风险中性概率的r是去年化的吗

问题如下：

An analyst wants to calculate the risk-neutral probability of an up-move for a three-month European call option on ABC stock, he has collected below information: continuously compounded risk-free rate is 4%, ABC stock pays a continuous dividend yield of 2%, and ABC has an annual standard deviation of 8%. Which of the following is correct?

选项：

A.

0.55.

B.

0.62.

C.

0.79.

D.

0.86.

解释：

A is correct.

考点：A One-Step Binomial Model-Risk Neutral Method

解析：首先分别计算 up 和 down-move factors:

$U=e^{\sigma\sqrt t}=e^{0.08\sqrt{0.25}}=1.041$

$D=\frac1U=\frac1{1.041}=0.961$

因此上升的概率 $\pi_u=\frac{e^{(r-q)t}-D}{U-D}=\frac{e^{(0.04-0.02)\times0.25}-0.961}{1.041-0.961}=\frac{0.044}{0.08}=0.55$