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lynn666 · 2023年02月08日

是不是因为问题里问了是volatility component所以才不用计算drift项呀?

NO.PZ2022071105000002

问题如下:

An analyst at an investment bank uses interest-rate trees to forecast short-term interest rates. The analyst

applies the following model for estimating monthly changes in a short-term interest rate tree:

dr = λ(t)*dt + σ(t)*dw

In this process, λ(t) represents the drift in month t, σ(t) represents the volatility in month t, dt is the time

interval measured in years, and dw is a normally distributed random variable with a mean of zero and a

standard deviation of the square root of dt. The analyst uses the following information to make the

calculations:

• Current level of short-term interest rate: 3.1%

• Drift in month 1 (λ(1)): 0.0024

• Drift in month 2 (λ(2)): 0.0036

• Annualized volatility of the interest rate in month 1 (σ(1)): 0.0060

• Annualized volatility of the interest rate in month 2 (σ(2)): 0.0080

• Probability of an upward or downward movement in interest rates: 0.5

What is the volatility component of the change in interest rate from the upper node of month 1 to the upper

node of month 2?

选项:

A.

23 bps

B.

26 bps

C.

40 bps

D.

45 bps

解释:

中文解析:

A是正确的。在日期1和日期2之间的利率变化的波动性对日期2上的任何节点的影响都是相同的。由于dw的标准差为√dt,所以收益率的标准差为σ(t)*dw=σ(t)*√dt。因此,利率变化的波动性成分是0.0080√1/12=0.0023,23 bps,上升或下降。

B是不正确的。这个答案的选择包括在日期2向上节点的漂移和波动。0.0036/12+0.0080√1/12=0.0003+0.0023=0.0026。

C是不正确的。这个答案包括在日期1和日期2时的波动性影响。0.0060√1/12+0.0080√1/12=0.0040。

D不正确。这个答案包括从日期2的初始利率到上节点的漂移和波动性影响。

A is correct. The impact of volatility to the change in the interest rate between date 1 and

date 2 will be the same at any node on date 2. Since the standard deviation of dw is √dt,

the standard deviation of the rate change is σ(t)*dw = σ(t)*√dt. So, the volatility

component of the change in interest rate is 0.0080√1/12 = 0.0023, 23 bps, up or down.

B is incorrect. This answer choice includes drift and volatility to the upper node at date 2.

0.0036/12 + 0.0080√1/12 = 0.0003 + 0.0023 = 0.0026

C is incorrect. This includes the volatility impact at date 1 and date 2. 0.0060√1/12 +

0.0080√1/12 = 0.0040

D is incorrect. This includes the drift and volatility impact from the initial rate to the upper

node at date 2.

如题。。。。。。。。。。

1 个答案
已采纳答案

李坏_品职助教 · 2023年02月08日

嗨,从没放弃的小努力你好:


是的,题目问的是What is the volatility component,不用考虑drift了。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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