本論文透過蒙地卡羅模擬探討在市場利率模型下利率上限契約的評價與避險。吾人將本論文分為兩部分分析，第一部分著重在間斷型態利率界限選擇權的評價。由於界限選擇權相對於標準歐式選擇權來的便宜，而成為近年來市場上風險管理者所喜愛的避險工具。因此我們將探討隨著市場利率模型中遠期利率波動度的變動，對間斷型態界限利率上限選擇權價值的影響。第二部分著重在利率上限契約的避險。我們選用不同到期日的零息債券當作避險工具，至於這些零息債券的到期日及數目的選擇則是我們所要討論的主題。由模擬的結果顯示，我們可簡化成只選用四張不同到期日的債券便可達到與選用N+1張不同到期日債券相似的結果(N為利率上限契約的重設次數)。 In this paper, the LIBOR Market Model is implemented to price and hedge interest rate caps by Monte Carlo simulation. The study falls into two parts. In the first part, we focus on pricing discrete interest rate barrier caps. Barrier caps, less expensive than vanilla caps, have become very popular in recent year as useful hedging instruments for risk management strategies, and we use Monte Carlo procedure to value discrete barrier caps based on the LIBOR Market Model. In the second part of the study, we focus on the hedging of vanilla caps. The choices of the number and maturity of the hedging instruments which use the zero coupon bonds are the subject in this paper. We replicate numbers of hedging portfolios of interest rate caps and test the hedging performance of these portfolios by simulation. The numerical results of the hedging of interest rate caps show that we can simplify zero coupon bonds with N+1 maturities to be using zero coupon bonds with four maturities. Here, N is the number of reset dates. The result suggests that we can choose zero coupon bonds with four maturities, as hedging instruments of interest rate cap, mature most closely at the initial and end life of the interest rate cap respectively.
