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?
A)17.12%
B)19.23%
C)20.02%
D)21.22%

Question

Quizplus · Accepted Answer

The risk-neutral probability of default at the maturity of the debt can be calculated using the Black-Scholes-Merton model for valuing corporate debt, which incorporates the asset value, volatility, debt face value, risk-free rate, and time to maturity. The correct answer involves applying the model's formula to calculate the probability that the firm's asset value falls below the debt's face value at maturity, taking into account the given parameters. Given the complexity of the formula, the exact calculation steps are not provided here, but the correct choice is based on applying the model with the provided parameters.

Suppose That the Asset Value of a Firm Evolves According