A numerical method for pricing spread options on LIBOR rates with a PDE model

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• 作者：M. Suá ; rez-Taboada ; C. Vá ; zquez
• 关键词：Spread options ; LIBOR Market Model ; Black&#x2013 ; Scholes PDE ; Crank&#x2013 ; Nicholson-characteristics ; Finite elements ; Monte Carlo simulation
• 刊名：Mathematical and Computer Modelling
• 出版年：2010
• 出版时间：October 2010
• 年：2010
• 卷：52
• 期：7-8
• 页码：1074-1080
• 全文大小：475 K

文摘

In this paper we present a new numerical method for solving a Black–Scholes type of model for pricing a class of interest rate derivatives: spread options on LIBOR rates. The interest rates are assumed to follow the recently introduced LIBOR Market Model. The Feynman–Kac theorem provides a PDE model for the spread option pricing problem which is initially posed in an unbounded domain. After a localization procedure and the consideration of appropriate boundary conditions in a bounded domain, we propose a Crank–Nicholson characteristic time discretization scheme combined with a Lagrange piecewise quadratic finite element for the spatial discretization. In order to illustrate the performance of the PDE model and the numerical methods, we present a real example of spread option pricing.