A FAST AND EXACT SIMULATION FOR CIR PROCESS By ANQI SHAO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA
of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A FAST AND EXACT SIMULATION FOR CIR PROCESS By Anqi Shao May 2012 Chair: Liqing Yan Major: Mathematics We present a fast and exact simulation method for the CIR process. Traditional simulation method relies on an algorithm to generate a non central chi square random variable, which is quite slow when the degrees of freedom is less than 1, and the non centrality parameter is large. Thus it's only applicable when people are just interested in simulating the process along a few time points, for example, European options prices. But for some exotic options which depends on the process on a lot of time points, for example Asian option prices, this method is very slow and inefficient. In this paper we analyze the algorithm to see its limitation, and propose a new algorithm which is much faster. This method enables fast and exact simulation of the CIR process on a large number of time grids. Numerical results on option pricing based on Heston model is rather encouraging, compared with other simulation schemes.