کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4642609 1341349 2007 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On smoothing of the Crank–Nicolson scheme and higher order schemes for pricing barrier options
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
On smoothing of the Crank–Nicolson scheme and higher order schemes for pricing barrier options
چکیده انگلیسی

Most option pricing problems have nonsmooth payoffs or discontinuous derivatives at the exercise price. Discrete barrier options have not only nonsmooth payoffs but also time dependent discontinuities. In pricing barrier options, certain aspects are triggered if the asset price becomes too high or too low. Standard smoothing schemes used to solve problems with nonsmooth payoff do not work well for discrete barrier options because of discontinuities introduced in the time domain when each barrier is applied. Moreover, these unwanted oscillations become worse when estimating the hedging parameters, e.g., Delta and Gamma. We have an improved smoothing strategy for the Crank–Nicolson method which is unique in achieving optimal order convergence for barrier option problems. Numerical experiments are discussed for one asset and two asset problems. Time evolution graphs are obtained for one asset problems to show how option prices change with respect to time. This smoothing strategy is then extended to higher order methods using diagonal (m,m)(m,m)—Padé main schemes under a smoothing strategy of using as damping schemes the (0,2m-1)(0,2m-1) subdiagonal Padé schemes.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 204, Issue 1, 1 July 2007, Pages 144–158
نویسندگان
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