Numerical Analysis On The Vasicek Interest Rate Model by Semi-infinit Programming

Abstract

在過去，利率的變化一直被視為一個隨機過程。在本論文中，我們假設利率的隨機變化行為可由一組隨時間變化之定性參數來決定的。這個概念被套用在短期與遠期利率模型上，並分別採用單點和階梯型函數的參數來進行分析。針對利率模型，運用semi-infinite programming方法，來求出模型中的參數值，使模型和真實利率變動的差為最小。計算所得到的模型，除利率曲線外並包含變動的上下界，如此一來，可涵蓋真實利率變動行為。

Although interest rate is a stochastic process, in this thesis we model the random behavior as a perturbation w(t) In every time interval t in [t_{i-1},t_i]. We formulate short-rate model as a deterministic perturbation model which is a solution of a semi-infinite Programming problem. The solution can get upper bound and lower bound value. these curve can bound the yield curve.