By Gunter Loeffler, Peter N. Posch
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Extra info for Credit Risk Modeling using Excel and VBA
13) is useful, examine when the assumption d1 = 1 holds. Through the properties of the normal distribution, d1 lies between 0 and 1. For large d1 , d1 approaches unity. 3), we see that they have the same structure, and differ only in the drift rate and the sign of the variance in the numerator. Thus, a large d1 goes along with a high distance to default, and a low default probability. 13) is reasonable. The option pricing equations are entered in B13:B16. We could again use our Bd1 function. For the sake of variation, we type the formulae for d1 and d2 in cells B13 and B14, respectively.
7, the approach is applied to Enron. 15), respectively. The starting value for the asset value is equity value plus book value of liabilities; the starting value for the asset correlation is equity correlation times Et /At . 19). We then use the Solver to minimize the squared percentage errors between the observed values (for equity value and volatility) and their model counterparts. We also determine the default probability (cell B29). 37%. 5 years. Within our framework, it is not obvious how to convert it to an annual default probability, as the model does not allow interim defaults.
5 from 1 to 5), we would have failed to model the fact that the firm makes payments before maturity – like regular interest on bonds and loans, or dividends. It may be safe to ignore such interim payments over a horizon of one year. A one-year bond with annual coupon payments is in fact a zero-coupon bond, and firms usually do not pay out large dividends shortly before default. However, for a horizon of several years, interim payments should enter our valuation formula in a consistent way. In the following, we will implement such an approach.
Credit Risk Modeling using Excel and VBA by Gunter Loeffler, Peter N. Posch