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yanan · 2024年10月02日

为啥是downward sloping

NO.PZ2023100703000096

问题如下:

A hedge fund risk manager plans to adopt an interest rate term structure model whose risk neutral dynamics display mean reversion and a time-varying drift and consider Vasicek model as one of the candidates. Which of the following is correct about the Vasicek model?

选项:

A.It gives rise to a downward-sloping term structure of volatility and allows for a time dependent drift.

B.The short-term rates tend toward a long run equilibrium value and the expected value of the change in short-term rates is always zero over time.

C.Shocks to short-term rates affect all rates equally, giving rise to parallel shifts.

D.There is no mean reversion and the risk premium corresponds to a constant drift in Vasicek model.

解释:

The Vasicek model incorporates mean reversion. The flexibility of the model also allows for risk premium, which enters into the model as constant drift or a drift that changes over time. In a model with mean reversion, shocks to the short rate affect short term rates more than longer-term rates and give rise to a downward-sloping term structure of volatility. B is incorrect as the drift of Vasicek model is not always zero. C is incorrect because shocks to the short rate affect short-term rates more than longerterm rates as Vasicek model comes with mean reversion. D is incorrect. The Vasicek model incorporates mean reversion. The flexibility of the model also allows for risk premium, which enters into the model as a constant drift or a drift that changes over time.

均值复归的话,不是有上有下吗

1 个答案

李坏_品职助教 · 2024年10月02日

嗨,努力学习的PZer你好:


A选项的意思是,V model会让利率的波动率期限结构向下倾斜。


正是由于均值回归的存在,市场的shock对于V model里面的短期利率的影响,大于对长期利率的影响。所以短期波动率变化更大。这里的期限结构说的不是利率期限结构,而是波动率的期限结构。

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努力的时光都是限量版,加油!

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