An Ingenious, Piecewise Linear Interpolation Algorithm for Pricing Arithmetic Average Options

Abstract. 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 ap...

• Type: Conference
• Year: 2007
• Where: AAIM
• Authors: Tian-Shyr Dai, Jr-Yan Wang, Hui-Shan Wei
• Keywords: AAIM 2007, Algorithms, Arithmetic Average, Arithmetic Average Options, Numerical Algorithms