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长短期限:哪一个 gamma 更高

Long short maturity

专题
Finance / 金融
难度
L4

题目详情

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

Γ=φ(d1)Sστ,τ=Tt.\Gamma=\frac{\varphi(d_1)}{S\sigma\sqrt{\tau}},\quad \tau=T-t.

在平值附近 φ(d1)\varphi(d_1) 近似常数,因此

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