以LIBOR市場模型評價利率衍生性商品：結合二項樹方法

Abstract

本研究採用Ho、Stapleton和Subrahmanyam所提出的結合二項樹方法來建造LIBOR市場模型的遠期利率演進過程。此結合二項樹評價法對於評價利率衍生性金融商品與之前所提出的利率模型相比，提供了我們一個計算方便且準確的數值結果。此外在評價過程中，此結合二項樹評價法也比蒙地卡羅模擬法來的省時且有效率。而用此結合二項樹評價法所計算出來的債券選擇權和利率上限買權價值與理論值的誤差也在容忍的誤差範圍內。

In this thesis, we adapt the recombining node methodology proposed by Ho, Stapleton, and Subrahmanyam to implement the LIBOR market model (LMM). The lattice method we proposed is more efficient in comparison with Monte Carlo simulation as pricing the interest rate derivatives. The results of the bond option value and the caplet value are approximate to the theoretical value respectively.