开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

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

----------------------------------------------
加油吧,让我们一起遇见更好的自己!

  • 1

    回答
  • 0

    关注
  • 323

    浏览
相关问题

NO.PZ2020033001000094 问题如下 Vincent is forecasting spot rate changes via short rate term structure mols. The current short-term interest rate is 6% with a volatility of 100bps., a normally stributeranm variable with me0 anstanrviation \sqrt{}​, is -0.5 after one quarter passes. Assume a constant interest rate ift, λ, of 0.48%. Whis the new spot rate? A.5.37%. B.5.62%. C.5.76%. 4.24% B is correct.考点Mol 2解析Using Mol 2 (with constant ift). The change in the spot rate is computeas: = λ + σ = (0.48% /4) + (1% x -0.5) = -0.38%The new spot rate in one quarter is:6% - 0.38% = 5.62% 老师您好,请问直接给的数据用的也没有说是a quarter的,不用换算一下吗?

2023-08-09 20:39 1 · 回答

NO.PZ2020033001000094问题如下 Vincent is forecasting spot rate changes via short rate term structure mols. The current short-term interest rate is 6% with a volatility of 100bps., a normally stributeranm variable with me0 anstanrviation \sqrt{}​, is -0.5 after one quarter passes. Assume a constant interest rate ift, λ, of 0.48%. Whis the new spot rate? A.5.37%.B.5.62%.C.5.76%.4.24% B is correct.考点Mol 2解析Using Mol 2 (with constant ift). The change in the spot rate is computeas: = λ + σ = (0.48% /4) + (1% x -0.5) = -0.38%The new spot rate in one quarter is:6% - 0.38% = 5.62% 请问此题目中是负0、5表示什么含义?

2023-08-06 04:16 1 · 回答

NO.PZ2020033001000094 问题如下 Vincent is forecasting spot rate changes via short rate term structure mols. The current short-term interest rate is 6% with a volatility of 100bps., a normally stributeranm variable with me0 anstanrviation \sqrt{}​, is -0.5 after one quarter passes. Assume a constant interest rate ift, λ, of 0.48%. Whis the new spot rate? A.5.37%. B.5.62%. C.5.76%. 4.24% B is correct.考点Mol 2解析Using Mol 2 (with constant ift). The change in the spot rate is computeas: = λ + σ = (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,计算的时候趋势项ift 当中λ* ,这里的我代入了(-0.5)^2, 题目中的 是一个正态分布,均值是0,标准差是开方=-0.5,所以 就等于-0.5的2次方。这样的理解有没有问题?

2023-07-03 10:07 1 · 回答

NO.PZ2020033001000094 问题如下 Vincent is forecasting spot rate changes via short rate term structure mols. The current short-term interest rate is 6% with a volatility of 100bps., a normally stributeranm variable with me0 anstanrviation \sqrt{}​, is -0.5 after one quarter passes. Assume a constant interest rate ift, λ, of 0.48%. Whis the new spot rate? A.5.37%. B.5.62%. C.5.76%. 4.24% B is correct.考点Mol 2解析Using Mol 2 (with constant ift). The change in the spot rate is computeas: = λ + σ = (0.48% /4) + (1% x -0.5) = -0.38%The new spot rate in one quarter is:6% - 0.38% = 5.62% 老师上课一般用σ * √ 代替,这道题我的理解是ε~N(0,1), 默认条件。 ~N(0, √ ) =λ+ε*σ * √ 所以我代入了0.48%/4 - 0.5*1%* √1/2​ 其实就是不太理解题目给的 服从正太分布均值为0,方差为√=-0.5这个条件。解析中这个-0.5是,但我感觉好像是想说 √ 是-0.5.

2022-11-03 10:51 1 · 回答

NO.PZ2020033001000094 Vincent is forecasting spot rate changes via short rate term structure mols. The current short-term interest rate is 6% with a volatility of 100bps., a normally stributeranm variable with me0 anstanrviation \sqrt{} ​, is -0.5 after one quarter passes. Assume a constant interest rate ift, λ, of 0.48%. Whis the new spot rate? 5.37%. 5.62%. 5.76%. 4.24% B is correct. 考点Mol 2 解析 Using Mol 2 (with constant ift). The change in the spot rate is computeas: = λ  + σ  = (0.48% /4) + (1% x -0.5) = -0.38% The new spot rate in one quarter is: 6% - 0.38% = 5.62%

2022-03-02 13:01 1 · 回答