Credit Default Swaps (CDS) for Non-Financial Firms — Mathematics
This article series will be about credit default swap premium calculation for Turkish BIST30 non-financial firms. First part will be general introduction of the concept, second part about mathematical background and third part about detailed calculations for specific firms.
The second part of the article will deal with some mathematics underlying the calculation of CDS for public non-financial firms. If you are not familiar with the underlying mathematics, you may skip (which I do not advise) to third part which has the results for BIST30 firms.
Let’s define the parameters for the calculation.
Then our basic formula will be
where N is normal cumulative distribution function. By using properties of normal distribution fuction and the fact that debt is assets minus equity, we can also derive present value of the risky debt as
Before continuing, let’s make an easy calculation where we have the value of asset volatility and value.
As mentioned in the first part, asset volatility and value cannot be observed directly but we can make use of the second formula where
