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上小学 · 2023年08月06日

请问DW这个参数什么时候需要考虑，什么时候不用管？

  1. FRM II
  2. Market Risk Measurement And Management

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%

请问此题目中DW是负0、5表示什么含义？

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1 个答案

李坏_品职助教 · 2023年08月06日

嗨，努力学习的PZer你好：


题目说的是 term structure model，而且给出了λ的值，所以这道题要用model 2的公式计算利率：

dw在这个公式里是一个正态分布的随机变量，是为了配合σ来表示利率变动幅度dr的volatility的。

这里dt=1，也就是1个quarter。

一个季度之后利率的变动dr = λ*dt + σdw = (0.48%/4)*1 + 1% * (-0.5)，一个季度之后的the new spot rate = 6%+dt。

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