本文利用Carr and Wu (2004)的隨時間改變Lévy 模型並放寬隨機利率假設下進行衍生性金融商品的評價，我們採取HJM(1992)的方法得到歐式一般選擇權及期貨選擇權之理論解。不僅如此，本文也得到此新模型的美式選擇權之上界理論解。此上界不但非常近似封閉解且十分利於提升美式選擇權評價及避險的效率。本文發展的新模型放寬了過往選擇權文獻所有的限制，並加入文獻中所提出資產報酬應具有：高峰、厚尾、利率與波動度為隨機波動等特徵。

This study examines the contingent claim valuation of risky assets in a stochastic interest rate economy using the time-changed Lévy processes model developed by Carr and Wu (2004). The proposed model adopts the approach of Heath, Jarrow and Morton’s (1992) to obtain an analytical solution of European options on risky assets and futures contracts. Furthermore, this investigation develops upper bounds for American options prices using the proposed model. The upper bounds derived in this study are not only very tight and accurate for American option pricing, but can also enhance assessment and hedging efficiency in real world markets. The asset returns obtained by the proposed model are more closely match actual market phenomena presented in the option literature because the leptokurtic and asymmetric features, interest rates and volatility are stochastic over time.