Pricing an Arithmetic Average Reset Option Using the Green Function Method

算術平均重設選擇權之評價－使用格林函數法

蕭義龍(Yi-Long Hsiao) ； 王明隆(Andrew Ming-Long Wang) ； 陳家羽(Chia-Yu Chen)

《Asia Pacific Management Review》 18卷2期 (2013/06) Pp. 125-142

https://doi.org/10.6126/APMR.2013.18.2.01

摘要

本研究以格林函數法來探討算數平均重設選擇權之評價。在Black-Scholes架構假設下，算數平均重設選擇權之積分表現式為一系列Black-Scholes偏微分方程式之初始值問題，屬於路徑相依型之選擇權評價，透過數值積分可獲得精確解。本研究方法亦可適用於幾何平均型之重設選擇權評價，最後並以數值例進一步探討比較其中差異。

關鍵字

算數平均 ； 重設選擇權 ； 格林函數

並列摘要

This study investigates the pricing of the arithmetic average reset option. The option price is formulated as the solution of the Black-Scholes equation. In addition, the valuation is derived from a series of initial value problems based on the Green function through integration. Finally, the reset option price is numerically calculated. Throughout the numerical method, we can derive reset option prices of both arithmetic average and geometric average reset options. This study also presents the numerical examples for comparison.

並列關鍵字

Reset option ； Asian option ； arithmetic average ； green's function

參考文獻

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Chang, C.C., Chung, S.L., Shackleton, M. (2004) Pricing options with American-style average reset features. Quantitative Finance 4, 292-300.

Cheng, W.Y., Zhang, S. (2000) The analytics of reset options. Journal of Derivatives Fall, 59- 71.