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lcrcp3 · 2023年10月09日

如题

  1. CFA II
  2. Derivative

NO.PZ2023041003000057

问题如下：

GI Stock and Option Information

If the price of GI stock approaches $75 over the next 30 days, which of the fol­lowing changes in option parameter measures will most likely be observed?

选项：

A.

Decreases in vega and the absolute value of theta

B.

Increases in vega and the absolute value of theta

C.

A decrease in vega and an increase in the absolute value of theta

解释：

Typically, theta is negative for options. The speed of the option value decline increases, however, as time to expiration decreases. Vega is high when options are at or near the money. During the next 30 days, the options will approach expiration and approach being at the money.

A is incorrect.

C is incorrect. Vega increases as the options become closer to at-the-money.

这题什么意思？现在股价是77，看涨或看跌期权执行价格是75，未来30天股价是75，然后呢？跟波动率和到期时间增大还是减小有什么关系？

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1 个答案

李坏_品职助教 · 2023年10月09日

嗨，努力学习的PZer你好：


vega是期权价格相对于σ（波动率）的一阶偏导数，vega并不是波动率本身。

theta是期权价格相对于time passing（逝去的时间）的一阶偏导数，theta并不是时间本身。


平值期权（at the money）的vega是最大的，所以vega会变大。随着期权临近到期日，价值会加速流失（time value加速下降），也就是theta的绝对值在变大，所以选B。

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