کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5776705 | 1632158 | 2017 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Numerical pricing of American options under two stochastic factor models with jumps using a meshless local Petrov-Galerkin method
ترجمه فارسی عنوان
قیمت گذاری عددی گزینه های آمریکایی تحت دو مدل فاکتور تصادفی با جهش با استفاده از روش محلی پتروف-گالکرین
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات محاسباتی
چکیده انگلیسی
The most recent update of financial option models is American options under stochastic volatility models with jumps in returns (SVJ) and stochastic volatility models with jumps in returns and volatility (SVCJ). To evaluate these options, mesh-based methods are applied in a number of papers but it is well-known that these methods depend strongly on the mesh properties which is the major disadvantage of them. Therefore, we propose the use of the meshless methods to solve the aforementioned options models, especially in this work we select and analyze one scheme of them, named local radial point interpolation (LRPI) based on Wendland's compactly supported radial basis functions (WCS-RBFs) with C6 , C4 and C2 smoothness degrees. The LRPI method which is a special type of meshless local Petrov-Galerkin method (MLPG), offers several advantages over the mesh-based methods, nevertheless it has never been applied to option pricing, at least to the very best of our knowledge. These schemes are the truly meshless methods, because, a traditional non-overlapping continuous mesh is not required, neither for the construction of the shape functions, nor for the integration of the local sub-domains. In this work, the American option which is a free boundary problem, is reduced to a problem with fixed boundary using a Richardson extrapolation technique. Then the implicit-explicit (IMEX) time stepping scheme is employed for the time derivative. Numerical experiments are presented showing that the proposed approaches are extremely accurate and fast.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 115, May 2017, Pages 252-274
Journal: Applied Numerical Mathematics - Volume 115, May 2017, Pages 252-274
نویسندگان
Jamal Amani Rad, Kourosh Parand,