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We will not show how to implement this transformation in a spreadsheet. With many variables, it would involve a lot of similar calculations, making it a better idea to set up a user defined function that maps a variable into a default rate for a chosen number of ranges. 0000001) transform(i, 1) = Log(transform(i, 1) / (1 − transform(i, 1))) Next i XTRANS = transform End Function After dimensioning the variables, we loop through each range, j=1 to numranges. 12. That is why we see the same commands: SUMIF to get the number of defaults below a certain percentile, and COUNTIF to get the number of observations below a certain percentile.

Values larger than zero. To speed up the numerical search procedure, it is also advisable to choose the initial values such that they are already close to the values that solve the system. A good choice for the initial asset value in cell B9 is the market value of equity plus the book value of liabilities. 12). 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.

Set equal to the standard deviation of the log asset returns computed with the At−a . For any further iteration k = 1 , end Iteration k: Insert At−a and from the previous iteration into the Black–Scholes formulae d1 and d2 . 7) to compute the new At−a . Again use the At−a to compute the asset volatility. We go on until the procedure converges. One way of checking convergence is to examine the change in the asset values from one iteration to the next. If the sum of squared differences between consecutive asset values is below some small value (such as 10−10 ) we stop.