Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme

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• 作者：Ron Tat Lung Chan (1)
  Simon Hubbert (2)
  
• 关键词：European options ; American options ; Jump ; diffusion models ; Radial basis functions ; Cubic spline ; C6 ; G12 ; G13
• 刊名：Review of Derivatives Research
• 出版年：2014
• 出版时间：July 2014
• 年：2014
• 卷：17
• 期：2
• 页码：161-189
• 全文大小：
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• 作者单位：Ron Tat Lung Chan (1)
  Simon Hubbert (2)
  
  1. UEL Royal Docks Business School, University of East London, Docklands Campus 4-6 University Way, London?, E16 2RD, UK
  2. School of Economics, Mathematics and Statistics, Birkbeck, University of London, Malet Street, London, WC1E 7HX, UK
  
• ISSN：1573-7144

文摘

This paper will demonstrate how European and American option prices can be computed under the jump-diffusion model using the radial basis function (RBF) interpolation scheme. The RBF interpolation scheme is demonstrated by solving an option pricing formula, a one-dimensional partial integro-differential equation (PIDE). We select the cubic spline radial basis function and adopt a simple numerical algorithm (Briani et al. in Calcolo 44:33-7, 2007) to establish a finite computational range for the improper integral of the PIDE. This algorithm reduces the truncation error of approximating the improper integral. As a result, we are able to achieve a higher approximation accuracy of the integral with the application of any quadrature. Moreover, we a numerical technique termed cubic spline factorisation (Bos and Salkauskas in J Approx Theory 51:81-8, 1987) to solve the inversion of an ill-conditioned RBF interpolant, which is a well-known research problem in the RBF field. Finally, our numerical experiments show that in the European case, our RBF-interpolation solution is second-order accurate for spatial variables, while in the American case, it is second-order accurate for spatial variables and first-order accurate for time variables.