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Default probability between 2 dates

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igitur

Default probability between 2 dates

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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Peter Caspers-4

Re: Default probability between 2 dates

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
>
> ------------------------------------------------------------------------------
> Monitor 25 network devices or servers for free with OpManager!
> OpManager is web-based network management software that monitors
> network devices and physical & virtual servers, alerts via email & sms
> for fault. Monitor 25 devices for free with no restriction. Download now
> http://ad.doubleclick.net/ddm/clk/292181274;119417398;o
> _______________________________________________
> QuantLib-dev mailing list
> [hidden email]
> https://lists.sourceforge.net/lists/listinfo/quantlib-dev
>

Peter Caspers-4

Re: Default probability between 2 dates

I messed it up, right. A is the event to default until t2. B is the
event to survive until t1. Hopefully.
Peter

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
>>
>> ------------------------------------------------------------------------------
>> Monitor 25 network devices or servers for free with OpManager!
>> OpManager is web-based network management software that monitors
>> network devices and physical & virtual servers, alerts via email & sms
>> for fault. Monitor 25 devices for free with no restriction. Download now
>> http://ad.doubleclick.net/ddm/clk/292181274;119417398;o
>> _______________________________________________
>> QuantLib-dev mailing list
>> [hidden email]
>> https://lists.sourceforge.net/lists/listinfo/quantlib-dev
>>

igitur

Re: Default probability between 2 dates

In reply to this post by Peter Caspers-4

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 <[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
>

> ------------------------------------------------------------------------------
> Monitor 25 network devices or servers for free with OpManager!
> OpManager is web-based network management software that monitors
> network devices and physical & virtual servers, alerts via email & sms
> for fault. Monitor 25 devices for free with no restriction. Download now
> http://ad.doubleclick.net/ddm/clk/292181274;119417398;o
> _______________________________________________
> QuantLib-dev mailing list
> [hidden email]
> https://lists.sourceforge.net/lists/listinfo/quantlib-dev
>

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