From your reading, recall that in structural model, company equity is similar to a call option on the company's assets with a strike price equal to the payoff value of the debt.

Assume that you know the following about a company:

Current asset value $($millions$)802$

Expected return on assets $4\mathrm{.}4$

Risk free rate $1\mathrm{.}2$

Face value of debt $($millions$)524$

Time to debt maturity $3$

Asset return volatility $($stdev$)0\mathrm{.}49$

Using the option pricing model, what is the probability of default over the debt's time to maturity? Enter answer in percents.

Calculate the d$1$ parameter:

$\backslash$sigma

$\backslash$sigma

Now, we find the probability of default:

Probability of Default

Using a standard normal distribution table or a calculator,

is approximately

Therefore, the probability of default over the debt's time to maturity is approximately

Find the NDF at $1\mathrm{.}436$: This can be done with a calculator or NDF table, giving you approximately

Calculate the probability of default:

Therefore, the probability of default over the debt's time to maturity is approximately

Explanation:

Asset volatility is a crucial parameter affecting option pricing and risk management in financial models.$+$

Answer

FINAL SOLUTION:

The probability of default over the debt's time to maturity is