標題: 利率下限評價模型之數值分析
Numerical Analysis for Interest Rate Floor Valuation
作者: 李蘭蘭
Lan-Lan Lee
王克陸
Dr. Kelu Wang
財務金融研究所
關鍵字: 利率衍生性;利率下限;二元利率樹;三元利率樹;蒙地卡羅;Interest rate derivatives;Floor;Binomial tree;Trinomial tree;Monte carlo
公開日期: 2003
摘要: 任何金融商品推出後的成敗,決定於其需求與價格,而其價格之訂定是否合理,更是關鍵之所在。因此,相關利率商品價格訂定所需考慮的因素有哪些?其訂價方式又有哪些?如何正確地評價選擇權?為本論文所探討的課題。本論文研究主體為利率選擇權之利率下限,評價利率下限時,必須先建構利率模型,將利率的隨機過程加以描述,並根據該隨機過程,利用數值方法以求出利率下限的價格。但是,在多數利率衍生性商品或是利率模型往往並不易求得公式解。雖然從理論上可以得知,透過模擬次數的增加及切割期數,則模擬的價格期望值必然會收斂到理論價格。但切割模擬的次數到達多少才能將誤差降低到可接受的範圍內,故如何判斷求出的數值解是否合理、正確,才是主要問題。本文作法是先透過, Vasicek 模型與Hull和White之extended Vasicek模型,在特殊假設下求出利率下限之公式解。接下來再透過數值方法來評價Vasicek 模型、CIR模型與Hull-White模型,進而觀察切割的誤差隨著割切次數增加時的變化情形,以供參考。又由於Hull and White所提出的三元利率樹,可以建構出與市場完全一致的利率期間結構,且收斂速度極快。因此,本文將透過結合Hull and White三元利率樹與蒙地卡羅模擬的方式來評價路徑相依之利率下限,使其模擬出的利率隨機過程能與市場一致,並比較其差異性。
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
Appears in Collections:Thesis


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