利率衍生性商品之定價

Pricing of Interest Rate Derivatives

吳冠勳(Wu, Guan-shiun)

指導教授 ： 吳庭斌

國立臺北大學/商學院/統計學系/碩士(2009年)

摘要

自民國八十二年政府開放利率交換業務以來，國內利率市場發展漸趨成熟，金融機構及民間企業對於資產與負債之利率風險控管日益重視，對於利率避險的需求也愈來愈大。然而為了滿足避險者及投機客等各類投資者的交易需要，發展出各式各樣的利率衍生性商品，諸如利率交換(Interest Rate Swap)、利率遠期契約(Interest Rate Forward)、利率下限(Floor)、利率上限(Caps)...等。利率價差選擇權同為利率衍生性商品中的一種；其在國外非常盛行，然而卻沒有一個固定評價公式，主要原因在於，利率模型的多樣性，以及一般價差選擇權無法直接求出封閉解，且針對殖利率價差選擇權與LIBOR利率價差選擇權評價之文獻少之又少，因此本文在HJM利率模型下，利用 Borovkova,Permana and Weide (2007) 提出的動差配適法，求出殖利率價差選擇權與LIBOR利率價差選擇權之近似評價公式，以供大家參考。

關鍵字

利率價差選擇權 ； 利率衍生性商品 ； HJM利率模型

並列摘要

HJM model is a very general interest rate model, it only required inputs are the initial yield curve and volatility structure for pure discount bond. This paper discussed the problem of pricing a spread option on the difference of two interest rates under Heath, Jarrow and Morton (hereafter HJM) model. We know that there is no closed form of spread option. This paper will introduce a method which proposed by Borovkova,Permana and Weide (2007). By this method, we will price the yield rate spread options and the LIBOR rate spread option. Finally, we can compare with Monte Carlo simulation and confirm on accuracy of this method .

並列關鍵字

Spread of Interest Rate Option ； Interest Rate Derivative ； Heath-Jarrow-Morton model

參考文獻

1. Heath, D., R. Jarrow and A. Morton, Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation, Econometrica 60,1992, pp. 77-105.

3. Pearson, N. D., ”An Efficient Approach for Pricing Spread Options.” Journalof Derivatives, Fall 1995, pp.76-91.

4. Qiang Fu, ”On the valuation of an option to exchange one interest rate for another.” Journal of Banking & Finance 20,1996, pp. 645-653.

6. Chang. C.C and S.L. Chung , ”Pricing Asian Style Interest Rate Swaps.”The Journal of Derivatives, 2002, pp. 45-55.

7. S. Borovkova, F. Permana and H. v.d.Weide ”A closed form approach tothe valuation and hedging of basket and spread options.” The Journal of Derivates, Vol.14, No. 4 ,2007, pp. 8-24.