隨機利率模型下的隨機價格

Abstract

在本篇研究中，我們將利用Wilhelm的方法去找出一般的隨機利率模型並且證明這個方法是等價於Ho-Lee模型,Hull-White模型以及Heath-Jarrow-Morton模型。然而我們發現當Wilhelm利用隨機折現的方法將隨機利率與股價合併時出現錯誤，因此在本篇研究中，我們將利用另一個方法來找出Wilhelm出錯的地方。最後，我們也證明出Ho-Lee模型和Black-Scholes可以同時存在。

In this article, we use Wilhelm’s method to give general stochastic interest rate model and show that this model is equivalent to Ho-Lee model, Hull-White model and Heath-Jarrow-Morton model. However we discover that Wilhelm’s was wrong when he incorporated stochastic interest rate with stock price by using stochastic discount. We use another approach to prove that what’s wrong which Wilhelm makes. Finally, we show that Ho-Lee model and Black-Scholes model can coexist.