N对应的值

问题如下：

A risk team at an investment bank uses the KMV model to estimate the distance to default and expected default frequency in evaluating default conditions of both potential and existing client firms. One such client currently has total assets valued at USD 20 billion, asset volatility of 28% per annum, short-term debt of USD 7 billion, and long term debt of USD 6 billion. The expected return on the firm’s assets is 5% per year and the risk free rate is 1% per year. The firm does not pay any dividends. The rating schedule at a 1-year horizon is shown in the table below:

What is the suggested credit rating of the firm at a 1-year horizon using the rating schedule provided?

选项：

A.

AA/A

B.

A/BBB+

C.

BBB+/BBB

D.

BBB-/BB

解释：

Explanation: D is the correct answer. Using the KMV model, default value of debt = Short-term + 0.5*Long-term debt. And, according to the Merton Model, the probability of default at a one-year horizon = N(-DD), where DD is the distance to default and:

where V = 20; X = 7 + 6/2 = 10; σ= 0.28; µ = 0.05; T-t = 1. And so,

PD = N(-2.5141) = N(-2.5) = 0.62