Re: [Quantlib-dev] Default probability between 2 dates

[Francois B. <ig...@gm...>]

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

much regards

Francois Botha

On 27 June 2015 at 18:20, Peter Caspers <pca...@gm...> 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 <ig...@gm...> 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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