Re: Default probability between 2 dates

Posted by igitur on Jun 29, 2015; 9:54pm
URL: http://quantlib.414.s1.nabble.com/Default-probability-between-2-dates-tp16682p16688.html

Thanks. Yes, I assumed that one would want the conditional probability. The formula makes sense now.

much regards

On 27 June 2015 at 18:20, Peter Caspers <[hidden email]> wrote:

Bonjour Francois,

the value that is returned (i.e. p2-p1) is the probability to default
between t1 and t2.

Your expression simplifies to (p2-p1) / ( 1-p1 ) and is the
probability to default between t1 and t2 *given that* (or *conditional
on* to speak more mathematically) you survive until p1. I.e. it is P(
A | B ) = P( A and B) / P( B ), where A is the event to default until
t1 and B likewise the event to default until t2. Whereas the first
expression is P( A and B ).

Sometimes I get spontaneous headaches to spot the difference between
the two (anybody else, too ?). But say you are likely to default until
t1 (p1=90%) already and certain to die until t2 (p2=100%), then the
value p2-p1 returned in QL is 10% (since until t1 a lot might happen
already ...). Your expression is 100% on the other hand, i.e. if you
are lucky and survive until t1, then you are really doomed and just
heading for your final destintation on t2 for sure.

Does it make sense that way ?

Best regards and a beautiful weekend for you
Peter

On 27 June 2015 at 16:31, Francois Botha <[hidden email]> wrote:
> Hi,
>
> Shouldn't the calculation of the default probability between 2 dates ( see
> https://github.com/lballabio/quantlib/blob/master/QuantLib/ql/termstructures/defaulttermstructure.cpp#L117
> ) be:
>     return 1.0 - (1.0 - p2) / (1.0 - p1);
>
> Survival probabilities are cumulative / multiplicative, right?
>
> Francois Botha
>

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