TY - JOUR
T1 - Property and numerical simulation of the Ait-Sahalia-Rho model with nonlinear growth conditions
AU - Jiang, Feng
AU - Yang, Hua
AU - Tian, Tianhai
PY - 2017/1/1
Y1 - 2017/1/1
N2 - The Ait-Sahalia-Rho model is an important tool to study a number of financial problems, including the term structure of interest rate. However, since the functions of this model do not satisfy the linear growth condition, we cannot study the properties for the solution of this model by using the traditional techniques. In this paper we overcome the mathematical difficulties due to the nonlinear growth condition by using numerical simulation. Thus we first discuss analytical properties of the model and the convergence property of numerical solutions in probability for the Ait-Sahalia-Rho model. Finally, an example for option pricing is given to illustrate that the numerical solution is an effective method to estimate the expected payoffs.
AB - The Ait-Sahalia-Rho model is an important tool to study a number of financial problems, including the term structure of interest rate. However, since the functions of this model do not satisfy the linear growth condition, we cannot study the properties for the solution of this model by using the traditional techniques. In this paper we overcome the mathematical difficulties due to the nonlinear growth condition by using numerical simulation. Thus we first discuss analytical properties of the model and the convergence property of numerical solutions in probability for the Ait-Sahalia-Rho model. Finally, an example for option pricing is given to illustrate that the numerical solution is an effective method to estimate the expected payoffs.
KW - Ait-Sahalia-Rho model
KW - Boundedness
KW - Convergence in probability
UR - http://www.scopus.com/inward/record.url?scp=85008661154&partnerID=8YFLogxK
U2 - 10.3934/dcdsb.2017005
DO - 10.3934/dcdsb.2017005
M3 - Article
AN - SCOPUS:85008661154
VL - 22
SP - 101
EP - 113
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 1
ER -