Suppose that B = $500 and A₀ = $470,α = 9%,r = 4%,σ = 17%,and δ = 0.If T = 8,what is the risk neutral default probability?

Question

Quizplus · Accepted Answer

To calculate the risk-neutral default probability, we need to use the Merton model formula:

P(D) = N(-d₂)

where N is the standard normal cumulative distribution function, and d₂ is given by:

d₂ = [ln(B/A₀) + (r - δ + 0.5σ²)T] / (σ√T)

Plugging in the numbers, we get:

d₂ = [ln(500/470) + (0.04 - 0 + 0.5*0.17²)*8] / (0.17*√8) = 0.2798

Using a standard normal distribution table or a calculator with a normal distribution function, we find:

N(-d₂) = N(-0.2798) = 0.3809

Therefore, the risk-neutral default probability is 38.09%, which is closest to choice C (38.3%).

Suppose That B = $500 and A₀ = $470,α =