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410140980 · 2023年07月03日

dt开方

NO.PZ2020033001000094

问题如下:

Vincent is forecasting spot rate changes via short rate term structure models. The current short-term interest rate is 6% with a volatility of 100bps.dw, a normally distributed random variable with mean 0 and standard deviation dt\sqrt{dt}, is -0.5 after one quarter passes. Assume a constant interest rate drift, λ, of 0.48%. What is the new spot rate?

选项:

A.

5.37%.

B.

5.62%.

C.

5.76%.

D.

4.24%

解释:

B is correct.

考点:Model 2

解析:

Using Model 2 (with constant drift). The change in the spot rate is computed as:

dr = λ dt + σ dw

dr = (0.48% /4) + (1% x -0.5) = -0.38%

The new spot rate in one quarter is:

6% - 0.38% = 5.62%

老师这道题,计算dr的时候趋势项drift 当中λ*dt ,这里的dt我代入了(-0.5)^2, 题目中的dw 是一个正态分布,均值是0,标准差是dt开方=-0.5,所以 dt就等于-0.5的2次方。

这样的理解有没有问题?

1 个答案

品职答疑小助手雍 · 2023年07月04日

同学你好,理解得不对,这题其实就是直接把dw这个(服从正态分布的)波动项,指定成一个确定数字 -0.5,作为条件给你了,不用反求dt什么的。

dt只是一个时间标志,在本题中就是一个季度(1/4年)

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