https://scholars.lib.ntu.edu.tw/handle/123456789/414524
Title: | The Never-Early-Exercise Condition and Analytical Price Upper Bounds of American Power Call Options | Authors: | 繆維中 張森林 李永新 |
Keywords: | 美式選擇權;提早履約;解析上界;冪次買權;American Options;Analytical Upper Bounds;Early Exercise;Power Call Options | Issue Date: | 2014 | Journal Volume: | 7 | Journal Issue: | 3 | Start page/Pages: | 1-24 | Source: | 期貨與選擇權學刊 | Abstract: | This paper discusses the sufficient condition under which the American power call options should never be early exercised. Unlike in the vanilla case where the dividend yield q = 0 is the only condition, for American power call options there actually exists a range of q such that early exercise is never optimal. We start with deriving the general (model free) condition on q for American power call options with power sufficient n > 1 or n < 0. For specific models, we provide alternative conditions which lead to a wider range of q and applicable to any n. When q does not satisfy these conditions, we also give the analytical upper bounds for the American power call prices. These analytical formulas are derived for the fundamental Black-Scholes model as well as two jump-diffusion models and the variance gamma model, with numerical examples given to demonstrate their validity.本文討論美式冪次買權永不提前履約的充份條件。在美式標準買權下,股利率q = 0是其不提前履約的唯一條件,但對美式冪次買權而言,則存在一個特定範圍的股利率q使得提前履約恆為非最佳。本文首先推導出不限定模型下,使其不提前履約的股利率q之一般化條件,可適用於冪次係數n > 1或n < 0的情形。針對某些特定模型,此股利率q的條件可再放寬且適用於任意的冪次係數n。當股利率q不滿足此不提前履約條件時,本文亦推導出若干模型下美式冪次買權價格的解析上界公式,包含基本的Black-Scholes模型,兩種跳躍擴散模型,以及variance gamma模型,並提供數值範例以驗證以上解析公式的有效性。 |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/414524 | ISSN: | 24108146 |
Appears in Collections: | 財務金融學系 |
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