利率衍生性商品之評價與風險管理--以Hull-White模型為例

The Valuation and Risk Management of Interest Rate Derivatives-- Take Hull-White Model for Example

楊承勳(Cheng-Shiun Yang)

指導教授 ： 許耀文

共同指導教授 ： 李賢源(Shyan-Yuan Lee)

國立臺灣大學/管理學院/國際企業學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.01950

摘要

論文摘要：
本文嘗試由眾多的利率模型當中，整理其模型優缺點，諸如：評價、避險，參數校正是否容易、可符合市場殖利率曲線選擇一個合適的評價模型、又可延伸至複雜的新奇式商品評價方法，故挑選Hull-White模型，需忍受其單因子之缺點，如：無法模擬鴕峰之殖利率曲線，但單因子模型最大的好處即參數估計容易、計算非封閉解的情況與大幅縮短計算時間，故不需像蒙地卡羅法需耗時模擬，也不像微分方程法可直接解出封閉解。

本文重心環繞在Hull-White三元利率樹模型參數之校正，先以市場波動率報價代入Black（1976）計算商品真實市價，再分別運用解析解與利率樹的方式使市場價格與模型價格誤差最小。最後再運用Hull-White模型管理投資組合之利率風險，將投資組合買入與賣出部位轉換為同一比較標準之波動率，使得買入與賣出利率商品之投資組合相互避險，非個別商品之避險，節省了極大的避險成本。

關鍵字

參數校正 ； Hull-White 模型 ； 利率風險管理 ； 利率衍生性商品

並列摘要

Abstract:
The thesis tries to edit the advantages and disadvantages of the interest rate models. The reasons why I choose the Hull-White Model are easy to compute the parameters, to save computing time, and to calculate accurate prices of exotic derivatives. It does not spend much time like Monte Carlo Simulation and can not get the close form solution directly like Partial Differential Equation.

The thesis focuses on the calibration of Hull-White model parameters. We can get the real market prices from quoted volatilities in the market. We can also get the model prices from analytical form solution or interest rate trinomial tree model. Then, to narrow the difference between the market price and model price as possible can let the model fit the real situation. After learning the skills to calibrate the parameters, I can use Hull-White model to manage interest rate risk. It can transform the long and short positions to the same hedging bases. So we can hedge the whole portfolio not individual derivative to save huge hedging cost.

並列關鍵字

Interest Rate Management ； Interest Rate Derivatives ； Calibration ； Hull-White Model

參考文獻

3. Black, F., 1976, “The Pricing of Commodity Contracts”, Journal of Financial Economics, Vol. 3, Jan-Mar, pp.167-179

4. Black, F., and M. Scholes, 1973. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, pp.637-654

5. Black, F., E. Derman, and W. Toy, 1990, “A One-factor Model of Interest Rates and Its Application to Treasury Bond Options.” Financial Analysts Journal, vol. 46, pp.33-39

6. Black, F., and P. Karasinski. 1991. ”Bond and Option Pricing When Short Rate Are Lognormal.” Financial Analysts Journal, vol. 47, no.4 (July/ August), pp.52-59

7. Cox, J. C., J.E. Ingersoll, and S. Ross,1981. ”The Relation Between Forward Prices and Futures Prices”, Journal of Financial Economics 9, pp.321-346