It is assumed that at this point, the reader is well versed in running simulations and optimizations in Risk Simulator. The example model used is the Probability of Default – External Options Model and can be accessed through Modeling Toolkit | Prob of Default | External Options Model (Public Company).
To run this model (Figure 2.1), enter in the required inputs such as the market value of equity (obtained from market data on the firm’s capitalization, that is, stock price times the number of shares outstanding), equity volatility (computed in the Volatility or LPVA worksheets in the model), book value of debt and liabilities (the firm’s book value of all debt and liabilities), the risk-free rate (the prevailing country’s risk-free interest rate for the same maturity as the debt), and the debt maturity (the debt maturity to be analyzed, or enter 1 for the annual default probability). The comparable option parameters are shown in cells G18 to G23. All these comparable inputs are computed except for Asset Value (the market value of asset) and the Volatility of Asset. You will need to input some rough estimates as a starting point so that the analysis can be run. The rule of thumb is to set the volatility of the asset in G22 to be one fifth to half of the volatility of equity computed in G10, and the market value of asset (G19) to be approximately the sum of the market value of equity and book value of liabilities and debt (G9 and G11).
Then, an optimization needs to be run in the Risk Simulator software in order to obtain the desired outputs. To do this, set Asset Value and Volatility of Asset as the decision variables (make them continuous variables with a lower limit of 1% for volatility and $1 for the asset, as both these inputs can only take on positive values). Set cell G29 as the objective to minimize as this is the absolute error value. Finally, the constraint is such that in cell H33, the implied volatility in the default model is set to exactly equal the numerical value of the equity volatility in cell G10. Run a static optimization using Risk Simulator.
If the model has a solution, the absolute error value in cell G29 will revert to zero (Figure 2.2). From here, the probability of default (measured in percent) and distance to default (measured in standard deviations) are computed in cells G39 and G41.
Then, using the resulting probability of default, the relevant credit spread required can be determined using the Credit Analysis – Credit Premium model or some other credit spread tables (such as using the Internal Credit Risk Rating model).
The results indicate that the company has a probability of default at 0.87% with 2.37 standard deviations to default, indicating good creditworthiness (Figure 2.2).