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410140980 · 2022年11月03日

standard deviation 后面这句怎么理解

NO.PZ2018122701000069

问题如下:

Model 1 has a no-drift assumption. Using this model, if the current short-term interest rate is 6%, annual volatility is 100bps, and dw is a normally distributed random variable with mean equals zero and standard deviation dt\sqrt{dt} of zero as its expected value. One month later, the realization of dw is -0.4. What is the change in the spot rate and the new spot rate?

选项:

Change in spot
New spot rate
A.
0.40%
-6.40%
B.
-0.40%
5.60%
C.
0.80%
6.80%
D.
-0.80%
5.20%

解释:

B is correct.

考点:Model I

解析:

dr = σ dw

dr = 1% x (-0.4) = -0.4% = -40 basis points

Since the initial rate was 6% and dr = -0.40%, the new spot rate in one month is:

6% - 0.40% = 5.60%

老师这里没调整月的时间,是因为这句standard deviation  dtof zero   as expected value

怎么理解这句话,什么时候需要调整什么时候不需要调整啊?

题目给dw就用dw不用调整时间?

1 个答案

品职答疑小助手雍 · 2022年11月03日

同学你好,只要记住一点,dw是考虑是根号dt之后的结果,就可以了。

给ε才需要考虑根号dt。