标题: 利率下限评价模型之数值分析
Numerical Analysis for Interest Rate Floor Valuation
作者: 李兰兰
Lan-Lan Lee
王克陆
Dr. Kelu Wang
财务金融研究所
关键字: 利率衍生性;利率下限;二元利率树;三元利率树;蒙地卡罗;Interest rate derivatives;Floor;Binomial tree;Trinomial tree;Monte carlo
公开日期: 2003
摘要: 任何金融商品推出后的成败,决定于其需求与价格,而其价格之订定是否合理,更是关键之所在。因此,相关利率商品价格订定所需考虑的因素有哪些?其订价方式又有哪些?如何正确地评价选择权?为本论文所探讨的课题。本论文研究主体为利率选择权之利率下限,评价利率下限时,必须先建构利率模型,将利率的随机过程加以描述,并根据该随机过程,利用数值方法以求出利率下限的价格。但是,在多数利率衍生性商品或是利率模型往往并不易求得公式解。虽然从理论上可以得知,透过模拟次数的增加及切割期数,则模拟的价格期望值必然会收敛到理论价格。但切割模拟的次数到达多少才能将误差降低到可接受的范围内,故如何判断求出的数值解是否合理、正确,才是主要问题。本文作法是先透过, Vasicek 模型与Hull和White之extended Vasicek模型,在特殊假设下求出利率下限之公式解。接下来再透过数值方法来评价Vasicek 模型、CIR模型与Hull-White模型,进而观察切割的误差随着割切次数增加时的变化情形,以供参考。又由于Hull and White所提出的三元利率树,可以建构出与市场完全一致的利率期间结构,且收敛速度极快。因此,本文将透过结合Hull and White三元利率树与蒙地卡罗模拟的方式来评价路径相依之利率下限,使其模拟出的利率随机过程能与市场一致,并比较其差异性。
The purpose of this study is to numerically analyze the floor of the interest rate option. We first obtain the closed-form solutions by special assumptions of Vasicek model and Hull-White extended Vasicek model. Then the numerical techniques provide a simple and intuitive method for valuing floor of Vasicek model, CIR model and Hull-White model. An exact value for the floor is obtained in the limit as ∆t tends to zero. The trinomial tree proposed by Hull and White can provide consistent initial term structure and converge faster to the continuous time limit. Therefore, Hull-White trinomial tree can be extended to deal with path-dependent options which can recover the initial term structure of interest rates. Finally, this paper showed their different results.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT009139502
http://hdl.handle.net/11536/60202
显示于类别:Thesis


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