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Article
Solution of Two-factor Models with Variable Interest Rates
Journal of Computational and Applied Mathematics
  • Lijing Lu, The University of Akron
  • C. B. Clemons, The University of Akron
  • G. W. Young, The University of Akron
  • Jianping Zhu, Cleveland State University
Document Type
Article
Publication Date
12-1-2008
Disciplines
Abstract

The focus of this work is on numerical solutions to two-factor option pricing partial differential equations with variable interest rates. Two interest rate models, the Vasicek model and the Cox–Ingersoll–Ross model (CIR), are considered. Emphasis is placed on the definition and implementation of boundary conditions for different portfolio models, and on appropriate truncation of the computational domain. An exact solution to the Vasicek model and an exact solution for the price of bonds convertible to stock at expiration under a stochastic interest rate are derived. The exact solutions are used to evaluate the accuracy of the numerical simulation schemes. For the numerical simulations the pricing solution is analyzed as the market completeness decreases from the ideal complete level to one with higher volatility of the interest rate and a slower mean-reverting environment. Simulations indicate that the CIR model yields more reasonable results than the Vasicek model in a less complete market.

DOI
10.1016/j.cam.2007.10.014
Citation Information
Li, J., Clemons, C., Young, G., , & Zhu, J. (2008). Solution of Two-factor Models with Variable Interest Rates. Journal of Computational and Applied Mathematics, 222(1), 30-41. doi:10.1016/j.cam.2007.10.014