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Yazdani, Salamn, Hadizadeh Yazdi, Mahmoud, Fakoor, Vahid. (1401). An asymptotic computational method for the nonlinear weakly singular integral models in option pricing. فیزیولوژی و بیوتکنولوژی آبزیان, 11(1), 171-185. doi: 10.22124/jmm.2023.23444.2096
Salamn Yazdani; Mahmoud Hadizadeh Yazdi; Vahid Fakoor. "An asymptotic computational method for the nonlinear weakly singular integral models in option pricing". فیزیولوژی و بیوتکنولوژی آبزیان, 11, 1, 1401, 171-185. doi: 10.22124/jmm.2023.23444.2096
Yazdani, Salamn, Hadizadeh Yazdi, Mahmoud, Fakoor, Vahid. (1401). 'An asymptotic computational method for the nonlinear weakly singular integral models in option pricing', فیزیولوژی و بیوتکنولوژی آبزیان, 11(1), pp. 171-185. doi: 10.22124/jmm.2023.23444.2096
Yazdani, Salamn, Hadizadeh Yazdi, Mahmoud, Fakoor, Vahid. An asymptotic computational method for the nonlinear weakly singular integral models in option pricing. فیزیولوژی و بیوتکنولوژی آبزیان, 1401; 11(1): 171-185. doi: 10.22124/jmm.2023.23444.2096

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
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