A direct LU solver for pricing American bond options under Hull-White model

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• 作者：A. Falcó ; ^a ; ^{afalco@uchceu.es" class="auth_mail" title="E-mail the corresponding author} ; Ll. Navarro^b ; ^{lluis.navarro@ua.es" class="auth_mail" title="E-mail the corresponding author} ; C. Vá ; zquez^c ; ^{carlosv@udc.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：American bond options ; Interest rate models ; Crank&ndash ; Nicolson method ; Linear complementarity problem ; LU decomposition
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：442-455
• 全文大小：772 K

文摘

The main goal of this paper is to propose a novel numerical algorithm to price American options on bonds. For this purpose, we illustrate the performance of this method by means of the valuation of an American Put Option on a discount bond under the extended Vasicek model due to Hull and White (HW) and using the consistent forward rate curves. In particular, an implicit Crank–Nicolson (CN) scheme in time is applied obtaining a discretized linear complementarity problem (LCP) and then we introduce a direct LU based method to solve the LCP. Finally, we carry out numerical experiments to examine the convergence of this method and to testify the efficiency and effectiveness of this numerical scheme against other standard approaches.