Browsing by Author "Wei, Hui-Shan"

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Adaptive placement method on pricing arithmetic average options
(2008-03-01)
Dai, Tian-Shyr
;
Wang, Jr-Yan
;
Wei, Hui-Shan
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Since there is no analytic solution for arithmetic average options until present, developing an efficient numerical algorithm becomes a promising alternative. One of the most famous numerical algorithms is introduced by Hull and White (J Deriv 1:21-31, 1993). Motivated by the common idea of reducing the nonlinearity error in the adaptive mesh model in Figlewski and Gao (J Financ Econ 53:313-351, 1999) and the adaptive quadrature method, we propose an adaptive placement method to replace the logarithmically equally-spaced placement rule in the Hull and White's model by placing more representative average prices in the highly nonlinear area of the option value as the function of the arithmetic average stock price. The basic idea of this method is to design a recursive algorithm to limit the error of the linear interpolation between each pair of adjacent representative average prices. Numerical experiments verify the superior performance of this method for reducing the interpolation error and hence improving the convergence rate. To show that the adaptive placement method can improve any numerical algorithm with the techniques of augmented state variables and the piece-wise linear interpolation approximation, we also demonstrate how to integrate the adaptive placement method into the GARCH option pricing algorithm in Ritchken and Trevor (J Finance 54:377-402, 1999). Similarly great improvement of the convergence rate suggests the potential applications of this novel method to a broad class of numerical pricing algorithms for exotic options and complex underlying processes.
An ingenious, piecewise linear interpolation algorithm for pricing arithmetic average options
(2007)
Dai, Tian-Shyr
;
Wang, Jr-Yan
;
Wei, Hui-Shan
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Pricing arithmetic average options continues to intrigue researchers in the field of financial engineering. Since there is no analytical solution for this problem until present, developing an efficient numerical algorithm becomes a promising alternative. One of the most famous numerical algorithms for pricing arithmetic average options is introduced by Hull and White [10]. In this paper, motivated by the common idea of reducing the nonlinearity error in the adaptive mesh model [7] and the adaptive quadrature numerical integration method [6], the logarithmically equally-spaced placement rule in the Hull and White's model is replaced by an adaptive placement method, in which the number of representative average prices is proportional to the degree of curvature of the option value as a function of the arithmetic average price. Numerical experiments verify the superior performance of our method in terms of reducing the interpolation error. In fact, it is straightforward to apply this method to any pricing algorithm with the techniques of augmented state variables and the piece-wise linear interpolation approximation.