TY - GEN

T1 - An ingenious, piecewise linear interpolation algorithm for pricing arithmetic average options

AU - Dai, Tian-Shyr

AU - Wang, Jr Yan

AU - Wei, Hui Shan

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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.

AB - 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.

KW - Adaptive placement

KW - Arithmetic average options

KW - Logarithmically equally-spaced placement

UR - http://www.scopus.com/inward/record.url?scp=38149088733&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-72870-2_25

DO - 10.1007/978-3-540-72870-2_25

M3 - Conference contribution

AN - SCOPUS:38149088733

SN - 9783540728689

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 262

EP - 272

BT - Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings

Y2 - 6 June 2007 through 8 June 2007

ER -