隨機利率下歐式遠期生效選擇權之評價與避險

Pricing and Hedging of European Forward Start Option under Stochastic Interest Rate

10.6545/JFS.2002.10(1).1

謝承熹(Cheng-Hsi Hsieh)

歐式遠期生效選擇權 ； Heath-Jarrow-Morton模型 ； 遠期測度評價法 ； European Forward Start Option ； Heath-Jarrow-Morton Model ； Forward Measure ； Method

財務金融學刊

10卷1期（2002 / 04 / 30）

1 - 22

繁體中文

在利率不為常數的經濟體下，本文評價歐式遠期生效選擇權，並分析其避險比率。首先，本文假設利率的隨機過程遵循Heath-Jarrow-Morton（1992）模型，並在遠期利率波動結構僅為時間函數的假設下，利用遠期測度評價法推導歐式遠期生效選擇權之評價封閉解。接著本文分析隨機利率下，歐式遠期生效選擇權的各種避險比率；文中發現，在權利生效前，股價報酬波動率為逾期生效選擇權最重要的風險。最後本文比較常數利率與隨機利率下，歐式遠期生效選擇權的價格，並探究在不同的參數組合下之價格差異程度。

This paper studies how to price and hedge the European forward start option under stochastic interest rate. The interest rates are, first, supposed to follow the Heath-Jarrow-Morton framework. By further assuming the volatility of the forward interest rate is a deterministic function of time and applying forward measure method, closed-form solution for the European forward start option can then be derived. At the second step, the hedge ratios of the European forward start option are analyzed under stochastic interest rate. It is shown, in this paper, that the risk of the volatility of stock return is the most important risk of the European forward start option before the option becomes effective. We, lastly, compare the premiums of the European forward start option under stochastic and non-stochastic interest rate, and discuss the difference of premiums with different parameter inputs.

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