A Numerical method for solving the problem of Pricing American Options under the CIR stochastic interest rate model

Subject Areas : Financial engineering

Abodolsadeh  neisy ¹ (Department of Mathematics, Faculty of mathematics Science and Computer, Allameh Tabataba’i University, Dr. Beheshti and Bokharest Ave., Tehran, Iran)
maryam  safaei ² (Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran)
Nader  Nematollahi ³ (Department of Statistics, Faculty of Mathematics Science and Computer, Allameh Tabataba’I University, Dr. Beheshti and Bokharest Ave., Tehran, Iran)

Received: 2017-12-06 Accepted : 2018-01-27 Published : 2018-06-22

Keywords: Componentwise splitting method, American option pricing, CIR stochastic interest rate model, Linear complementarity problem,

Abstract :

The main purpose of this study is to derive the price of American put option, when the interest rate follows a stochastic process. For this purpose, first underlying asset model is expanded to CIR stochastic interest rate model. Then, the problem of American option pricing under CIR stochastic interest rate model is formulated as a two-dimensional linear complementarity problem (LCP). We propose a two-cycle componentwise splitting method for solving this two-dimensional LCP. In this method, the two-dimensional LCP, obtained for the valuation of an American option, is decomposed into six one-dimensional LCPs in several fractional time steps, and then each LCP is solved numerically in two steps. So that in the first step, the tridiagonal systems of equations are solved, and then in the second step (update step), the obtained values of option prices are modified and updated according to the conditions of the American option pricing problem. Finally, the numerical results obtained by splitting introduced method are compared with the Monte Carlo simulation results