對數常態遠期LIBOR模型的校準和分析

Abstract

在本文分別採用了Hull (2000) 和Brigo (2005) 在LIBOR市場模型的波動率假設，並針對其校準及模擬的結果進行分析。為了在LIBOR市場模型的假設下，計算swap option的波動率，我們採用了Brigo (2005) 提到的近似公式。文中採用歐洲同業拆款利率 (Euribor) 的cap和swap option兩種利率商品的市場報價校準參數化之波動率及相關係數，再使用蒙地卡羅模擬利率路徑，來計算cap的價格；以及利用上述所提到的近似公式，來計算swap option的波動率。最後，對這兩種不同的波動率參數假設，進行分析和比較，並且指出同時對cap和swap option進行參數校正會得到較好的結果。

In this thesis I concern about the volatility structure of the LIBOR market model. Two different parametric assumptions of the covariance structure of the LIBOR market model and their corresponding calibration methods suggested by Hull (2000) and Brigo (2005) would be followed and examine the impacts on the framework of the LIBOR market model. I also examine the analytic approximation for pricing the swap option presented by Brigo (2005). The parameters are calibrated based on the market prices of the caps and swap options in the Euribor market. To compare the performance of these two frameworks, I value the caps using Monte Carlo simulation and calculate the swap option volatility through the analytical approximation proposed by Brigo (2005). Finally, the benefits of both considering the caps and swap option matrix before calibrating will be presented.