What does TimeStep stand for?

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.

Luisa

Answer 1

[Gabo]

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.

Gabo

[Luisa]

Gabo,

thanks again for your help!

As I gather, you can remove the integral that makes the formula cumbersome to compute assuming that the credit event can only occur a finite number of times per year (obviously with a loss of accuracy depending on the number of finite points chosen).

It means that by leaving TimeStep at its default value you assume that a credit event can happen only every 10 days per year while if you wanted to set a monthly discretization frequency you should change TimeStep to 30 (days). Is it correct?

[Gabo]

Yes, for a monthly discretization, set TimeStep to 30.

[Luisa]

Thank you!