American options, Comput Appl Math, 37, 4, 4856-4876 (2018) · Zbl 1404.65287
[19] Cuomo, S.; Sica, F.; Toraldo, G., Greeks computation in the option pricing problem by means of RBF-PU methods, J Comput Appl Math, 376, Article 112882 pp. (2020) · Zbl 1437.91453
[20] Wen, P. H.; Hon, Y. C.; Li, M.; Korakianitis, T., Finite integration method for partial differential equations, Appl Math Model, 37, 24, 10092-10106 (2013) · Zbl 1427.65308
[21] Black, F.; Scholes, M., The pricing of options and corporate liabilities, J Political Econ, 81, 3, 637-654 (1973) · Zbl 1092.91524
[22] Li, M.; Hon, Y. C.; Korakianitis, T.; Wen, P. H., Finite integration method for nonlocal elastic bar under static and dynamic loads, Eng Anal Bound Elem, 37, 5, 842-849 (2013) · Zbl 1287.74051
[23] Li, M.; Tian, Z. L.; Hon, Y. C.; Chen, C. S.; Wen, P. H., Improved finite integration method for partial differential equations, Eng Anal Bound Elem, 64, 230-236 (2016) · Zbl 1403.65264
[24] Li, M.; Chen, C. S.; Hon, Y. C.; Wen, P. H., Finite integration method for solving multi-dimensional partial differential equations, Appl Math Model, 39, 17, 4979-4994 (2015) · Zbl 1443.65391
[25] Yun, D. F.; Wen, Z. H.; Hon, Y. C., Adaptive least squares finite integration method for higher-dimensional singular perturbation problems with multiple boundary layers, Appl Math Comput, 271, 232-250 (2015) · Zbl 1410.65273
[26] Li, Y.; Li, M.; Hon, Y. C., Improved finite integration method for multi-dimensional nonlinear burgers’ equation with shock wave, Neural Parallel Sci Comput, 23, 63-86 (2015)
[27] Li, Y.; Hon, Y. C., Finite integration method with radial basis function for solving stiff problems, Eng Anal Bound Elem, 82, 32-42 (2017) · Zbl 1402.65051
[28] Sam, C. N.; Hon, Y. C., Generalized finite integration method for solving multi-dimensional partial differential equations, Eng Anal Bound Elem, 99, 248-259 (2019) · Zbl 1464.65280
[29] Lei, M.; Sam, C. N.; Hon, Y. C., Generalized finite integration method with Volterra operator for multi-dimensional biharmonic equations, Eng Anal Bound Elem, 111, 22-31 (2020) · Zbl 1464.65236
[30] Liskovets, O., The method of straight lines, J Differ Uravneniya, 1, 1662-1678 (1965)
[31] Kadalbajoo, M. K.; Kumar, A.; Tripathi, L. P., Radial-basis-function-based finite difference operator splitting method for pricing American options, Int J Comput Math, 95, 11, 2343-2359 (2018) · Zbl 1499.65400
[32] Aimi, A.; Guardasoni, C., Multi-asset barrier options pricing by collocation BEM, MDPI J Axioms, 10, 301, 1-19 (2021)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.