本篇論文主要使用無母數核回歸的統計方法來估計連續時間利率隨機過程。過去雖已有文獻提出此方法估計，但也僅止于估計單一國家的利率隨機過程。本文嘗試同時估計兩相關國家利率隨機過程，實際驗證美國和日本1979年至2002年歐洲境外美元和日圓利率日資料。若飄移項和擴散項會受到兩國家短期利率影響，除了有些結果如飄移項具有均數複歸等性質和 Stanton (1997) 所做出結論相同外，仍發現Stanton (1997) 所估計美國利率隨機過程的結果，近似於本模型固定日本短期利率爲零時所估計的特殊變因。最後使用估計出來的兩國瞬間短期利率，並應用於跨通貨利率上(下)限型衍生性商品的定價。

This article present a technique for nonparametrically estimating continuous-time interest rate stochastic process that are observed at discrete intervals. Although this technique had been brought up, that article just present to estimate interest rate stochastic process of one country. This article attempts to estimate two country’s interest rate stochastic process with each other. We illustrate the methodology by using daily eurodollars and euroyen data, from January 1979 to December 2002. Stanton (1997) finds that American short rate has mean reversion property, but he does not consider about foreign short rate. If foreign short rate can effect drift and diffusion of domestic short rate, we find some other conclusions different form Stanton (1997). When we consider foreign short rate in our model, Stanton’s (1997) conclusion is just only our model that given Japan short rate is zero. Eventually, we use our model to apply to value cross-currency interest rate cap and floor.

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