多資產趨勢選擇權之評價

Abstract

這篇論文主要是以Martingale 評價方法來推導多資產趨勢選擇權的封閉解。主要的貢獻在於提供了一個一般化的評價公式，能應用在其他不同種類的加權平均選擇權上。而趨勢選擇權，是由Leippold and Syz (2007) 所提出的一種新型選擇權，此種選擇權的報酬是利用迴歸分析的方式，求出標的物過去已實現的價格趨勢為依據，所以具有避免選擇權在接近到期日時的時間風險。而多資產選擇權則具有投資組合分散風險的效果，所以本篇結合多資產選擇權的性質於趨勢選擇權上，提供一個可能同時具有選時及選股特性的新投資商品之選擇。

This thesis provides a closed-form formula for the rainbow trend options by using the Martingale pricing method. The main contribution of this thesis is to propose a general pricing formula which can be applied to price various kinds of rainbow weighted aver-age options. The trend option is a new exotic option mentioned in Leippold and Syz (2007); its payoff is based on the trend of the realized underlying sampled prices over a specific period such that it has the superiority in avoiding the timing risk. And rainbow options have a known effect on non-system risk diversification. The attractiveness to combine the two features is to satisfy the need of investors for avoiding the timing risk and enjoying the diversification effect simultaneously. Moreover, the remarkable feature that the delta of the rainbow trend option tends to zero at maturity in some special cases is found in this paper.