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My method is:
1. Define the Default Point
Moody’s using ST Debt + half LT Debt
2. Set Up Formulas for N(d1)
Using Black-Scholes model, assuming the Default Point, risk-free rate and term are given
Leave asset value and asset volatility blank, which would be solved later
3. Given the equity value is a call option on asset value, we can generate equity value assuming d1, d2, Default Point and Asset Value are calculated above
4. Given the relationship between share volatility and asset volatility is given, we can generate equity volatility assuming d1, asset volatility, asset value and equity value are calculated above.
5. Set the criteria the equity value calculated in Step 3 is close to what we input
6. Set the criteria the equity volatility calculated in Step 4 is close to what we input
7. Using solver to find out asset value and asset volatility
This is considered as the initial model which requires a lot of modifications which is more appropriate to Chinese application. Current I am applying using list company or index data to estimate the non-list company PD. It seemed that the model is quite focusing of leverage while the rest factors such as profitability, liquidity and cash flow can not be fully considered. Therefore, another rating method is applied as a support for adjustment.
If ther e is a good data base as Moody's, or complex Monte Carlo Method used for each variables, the estimate would be more appropriate. However, the timing and validation would become issues as well.
Hope this would be helpful.
Kind regards,
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