长短期限

Long short maturity

专题: Finance / 金融
难度: L4
来源: QuantQuestion

个人笔记

题目详情

金融数学题：长短期限：哪一个 gamma 更高。

英文原题

Two standard options have exactly the same features, except that one has long maturity, and the other has short maturity. Which one has the higher gamma?

解析

vanilla 期权

\Gamma=\frac{\varphi(d_1)}{S\sigma\sqrt{\tau}},\quad \tau=T-t.

在平值附近 $\varphi(d_1)$ 近似常数，因此

\boxed{\tau\text{ 越短，gamma 越大（尤其 ATM 附近）}}.

英文解析

\Gamma=\frac{\varphi(d_1)}{S\sigma\sqrt{\tau}},\quad \tau=T-t.