کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4639631 1341242 2012 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Tri-diagonal preconditioner for pricing options
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Tri-diagonal preconditioner for pricing options
چکیده انگلیسی

The value of a contingent claim under a jump-diffusion process satisfies a partial integro-differential equation (PIDE). We localize and discretize this PIDE in space by the central difference formula and in time by the second order backward differentiation formula. The resulting system Tnx=b in general is a nonsymmetric Toeplitz system. We then solve this system by the normalized preconditioned conjugate gradient method. A tri-diagonal preconditioner LnLn is considered. We prove that under certain conditions all the eigenvalues of the normalized preconditioned matrix (Ln−1Tn)∗(Ln−1Tn) are clustered around one, which implies a superlinear convergence rate. Numerical results exemplify our theoretical analysis.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 236, Issue 17, November 2012, Pages 4365–4374
نویسندگان
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