返回题库

期权Theta（Θ）

Theta

专题
Finance / 金融
难度
L4

题目详情

A. 欧式期权什么时候可能有正 theta？

B. 你多头看涨并做 delta 对冲，标的轻微上/下波动时你会赚钱吗？这算套利吗？

Θ=∂f∂t\Theta = \frac{\partial f}{\partial t}

For a European call on a nondividend-paying stock: >Θ>=>− S N′(d1) σ2 τ>  −  >r K e−rτ N(d2),>> \Theta > = > -\,\frac{S\,N'(d_1)\,\sigma}{2\,\sqrt{\tau}} > \;-\; > r\,K\,e^{-r\tau}\,N(d_2), > always negative.

A. When can a European option have positive theta?

B. You are long a call, delta-hedged by shorting the underlying. If SS moves up or down slightly, do you profit? Is that arbitrage?

解析

A. 可能为正的情况：

  • 深度实值看跌在某些参数下可能出现正 theta；
  • 高分红收益率下的看涨也可能出现正 theta。

B. delta 对冲后，你会因为 gamma 从小幅波动中获利，但会被负 theta（时间价值衰减）抵消；总体并非无风险套利。

Original Explanation

AnswerA:

  • A deep-in-the-money put might have positive theta if S≪K.S\ll K.
  • A call with high dividend yield can have positive theta.
    Otherwise, standard calls/puts on a nondividend-paying stock have negative theta.

AnswerB:
Yes, you gain from gamma if SS changes. But it’s offset by negative theta over time. So not a free lunch.