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和棋 · 2021年03月17日

为什么volatility会影响Firm Value？

  1. FRM II
  2. Credit Risk Measurement And Management

NO.PZ2016082406000039

问题如下：

Using the Merton model, the value of the debt increases if all other parameters are fixed and

I. The value of the firm decreases.

II. The riskless interest rate decreases.

III. Time to maturity increases.

IV. The volatility of the firm value decreases.

选项：

A.

I and II only

B.

I and IV only

C.

II and III only

D.

II and IV only

解释：

ANSWER: D

The value of credit-sensitive debt is B=Ke−(r+s)tB=Ke^{-(r+s)t}.  This increases (1) if the risk-free interest rate decreases, or (2) if the credit spread decreases, or (3) if the maturity decreases. The credit spread decreases if the value of the firm goes up, or if the leverage goes down, or if the volatility goes down. Hence, the value of debt increases if the riskless rate decreases or if the volatility decreases.

为什么volatility会影响Firm Value？

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1 个答案

小刘_品职助教 · 2021年03月17日

同学你好，

这道题没有说 volatility会影响Firm Value，说的是volatility会影响credit spread，你指的是第4个 statement吗？

这个有助教老师的这个理解方法，我觉得还比较好~

直接从merton模型的延伸，kmv来看会更简单一些。其实就是从Nd1，Nd2延伸出来的。

KMV里DD的公式如下：可以看到波动变小的时候分子减的数小了（分子变大），分母变小，这时候DD会增加，DD增大的话就更不容易违约，也就是债券信用风险更小，价值会上升


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