Exam 30: Structural Models of Default Risk

Suppose that the asset value of a firm evolves according to a lognormal diffusion,as in Merton (1974).The current value of the firm's assets is $100 million,and its volatility is 24.24%.Suppose too that the firm has only one issue of debt outstanding: zero-coupon debt with a maturity of three years,and a face value of $70 million.Finally,suppose that the risk-free rate of interest is 4% (continuously-compounded terms)for all maturities.What is the risk-neutral probability of the firm defaulting at maturity of the debt?

The Merton (1974)model assumes that the value of the firm is distributed

A firm's current value is $10 billion.The firm has one-year zero-coupon debt with face value $7 billion.The standard deviation of firm asset value is $2 billion.What is the firm's "distance-to-default" as measured by the Moody's KMV approach?

Equity and debt in a firm are option-like mainly because

Equity holders in a leveraged firm have

Credit-scoring models primarily rely on:

A firm has one-year zero-coupon debt with face value $7 billion.Assuming the firm value at the end of the year is normally distributed with a mean of 10 billion and a standard deviation of 2 billion,,what is the probability that the firm's assets will not be sufficient to repay the debt at the end of the year?

Zero-coupon risky debt value in a firm is equal to

Suppose that a firm's value $V$ grows over one year at a simple rate $^{\circ}_{R}$ that has a mean of $0.10$ and a variance of $0.04$ .If the firm's current value is $10 billion and it has one-year zero-coupon debt of face value $7 billion,what is the probability that the firm's assets will not be sufficient to repay the debt at the end of the year? Assume the firm value at the end of the year is normally distributed.

Zero-coupon debt value rises when,ceteris paribus

Given a firm value of $V = 100$ ,debt face value of $D = 60$ ,asset volatility of $\sigma = 30 \%$ ,and a risk free rate of $r = 3 \%$ ,conditional on default,the expected recovery rate in the Merton model for debt of maturity five years will be:

A firm's current value is $£$ 1 billion .The firm has one-year zero-coupon debt outstanding with a face value of $£$ 0.6 billion.What is the one-year "distance to default" (in the Moody's KMV approach)if the standard deviation of firm value is 30%?

Altman's Z-score model may be used to:

Credit spreads in the Merton (1974)model will be increasing,ceteris paribus,when

The Geske model generalizes the Merton model to allow for

Unobserved firm volatility is an obstacle in the implementation of the Merton model.One popular way to overcome this is to

Which of the following statements best describes the relation of the real-world ( $P$ )and risk-neutral ( $Q$ )probabilities of default?

The structural model framework is a parsimonious one,yet needs to accommodate complex capital structures.Which of the following approaches is not a simplification of the complexity of the real-world situation?

A firm's current value is 1 billion.The firm has one-year zero-coupon debt of face value €0.6 billion.Assume an expected growth rate of the firm's assets of 0% and a standard deviation of asset value of 0.3 billion.If the firm asset value at year end is normally distributed,what is the probability that the firm's assets will not be sufficient to repay the debt at the end of the year?

In order to obtain the probability of default in the Merton (1974)model under the real-world probability measure,we need to make the following change in calculating $N \left( d _ { 2 } \right)$ in the formula :