Python for Finance

Credit Risk Analysis
Here ST is the terminal stock price at maturity date, T is the maturity date, K is the
exercise price, and max() is the maximum function. The similarity between the
preceding two equations suggests that we could treat equity as a call option with
the debt level as our exercise price. With appropriate notations, we will have the
following formulas for a firm's equity. The KMV model is defined here:
On the other hand, the following relationship between the volatilities of the equity
and the total assets holds. In the following equation, we have:
Since d1 and d 2
are defined by the previous equations, we have two equations
for two unknowns (A and ); see the following formulas. Thus, we could use
trial-and-error or simultaneous equation methods to solve those two unknowns.
Eventually, we want to solve the following two equations for A and :
We should pay attention to the estimated A (market value of total assets) from the
preceding equation since it is different from the summation of market value of assets
plus the book value of the debt.
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