三項關於歐式選擇權特性之註解

A Note on Three Properties of European Options

在文獻上（包括教科書），歐式選擇權有三個特性尚未被完整地探討，至少留點曖昧的爭議，以致影響眾多的讀者（包括學生）。第一個與第二個特性分別為歐式買權與賣權的權利金與其到期時間長短的關係是否一定為正相關？第三個特性為歐式賣權的時間價值可以為負嗎？對於第一、二個議題，文獻（包括教科書）的意見分歧且未有精確的解釋。至於第三個議題，依據傳統上對選擇權內在價值的定義，歐式賣權的時間價值可能為負。此現象是否可容許而且有意義？有何經濟及實務意涵？本文旨在深度地討論這三個議題並提出精確的解釋、探討其原因及實務意涵。

There are three less-explored, and still ambiguous, properties regarding European options in literature (including textbooks), so that many readers (including students) can be influenced. The first and second properties are how the European call and put premiums, respectively, related to their time to expirations? Do they must be positively related? And the third one is that can the time value of a European put be negative? For the first two issues, literature (including textbooks) provide inconsistent views and do not give an accurate explanation. For the third issue, according to the conventional definition of intrinsic value, the time value of the European put can be negative. Is this admissible and meaningful? What are the economic and practical implications? The purpose of this article is to explore these three issues in depth, giving affirmative answers and providing the economic and practical implications for the three issues.