Boundary Conditions For Mean-Reverting Square Root Process
نویسنده
چکیده
The Cox-Ingersoll-Ross (CIR) interest rate model is used to model interest rates and interest rate derivatives. We study the term structure equation for single-factor models that predict non-negative interest rates. It is shown using finite difference techniques that if the boundary is attainable, then this boundary behaviour serves as a boundary condition and guarantees a uniqueness of solutions. However, if the boundary is non-attainable, then the boundary condition is not needed to guarantee uniqueness. The finite difference solution is verified by use of non-negative numerical approximations.
منابع مشابه
Convergence of Monte Carlo Simulations involving the Mean-Reverting Square Root Process∗
The mean-reverting square root process is a stochastic differential equation (SDE) that has found considerable use as a model for volatility, interest rate, and other financial quantities. The equation has no general, explicit, solution, although its transition density can be characterized. For valuing path-dependent options under this model, it is typically quicker and simpler to simulate the ...
متن کاملA Study of Testing Mean Reversion in the Inflation Rate of Iran’s Provinces: New Evidence Using Quantile Unit Root Test
T his paper is to examine the mean reverting properties of inflation rates for Iran’s 25 provinces over the period from 1990:4 to 2017:7. To the end, we use various conventional univariate linear and non-linear unit root tests, as well as quantile unit root test by Koenker and Xiao (2004). Results of conventional unit root tests indicate that the null hypothesis of the unit root test...
متن کاملA Simple and Exact Simulation Approach to Heston Model
In this paper we will propose a simple approach to simulating Heston model efficiently and accurately. All existing simulation schemes so far directly work with the mean-reverting square root process of the variance in Heston model, instead we transform the variance to an equivalent volatility which follows a mean-reverting Ornstein-Uhlenbeck process. We will show it is more convenient to simul...
متن کاملAn Efficient Numerical Scheme for Simulation of Mean-reverting Square-root Diffusions
An efficient numerical scheme, which is based on the splitting-step idea [20], for simulation of mean-reverting square-root diffusions is presented in this paper. We prove positivity preservation for this scheme and an estimate of its local error in the second moment. A series of numerical experiments based on MATLAB programs is given to compare the suggested scheme with the schemes of the bala...
متن کاملEconomic Hysteresis Effects and Hitting Time Densities for CIR Diffusions
Using the so-called mean-reverting square-root process of Cox et al. (1985b) we generalize the work of Dias and Shackleton (2005) by introducing the mean reversion feature into the economic hysteresis analysis under stochastic interest rates and show that such issue highlights a tendency for a widening effect on the range of inaction, though both thresholds have risen when compared with the no ...
متن کامل