利用機率密度函數逼近法對Heath-Jarrow-Morton 模型下的利率衍生性商品定價

Using Density Approximation Method to Price the Interest Rate Relative Derivative on General Heath-Jarrow-Morton Model

洪瑋駿(Wei-Chun Hung)

指導教授 ： 李賢源

國立臺灣大學/管理學院/財務金融學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.00533

摘要

本文提供了一個遠期利率模型改善了Trolle and Schwartz (2009) 的模型，此模型可以解釋短期利率對於遠期利率的波動度的影響並且可保有利率恆正的性質。除此之外此模型可以藉由Duffie, Pan and Singleton (2000)提出的方法找出債券選擇權的解析解。本文藉由Filipovic, Mayerhofer and Schneider (2011)的方法找出了債券價格的機率密度函數提供了債券價格的另外一種計算方式。藉由對短期利率的隨機過程的分析，本文提供了逼近方法改善了Duffie, Pan and Singleton (2000)求出的公式過於複雜的問題。

關鍵字

Heath–Jarrow–Morton模型 ； 隨機波動度 ； unspanned volatility ； 債券選擇權評價 ； 機率密度函數

並列摘要

The new term structure model is provided in this paper. This model extends the model provided by Trolle and Schwartz (2009) so that the new model can explain the influence of spot rate on forward rate diffusion term. The advantages of this model are that it ensures the positive value on spot rate and volatility. Follow Duffie, Pan and Singleton (2000) framework, I provide an analytic solution on bond option pricing. Another contribution of this paper is that I use Filipovic, Mayerhofer and Schneider (2011) method to find the density of bond price and thus provide an alternative way to solve the bond option. In addition, by analyzing the spot rate dynamic, I provide a two entirely different approximation method to simplify the spot rate dynamic. And thus it makes the option pricing easier not only on Duffie, Pan and Singleton (2000) method but also Filipovic, Mayerhofer and Schneider (2011) method.

並列關鍵字

Heath–Jarrow–Morton model ； stochastic volatility ； unspanned volatility ； bond option pricing ； density approximation

參考文獻

Andersen, T. G., and Lund, J.（1997）,“Estimating Continuous-Time Stochastic Volatility Models of the Short-Term Interest Rate,”Journal of Econometrics 77, 343-77.

Ball, C. A., and Torous, W. N.（1999）,“The Stochastic Volatility of Short-Term Interest Rates: Some International Evidence”Journal of Finance 54, 2339-59.

Bhar, R., and Chiarella, C.（1997）,“Transformation of Heath-Jarrow-Morton Models to Markovian Systems,”European Journal of Finance 3, 1-26.

Bhar, R., Chiarella, C., El-Hassan, N., and Zheng, X.（1999）,“Reduction of Forward Rate Dependent HJM Models to Markovian Form: Pricing European Bond Options,”Working Paper, School of Finance and Economics, University of Technology Sydney.

Brennan, M., and Schwartz, E.（1979）,“A Continuous Time Approach to the Pricing of Interest Rates,”Journal of Banking and Finance 3, 133-155.