Valuation of Asian Interest Rate Options within the BGM Model

平均利率選擇權之評價：BGM利率模型

10.6545/JFS.2010.18(4).1

吳庭斌(Ting-Pin Wu)；傅瑞彬(Jui-Pin Fu)；陳松男(Son-Nan Chen)

亞式利率選擇權 ； BGM模型 ； 平賭過程評價方法 ； Asian Interest Rate Options ； BGM Model ； Martingale Pricing Method

財務金融學刊

18卷4期（2010 / 12 / 31）

1 - 35

英文

本文在BGM利率模型架構下，以Vorst近似方法評價亞式利率選擇權。文中修正Longstaff對平均利率的設定，改以LIBOR利率的算數平均數為標的利率，以符合實務。此外，評價公式的參數皆可由市場資料校準，校準方法亦詳細介紹於本文中。我們以蒙地卡羅模擬來驗證公式的準確性，發現此近似公式的評價結果非常接近模擬結果。因此，本文所介紹的評價公式，可以代替蒙地卡羅法，成為市場上評價平均利率選擇權的另一種選擇。

Within the BGM (Brace, Gatarek and Musiela, 1997) interest rate model, this article prices Asian interest rate options via the Vorst (1992) approximation approach. To consist with market practice, we modify the setting of the average rate in Longstaff (1995) by employing the arithmetic average of (market-observable) LIBOR rates. The LIBOR rates are specified directly rather than transformed from the unobservable short rates. Moreover, the parameters in our pricing formula can be easily calibrated from market data. The pricing formula is shown to be sufficiently accurate as compared with Monte Carlo simulation. The calibration procedure and the practical examples are also presented.

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