臺灣博碩士論文加值系統

衍生性金融商品的蓬勃發展促進利率模型推陳出新。繼HJM（1992）模型，打破傳統以即期利率作為出發點的型態，然而HJM模型的瞬間遠期利率不存在於市場，且瞬間遠期利率為常態分配的假設也不合常理，遂有市場模型應運而生。
本文使用市場模型評價歐洲美元期貨選擇權。修正Uratani 和Utsunomiya（1999），並應用Park（2001）於HJM模型下評價歐洲美元期貨選擇權的二元樹狀圖法，了解市場模型二元樹狀圖之構建，評價歐洲美元期貨選擇權。
實證結果發現，雖然兩個參數的指數波動度比一個參數的常數波動度配適績效差，產生的平均價格誤差較高，與其他實證文獻不符，但可確定的是相較於常數波動度，指數波動度的隱含波動度參數估計值穩定性較低。此外，深度價內選擇權的偏誤現象較其他價位的選擇權大，深度價外則不明顯。
造成實證結果與其他實證結果相異的原因之一為，採集樣本時未刪除嚴重深度價內及嚴重深度價外的選擇權，該類選擇權因流動性低、交易量小，若一併納入樣本中可能會發生評價誤差。本研究的樣本高達80.5274％為深度價內或深度價外選擇權，樣本分佈極不平均。此外，指數波動度函數之參數值可能僅是局部解，而非全域解。

Abstract
The popularity of the interest rate derivatives promotes the interest rate model. Although HJM(1992) came up with the new methodology, the instantaneously forward rates of the Normal distribution seemed abnormal and didn’t exist in the real market. The Market model tackled the problem. In contrast to HJM model, the Market model has two appealing features as follows: (1) the forward rates can be observed directly. (2) The forward rates follow the Lognormal distribution.
Based on some adjustment of Uratani and Utsunomiya(1999) and Park(2002), this research used the Binomial tree of the Market model to price Eurodollar futures option. The empirical results found the exponential volatility function has larger fitting errors than the constant volatility function. This didn’t match with other empirical results. However, we can make sure that the parameters of the exponential volatility function are more unstable than those of the constant volatility function. In addition, the pricing errors of the deep-in-the-money option are the most severe.
One of reasons resulted in discordances with other empirical results is this research didn’t get rid of deep-in-the-money and deep-out-of-the-money options. The trading activities of these options are very inactive. Besides, the parameter values of the exponential volatility function may be possible local solutions, not global solutions.

目 錄
第一章 緒論----------------------------------------------1
1.1研究動機-----------------------------------------1
1.2研究目的-----------------------------------------1
1.3研究架構-----------------------------------------2
第二章 文獻回顧------------------------------------------3
2.1利率期間結構-------------------------------------3
2.2利率模型-----------------------------------------4
2.2.1均衡模型-----------------------------------------4
2.2.2無套利模型---------------------------------------6
2.3數值解之樹狀法評價------------------------------13
2.3.1定態波動度之HJM、市場模型-----------------------13
第三章 研究方法-----------------------------------------16
3.1契約介紹----------------------------------------16
3.1.1歐洲美元期貨------------------------------------16
3.1.2歐洲美元期貨選擇權------------------------------17
3.2樹狀法於市場模型歐洲美元期貨選擇權之運用--------18
3.2.1波動度函數的設定--------------------------------20
3.2.2遠期LIBOR利率樹---------------------------------21
3.2.3歐洲美元期貨價格樹------------------------------26
3.2.4歐洲美元期貨選擇權價格樹------------------------27
第四章 實證結果與分析-----------------------------------31
4.1資料說明及處理----------------------------------31
4.2參數估計結果------------------------------------35
4.3樣本內價格誤差結果------------------------------37
第五章 結論與建議---------------------------------------46
5.1 結論-------------------------------------------46
5.2 後續研究建議-----------------------------------46
附錄-----------------------------------------------------48
參考文獻-------------------------------------------------56
圖 目 錄
圖3-1 樹狀圖於市場模型之實證流程圖----------------------19
圖3-2 常數波動度的遠期LIBOR利率重合二項樹---------------22
圖3-3 指數波動度的遠期LIBOR利率非重合二項樹-------------23
圖3-4 市場模型之遠期LIBOR利率樹-------------------------26
圖3-5 三月到期的歐洲美元期貨選擇權價格樹----------------27
圖3-6 計算三月到期的歐洲美元期貨選擇權價格時，所需使用的六月到期歐洲美元債券價格-----------------------------------29
圖4-1 2002年1月1日至1月31日止的倫敦銀行拆款利率---------33
圖4-2 不同交易日下波動度函數參數估計值------------------36
圖4-3 不同交易日的波動度函數值--------------------------37
圖4-4 不同交易日下最適期初遠期利率曲線------------------37
圖4-5 不同交易日之平均價格誤差（買權）------------------40
圖4-6 不同交易日之平均價格誤差（賣權）------------------42
表 目 錄
表3-1 本研究市場模型搭配波動度之歸納表-------------------23
表4-1 歐洲美元期貨與歐洲美元期貨選擇權樣本摘要-----------34
表4-2 樣本期間內之最適波動度參數估計值-------------------36
表4-3 不同波動度函數下價位與平均價格誤差的關係-----------39
表4-4 不同波動度函數於樣本期間內的價格預測誤差-----------45

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