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hillock1122 · 2021年03月07日

由DD计算PD在讲义中的哪里?

NO.PZ2016082406000037

问题如下:

The capital structure of HighGear Corporation consists of two parts: one five- year zero-coupon bond with a face value of $100 million and the rest is equity. The current market value of the firm’s assets is $130 million and the expected rate of change of the firm’s value is 25%. The firm’s assets have an annual volatility of 30%. Assume that firm value is lognormally distributed, with constant volatility. The firm’s risk management division estimates the distance to default using the Merton model, or ln(KV)δτ+0.5σ2τστ\frac{\ln(\frac{\text{K}}{\text{V}})-\delta\tau+0.5\sigma^2\tau}{\sigma\sqrt\tau}Given the distance to default, the estimated default probability is

选项:

A.

2.74%

B.

12.78%

C.

12.79%

D.

30.56%

解释:

ANSWER: A

We compute z=ln(KV)δτ+0.5σ2τστ=ln(100130)25%×5+0.5×30%2×530%5=1.919z=\frac{\ln(\frac{\text{K}}{\text{V}})-\delta\tau+0.5\sigma^2\tau}{\sigma\sqrt\tau}=\frac{\ln(\frac{\text{100}}{\text{130}})-25\%\times5+0.5\times30\%^2\times5}{30\%\sqrt5}=-1.919. The PD is then N(z)=N(1.919)=2.749%N{(z)}=N{(-1.919)}=2.749\%.

老师,根据公式算出了DD,但是翻了半天没找到怎么进一步算PD了~

1 个答案

小刘_品职助教 · 2021年03月07日

同学你好,

DD就是d2,所以PD=N(-d2)=N(-DD),记住就好啦