市場利率模型下利率上限契約的評價與避險

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姓名

張育瑞(Yu-Jui Chang) 查詢紙本館藏

畢業系所

財務金融學系

論文名稱

市場利率模型下利率上限契約的評價與避險
(Pricing and Hedging Interest Rate Caps in LIBOR Market Model)

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摘要(中)

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)。

摘要(英)

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.

關鍵字(中)

★ 利率上限契約
★ 蒙地卡羅模擬
★ 市場利率模型
★ 利率界限上限契約

關鍵字(英)

★ LIBOR Market Model
★ Monte Carlo Simulation
★ interest rate cap
★ interest rate barrier cap

論文目次

Contents
1. Introduction………………………………………………………………………1
2. Interest Rate Cap and Discrete Barrier Cap Agreements……………………4
2.1 Interest Rate Caps………………………………………...………………4
2.2 Discrete Barrier Interest Rate Caps………………...……………………6
3. The Model……………………………………………………………………8
3.1 LIBOR Market Model…………………………………………………..8
3.2 Interest Rate Cap Prices…………………….………………………11
4. Simulation………………………………………………………………………14
4.1 Simulation Routine……………………………………………………….14
4.2 Discounting Procedures………………………………….…………16
5. Numerical Results……………………………………………………………..18
5.1 Discrete Barrier Caps…………………………………………………...18
5.2 Effects of Volatility Structures………………………………………….19
6. Hedging Strategy………………………………………………………………23
6.1 Hedging Portfolios Constructions………………………………………23
6.2 Hedging Performance……………………………………………………26
7. Conclusion……………………………………………………………………….40
Reference…………………………………………………………………………….41
Table Contents
Table 4.1 Paths of LIBOR rates…………...…………………………………………16
Table 5.1 Prices of discrete barrier caps…….….……………….…………….…..…19
Table 5.2 Valuation of Up-and Out Barrier Cap at Different VolatilityLevels…….....21
Table 5.3 Valuation of Up-and Out Barrier Cap at Different Volatility Levels……...22
Table 6.1 Price Sensitivities of Hedging Portfolios…………………………………27
Table 6.2 Price Sensitivities of Hedging Portfolios of Different Maturity Caps..…..28
Table 6.3 Price Sensitivities in Upward Term Structure………………..………..…30
Table 6.4 Price Sensitivities in Downward Term Structure……………..…………30
Table 6.5 Hedging Performance of 2-year Interest Rate Cap……………..………32
Table 6.6 Hedging Performance of 4-year Interest Rate Cap……………..………33
Table 6.7 Hedging Performance of 6-year Interest Rate Cap……………..………34
Figure Contents
Figure 6.1 The shape of upward term structure………………………………….29
Figure 6.2 The shape of downward term structure………………………………29
Figure 6.3 2-year Cap Hedge Results……………………………………………35
Figure 6.4 4-year Cap Hedge Results……………………………………………35
Figure 6.5 6-year Cap Hedge Results……………………………………………36
Figure 6.6 2-year Cap Hedge Results under upward term structure……………..36
Figure 6.7 4-year Cap Hedge Results under upward term structure……………..37
Figure 6.8 6-year Cap Hedge Results under upward term structure……………..37
Figure 6.9 2-year Cap Hedge Results under downward term structure………….38
Figure 6.10 4-year Cap Hedge Results under downward term structure………….38
Figure 6.11 6-year Cap Hedge Results under downward term structure………….39

參考文獻

Reference
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指導教授

岳夢蘭(Meng-Lan Yueh)

審核日期

2004-7-2

推文