DNT Vega 敏感性

Say about the Vega

专题: Finance / 金融
难度: L4
来源: QuantQuestion

个人笔记

题目详情

金融数学题：Double No-Touch 的 vega。

英文原题

Suppose an option pays one if spot stays in a range $K1$ to $K2$ and zero otherwise. What can we say about the Vega?

解析

Double No-Touch（DNT）要求在到期前不触及任一障碍。波动率上升会提高触障概率、降低存活概率，因此价格下降。

\boxed{\text{DNT 的 vega 通常为负}}.

英文解析

This option, known as a double no- touch, will have a negative Vega. Vega measures the change in option price for a $1\%$ change in volatility. If volatility increases then the probability in the risk- neutral measure of hitting either barrier $K1$ or $K2$ increases and so the option price will decrease, giving a negative Vega.