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Danlei · 2021年11月20日

请问一下。

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%

a volatility of 100bps.dw, 

standard deviation \sqrt{dt}dt​, is -0.5 

这两个处如何解读成已知条件呢?

1 个答案
已采纳答案

李坏_品职助教 · 2021年11月20日

嗨,努力学习的PZer你好:


The current short-term interest rate is 6% with a volatility of 100bps.

这句话的意思是短期利率是6%,并且波动率(就是σ标准差)等于100个基点,1个基点=0.01%,所以是σ=1%。


dw, a normally distributed random variable with mean 0 and standard deviation √dt is -0.5 after one quarter passes.

这句话意思是dw是一个正态分布变量,均值为0,标准差等于-0.5

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