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An asymptotic computational method for the nonlinear weakly singular integral models in option pricing | ||
| Journal of Mathematical Modeling | ||
| دوره 11، شماره 1، خرداد 2023، صفحه 171-185 اصل مقاله (224.45 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2023.23444.2096 | ||
| نویسندگان | ||
| Salamn Yazdani1؛ Mahmoud Hadizadeh Yazdi* 1؛ Vahid Fakoor2 | ||
| 1Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran | ||
| 2Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Iran | ||
| چکیده | ||
| The integral representation of the optimal exercise boundary problem for generating the continuous-time early exercise boundary for the American put option is a well-known topic in the mathematical finance community. The main focus of this paper is to provide an efficient asymptotically computational method to improve the accuracy of American put options and their optimal exercise boundary. Initially, we reformulate the nonlinear singular integral model of the early exercise premium problem given in [Kim et al., A simple iterative method for the valuation of American options, Quant. Finance. 13 (2013) 885--895] to an equivalent form which is more tractable from a numerical point of view. We then obtain the existence and uniqueness results with verifiable conditions on the functions and parameters in the resulting operator equation. The asymptotic behavior for the early exercise boundary is also analyzed which is mostly compatible with some realistic financial models. | ||
| کلیدواژهها | ||
| Non-standard Volterra integral equation؛ weakly singular kernel؛ numerical treatments؛ asymptotic representation؛ option pricing | ||
| مراجع | ||
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[1] F. Aitsahlia, T. Lai, Exercise boundaries and efficient approximations to American option prices and hedge parameters, J. Comput. Finance. 4 (2001) 85–104. [2] K. Atkinson, W. Han, Theoretical Numerical Analysis: A Functional Analysis Approach, Springer, 2005. [3] M. Broadie, J. Detemple, American option valuation: new bounds, approximations and a comparison of existing methods, Rev. Financ. Stud. 9 (1996) 1211–1250 [4] H. Brunner, Volterra Integral Equations: An Introduction to Theory and Applications, Cambridge University Press, 2017. [5] H. Brunner, Collocation Methods for Volterra Integral and Related Functional Differential Equations, Cam- bridge University Press, 2004. [6] P. Carr, Randomization and the American put, Rev. Financ. Stud. 11 (1998) 597–626. [7] P. De Angelis, R. De Marchis, A.L. Martire, S. Patri, Non-standard Volterra integral equations: a mean-value theorem numerical approach, App. Math. Sci. 14 (2020) 423–432. [8] M. Horng, T. Horng, C. Tien, A method-of-lines approach for solving American option problems, Taiwanese J. Math. 23 (2019) 1253–1270. [9] C. Hou, T. Little, V. Pant, A new integral representation of the early exercise boundary for American put options, J. Comput. Finance. 3 (2000) 73–96. [10] J. Z. Huang, M. Subrahmanyam, G. Yu, Pricing and hedging American options: a recursive integration method, Rev. Financ. Stud. 9 (1996) 277–300. [11] N. Ju, Pricing by American option by approximating its early exercise boundary as a multipiece exponential function, Rev. Financ. Stud. 11 (1998) 627–646. [12] S. Kallast, A. Kivinukk, Pricing and hedging American options using approximations by Kim integral equa- tions, Rev. Financ. Stud. 7 (2003) 361–383 [13] I.J. Kim, B.G. Jang, K.T. Kim, A simple iterative method for the valuation of American options, Quant. Finance. 13 (2013) 885–895. [14] I.J. Kim, The analytic valuation of American options, Rev. Financ. Stud. 3 (1990) 547–572. [15] T. Kulik, C. Tisdell, Volterra integral equations on time scales: basic qualitative and quantitative results with applications to initial value problems on unbounded domains, Int. J. Difference Equ. 3 (2008) 103–133. [16] Y.K. Kwok, Mathematical Models of Financial Derivatives, Springer, 2008. [17] M. Lauko, D. Sevcovic, Comparison of numerical and analytical approximations of the early exercise bound- ary of American put options, ANZIAM J. 51 (2010) 430–448. [18] S. Lin, X. He, A new integral equation approach for pricing American-style barrier options with rebates, J. Comput. Appl. Math. 383 (2021) 113107. [19] J. Ma, K. Xiang, Y. Jiang, An integral equation method with high-order collocation implementations for pricing American put options, Int. J. Econ. Finance 2 (2010) 102–112. [20] K. Nedaiasl, A.F. Bastani, S. Rafiee, A product integration method for the approximation of the early exercise boundary in the American option pricing problem, Math. Methods Applied Sci. 42 (2019) 2825–2841. [21] D.B. Pachpate, On a nonstandard Volterra type dynamic integral equation on time scales, Electron. J. Qual. Theory Differ. Equ. 72 (2009) 1–14. [22] R. Stamicar, D. Sevcovic, J. Chadam, The early exercise boundary for the American put near expiry: numer- ical approximation, Can. Appl. Math Q. 7 (1999) 427-444. [23] S. P. Zhu, A new analytical approximation formula for the optimal exercise boundary of American put options, Int. J. Theor. Appl. Finance 9 (2006) 1141–1177. [24] S. Zhu, X. He, X. Lu, A new integral equation formulation for American put options, Quant. Finance. 18 (2018) 483–490. | ||
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