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題 名 | Pricing Options with Geometric Average Reset Feature=幾何平均重設選擇權的評價分析 |
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作 者 | 戴天時; 方裕元; | 書刊名 | 中原學報 |
卷 期 | 32:4 2004.12[民93.12] |
頁 次 | 頁515-526 |
分類號 | 563.54 |
關鍵詞 | 幾何平均重設選擇權; 選擇權評價; 路徑相依選擇權; 重設選擇權; Option pricing; Path-dependent derivative; Reset option; Geometric average trigger reset option; |
語 文 | 英文(English) |
中文摘要 | 幾何平均重設選擇權會根據標的物在某一段時間內的幾何平均價格,決定是否重設該選擇權的履約價格。類似的合約已在亞洲的金融市場上頻繁交易。Cheng and Zhang [2000]提出一個解析解的公式,但其 公式僅可處理包含單一重設時間點的重設選擇權,而且他們的公式也是不正確的。本篇論文提出一評價公 式,可評價包含任意多個重設時間點的重設選擇權。此外,本論文證明當標的物股票不配息時,重設選擇買權持有人不會提前履約,所以本論文的公式可推廣到美式的重設買榷。在本論文中分析重設選擇權相關的特性:例如選擇權價格和計算平均價格時所取樣的次數和取樣時間長度的關係,以及幾何平均和算數平均 重設選擇權價格的關係。本論文使用蒙地卡羅法來驗證上述這兩種重設選擇權的價格相近,所以本論文所提供的公式也可用來精確地估計算數平均重設選擇權的價格。此外,由於幾何平均重設選擇權的避險參數(Delta)不會隨標的物價格變化,而有明顯變動,但是 無均價條款設計的重設選擇權則有這個現象。所以使 用幾何平均重設選擇權可以大幅減少避險的困難。 |
英文摘要 | A geometric average trigger reset option resets the strike price based on the geometric average of the underlying asset's prices over a monitoring window. There can be mu1tiple monitoring windows, thus multiple resets. Simi1ar contracts have been traded on exchanges in Asia. Cheng and Zhang [2000] give an analytic formula for a more limited case which permits only a single reset; unfortunately their formula is incorrect. Our paper gives the correct ana-iytic formu1a that can handle an arbitrary number of monitoring windows. A reset calI wiII not be exercised early if the underlying asset does not pay dividends; hence our formula applies to American-style reset calIs in this case. Some properties of reset options are analyzed rigorously in the paper: like the reationship between the option prices and the number of samples in a monitoring window, the relationship between the option prices and the length of a monitoring window, and the relationship between the geometric and the arithmetic average trigger reset options. Monte Carlo simulatíon suggests that the European-style geometric average trigger reset option and the arithmetic version have similar option values. Thus our formula give cioseprices for the difficult arithmetic version. Besides, unlike the standard reset option, the geometric average trigger reset option does not have significant deltajumps. This useful property reduces the hedging risk dramatically. |
本系統中英文摘要資訊取自各篇刊載內容。