How probability of company change with volatility of equity


Assignment Problem: Merton Model

Consider a company with equity value equal to $80, and face value of debt of $50. The annual log-return on risk-free debt is 3%. If the debt of the company expires in 0.5 years, how does the probability of default of the company change as a function of the volatility of the equity?

Q1. Create a plot where the distance to default is on the y-axis and the volatility of the equity (from 0.1 to 1.5, in increments of 0.1) is on the x-axis.

Q2. Create a plot where the probability of default is on the y-axis and the volatility of the equity (from 0.1 to 1.5, in increments of 0.1) is on the x-axis.

Q3.  Comment on the results.

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