MATLAB: What does TimeStep stand for

cdsbootstrapfixed-income tool box

Hi guys,
I have a doubt about an input of the function cdsbootstrap, home someone can help me. Among the optional arguments there is TimeStep defined as "positive integer indicating the number of days to take as time step for the numerical integration" and set by default at 10 days. Does TimeStep represent the assumption about the frequency at which default can occur (e.g. once a week, once a month…)? Many thanks.

Best Answer

Hi Luisa,
TimeStep has more of a numerical meaning, although it might be interpreted as you describe, I think.
If you look at the protection leg formula in the reference page of cdsspread, you'll see an integral, which is approximated numerically with a finite sum (the second 'equal' sign should actually be an 'approx' sign). You discretize the time by choosing the tau's in those formulas. TimeStep is the difference between those tau's. Smaller values of TimeStep lead to a more accurate approximation of the integral, but it takes longer to evaluate. Depending on the particular survival curve you have, the results may be more or less sensitive to this parameter.
Note that the tau's are different from the t's in the RPV01 formulas. The t's are determined by the CDS contract, they are the premium payment dates. The tau's are arbitrarily chosen to perform the numerical integration.