摘要
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。
並列摘要
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.
參考文獻
[1] Cairns, A. J. G. Interest Rate Models: An Introduction, Princeton and Oxford 2004
[2] B. Oksendal, Stochastic Di erential Equations: An Introduction with Applications, Springer
[3] Black, F.,Scholes, M., The Pricing of Options and Corporate Liabilities, in: Journal of Political
[4] Heath,D., Jarrow R., Morton, A., (1992) Bond pricing and the Term structure of Interest Rates:
[5] Ho, T., Lee, S., Term Structure Movements and Pricing Interest Rate Contingent Claims, in:
延伸閱讀
- Lin, G. F. (2004). 隨機波動之利率模型設計 [master's thesis, Yuan Ze University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0009-0112200611362533
- 楊智惠（2012）。隨機利率對信用違約交換定價與避險的影響〔碩士論文，國立暨南國際大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0020-0202201213410600
- 陳柏任（2006）。隨機利率下之投資組合最佳化〔碩士論文，國立中央大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0031-0207200917340507
- 張哲維（2014）。動態隨機存取儲存器價格影響因素之研究〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2014.00257
- 蘇硯農（2017）。Does Preferred Stocks Almost Stochastic Dominate Common Stocks?〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU201704332