The Stability Analysis of Predictor–Corrector Method in Solving American Option Pricing Model

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• 作者：R. Kalantari ; S. Shahmorad ; D. Ahmadian
• 关键词：Penalty method ; American option pricing ; Finite difference method ; Rational approximation ; Method of lines ; Predictor–Corrector method
• 刊名：Computational Economics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：47
• 期：2
• 页码：255-274
• 全文大小：539 KB
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• 作者单位：R. Kalantari (1)
  S. Shahmorad (1)
  D. Ahmadian (1)
  
  1. Faculty of Mathematical sciences, University of Tabriz, Tabriz, Iran
  
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Economic Theory
  
• 出版者：Springer Netherlands
• ISSN：1572-9974

文摘

In this paper, a new technique is investigated to speed up the order of accuracy for American put option pricing under the Black–Scholes (BS) model. First, we introduce the mathematical modeling of American put option, which leads to a free boundary problem. Then the free boundary is removed by adding a small and continuous penalty term to the BS model that cause American put option problem to be solvable on a fixed domain. In continuation we construct the method of lines (MOL) in space and reach a non-linear problem and we show that the proposed MOL is more stable than the other kinds. To deal with the non-linear problem, an algorithm is used based on the predictor–corrector method which corresponds to two parameters, \(\theta \) and \(\phi \). These parameters are chosen optimally using a rational approximation to determine the order of time convergence. Finally in numerical results a second order convergence is shown in both space and time variables. Keywords Penalty method American option pricing Finite difference method Rational approximation Method of lines Predictor–Corrector method