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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.