| Summary: | 碩士 === 國立臺灣大學 === 財務金融學系研究所 === 86 === Hull and White (1993b) 三元利率樹可用於評價大多數的利率衍生性商品。然而，Hull
and White三元利率樹並不適用於路徑相依之利率選擇權的評價。蒙地卡羅模擬雖可用於
路徑相依之股票選擇權評價，但無法直接用於利率選擇權的評價，原因是蒙地卡羅模擬無
法產生與市場利率期間結構一致的路徑並使利率選擇權的評價產生極大的誤差。為了克服
這個問題，本文先建構 Hull and White 三元利率樹，接著在利率樹上以蒙地卡羅模擬出
所需的路徑。這種方法的好處是既可產生與市場一致的利率期間結構又能有效率地評價路
徑相依的利率選擇權。由於蒙地卡羅模擬收斂速度極慢，本文採用對消變異 (antithetic
variate) 以提高收斂速度。根據本文的研究結果顯示，以結合Hull and White三元利率
樹與蒙地卡羅模擬評價路徑相依之利率選擇權是非常有效率的方法。
Hull and White (1993b) trinomial tree has been extensively used to price a wid
e class of interest rate derivatives. This tree approach, however, is not suit
able to value the path-dependent interest rate options. Although it is possibl
e to apply Monte Carlo simulation to price such options, yet Monte Carlo simul
ation cannot recover the initial term structure of interest rates, which leads
to seriously mispricing interest rate derivatives. To circumvent this problem
, this paper firstly builds the Hull-White tree and then used Monte Carlo simu
lation to simulate the path in the tree. In this way, the built tree can both
be consistent with the initial term structure and be applied to price the path
-dependent interest rate derivatives. Moreover, to guarantee the Monte Carlo s
imulation converges fast to the continuous time limit, the antithetic variate
procedure is used to reduce the variation. The numerical evidence indicates th
at the built tree in this paper is an appropriate way to price the path-depend
ent interest rate derivatives.
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