Applying the Credit VaR Formula with the Standard Normal CDF

Summary

The document explains how to evaluate a credit VaR expression from a derivatives textbook when the intermediate normal quantiles seem to produce values different from the stated result. The calculation combines the standard normal quantile for the confidence level with a second quantile scaled by the square root of the default correlation parameter. It then divides by the square root of one minus that parameter to obtain a standardized threshold.

In the worked example, the expression evaluates to approximately negative 1.135. Applying the cumulative standard normal distribution to that threshold gives a probability of 12.8%, matching the book’s result. The answer also notes that spreadsheet function names differ across versions: the older cumulative distribution and inverse distribution names correspond to newer standard normal functions with an explicit cumulative option. The excerpt is a compact numerical clarification rather than a general derivation; it does not explain the credit model assumptions or discuss how the formula changes under other parameter choices.

Key ideas

• The formula first standardizes a combination of normal quantiles using the correlation parameter.
• The intermediate standardized threshold is approximately negative 1.135 in the cited example.
• Applying the standard normal cumulative distribution converts that threshold into the reported probability of 12.8%.
• Spreadsheet versions may use different names for cumulative normal and inverse normal functions.

Tags

# Credit VaR Formula


# Credit VaR Formula












in Chapter 23 of Hull's Options, Futures, and Derivatives he has an example (i.e. example 23.4) which shows how the Credit VaR formula is applied. The answer in the formula is 0.128. I can't seem to get the same answer since the N that get is either ±3.1951 or ±1.1351. It seems I need to get a distribution of N(0.551) = 0.128. May I ask how should be formula be understood? Thanks.

## Answer by Magic is in the chain (score 3)

https://quant.stackexchange.com/a/50400

Here is the excel formula with steps:

=NORMSDIST((NORMSINV(0.02)+NORMSINV(0.999)×SQRT(0.1))/SQRT(1−0.1))

=NORMSDIST((−2.054+3.09×SQRT(0.1))/SQRT(1−0.1))

=NORMSDIST(-1.135)

=12.8%

They keep changing the names of the function - e.g., NORMSDIST is NORM.S.DIST(-1.135,TRUE)in the recent versions, and same for NORMSINV = NORM.S.INV

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