کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4641876 1341322 2008 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Methods for the rapid solution of the pricing PIDEs in exponential and Merton models
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Methods for the rapid solution of the pricing PIDEs in exponential and Merton models
چکیده انگلیسی

The pricing equations for options on assets that follow jump-diffusion processes contain integrals in addition to the usual differential terms. These integrals usually make such equations expensive to solve numerically. Although Fast Fourier Transform methods can be used to to evaluate the integrals at all mesh points simultaneously, they are costly since the computational region must be extended in order to avoid problems with wrap around. Other numerical difficulties arise when the density function for the jump size is not smooth, as in the Kou double exponential model. We present new solution methods which are based on the fact that even when the problems contain time-dependent parameters the integrals often satisfy easily solved ordinary or parabolic partial differential equations. In particular, we show that by using the operator splitting method proposed by Andersen and Andreasen it is possible to reduce the solution of the pricing equation in the Kou and similar models to a sequence of ordinary differential equations at each time step. We discuss the methods and present results of numerical experiments.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 222, Issue 1, 1 December 2008, Pages 128–143
نویسندگان
,