Pricing American options under multi-states: a radial basis collocation approach

被引：0

作者：

Heidari S. ^{[1
]}

Azari H. ^{[1
]}

机构：

[1] Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, General Campus, Evin, Tehran

来源：

SeMA Journal | 2018年 / 75卷 / 2期

关键词：

American option; Free boundary problem; Radial basis functions; Regime-switching model;

D O I：

10.1007/s40324-017-0137-x

中图分类号：

学科分类号：

摘要：

In this paper, a mesh-free method based on Radial Basis Functions (RBFs) interpolation is proposed to evaluate American options written on stocks under a regime-switching model. Under this model, we need to solve coupled partial differential equations with free boundaries feature. In this respect, we apply the radial basis functions as spatial collocation scheme and Backward Euler scheme for the time derivative. We expand the solution vector in terms of Cubic functions as the radial basis functions and collocate system of equations at some collocation points. We applied the LU decomposition to solve the resulting system. Then numerical approximations of the free boundaries can be computed using the Newton’s iterative method. Numerical results are presented to indicate the accuracy of the RBFs interpolation for various combinations of parameters comparing with some recent proposed approaches. © 2017, Sociedad Española de Matemática Aplicada.

引用

页码：365 / 378

页数：13

共 19 条

[1]

Black F., Scholes M., The pricing of options and corporate liabilities, J. Polit. Econ., 81, pp. 637-654, (1973)

[2]

Bollen N.P.B., Valuing options in regime-switching models, J. Derivativ., 6, pp. 38-49, (1988)

[3]

Boyle P., A lattice framework for option pricing with two state variables, J. Financ. Quant. Anal., 23, pp. 1-12, (1988)

[4]

Boyle P., Draviam T., Pricing exotic options under regime switching, Insur. Math. Econ., 40, 2, pp. 267-282, (2007)

[5]

Buffington J., Elliott R.J., American options with regime switching, Int. J. Theor. Appl. Finance, 5, pp. 497-514, (2002)

[6]

Cont R., Tankov P., (2004)

[7]

Ekstrom E., Convexity of the optimal stopping boundary for the american put option, J. Math. Anal. Appl., 299, 1, pp. 147-156, (2004)

[8]

Hamilton J., A new approach to the economic analysis of nonstationary time series and the business cycle, Econ. J. Econ. Socc., 57, pp. 357-384, (1989)

[9]

Holmes A.D., Yang H., Zhang S., A front-fixing finite element method for the valuation of American options with regime switching, Int. J. Comput. Math., 89, 9, pp. 1094-1111, (2012)

[10]

Huang Y., Forsyth P.A., Labahn G., Methods for pricing American options under regime switching, SIAM J. Sci. Comput., 33, 5, pp. 2144-2168, (2011)

← 1 2 →