Sometimes I have an issue verbalising these tricky situations but I can try to offer some information on what mathematically is going on to retrieve unconditional and conditional PD, but it may or may not serve to better illustrate the confusing situation, but I do not believe this is wrong at all. Poisson processes are very clear in the fact that the probability of the event occurring in one time interval, is dependent on the length of the time interval, and is not at all relative to the order of it, and they are always independent of one another. The probability that the defaulting incident occurs within a time interval, is the unconditional PD, and perhaps unintuitively or intuitively, this decreases. Despite the time interval being the same 1 year, it decreases, this arises because deriving the probability of an event occurring WITHIN an interval of 2 values (t1 and t2) is: P(t1
the Terms used are confusing in the Definition of marginal probability it says it may be considered an unconditional probability. Marginal means unconditional. What we find here (1.98%) is definitely unconditional - it does not Change year to year, whereas what is called "unconditional" does Change.
@haoxue3 "instantaneuous" = "in any given instant" or arbitrarily small amount of time. This is just the core concept underlying calculus. The point in using "instantaneous" here is to distinguish it h(t) from a discrete measure (failure between two distinct points in time). In moving from discrete to continuous time we imagine the limit as del_t tends to 0 (or again, an arbitrary small fraction of time), so that h(t) can be said to occur in an instant rather than over a period.
Can you explain hazard rate in detail? What does "instantaneous" mean? I believe hazard rate is derived from survival analysis in statistics, if so, hazard rate is the same as conditional PD, but why one is 2% and the other is 1.98%? I don't quite get it.
Shouldn't the conditional prob be cumulatuve survival*uncoditional? Why do you divide it? The chance that it survives the first year and defaulting in the second should be a multiplication in my opinion. What am I missing here?
Your question is exactly why I am on this page now. Saw that in Schweser and couldn't fathom the why behind it. And what you have suggested should be done is what was done when mortality tables were considered in Chapter 2 of Book 3 in FRM Part 1.
According to Malz: the difference between the two- and one-year default probabilities-the probability of the joint event of survival through the first year and default in the second-is 1.94% above which is Unconditional or also called Joint PD = Conditional PD x Cum Survival.
Thanks for the vid. I guess what is missing , is a video which could explain intuitively the difference between uncdonditional and conditional default probability. When to use the unconditional and when to use conditional pd. Why would we want to condition the default pro in year 4 on the company having survived til the end of year 3 ? ... I need to think about this ;-)
why is the conditional prob not just = Cumulative Survival Previous Year * Unconditional PD, since Unconditional PD was explained as PD in a given year. The default in a given year can only happen with survival in the previous year, right?
This is fine but what if i want to predict the number time to failure..Not like this...trial and error..what is the prob of failure in 1,2,3,4,5...but directly a final number days the subject will survive..can I do that?
A couple things that were somewhat confusing to me here has to do with the concept of conditionality. When something is conditional, I'd expect for it to change depending on the condition. When something is unconditional, I'd expect for it remain unchanged regardless of the condition. You know... like uncontional love (a little joke). Here we see the opposite behaviors for the following PD's: The unconditional PD & conditional PD. The unconditional PD keeps changing. The conditional PD seems as though it is fixed. How could we explain this? Was there a typo in the spreadsheet? Like was it supposed to be the other way around? Thanks
the whole concept of 'condition PD' is quite amusing to me. So, you basically say that conditional PD in year 3 = probability of the company defaulting in year 3, provided that it survived up until year 2. I mean, how can I company default in year 3, if it had not survived up until year 2. Why is that even a condition? it is like saying: the probability that mr. Ben is alive in his 40th year provided that he did not die up until he is 40. Why would there ever be a question of Ben being alive or not when he is 40, if he is already dead before that. Why should that even be a condition?
![Hazard and Survival Functions - [Survival Analysis 5/8]](http://i.ytimg.com/vi/zAdF8WSyfsA/mqdefault.jpg)
![Hazard and Survival Functions - [Survival Analysis 5/8]](/img/tr.png)
Sometimes I have an issue verbalising these tricky situations but I can try to offer some information on what mathematically is going on to retrieve unconditional and conditional PD, but it may or may not serve to better illustrate the confusing situation, but I do not believe this is wrong at all.
Poisson processes are very clear in the fact that the probability of the event occurring in one time interval, is dependent on the length of the time interval, and is not at all relative to the order of it, and they are always independent of one another. The probability that the defaulting incident occurs within a time interval, is the unconditional PD, and perhaps unintuitively or intuitively, this decreases. Despite the time interval being the same 1 year, it decreases, this arises because deriving the probability of an event occurring WITHIN an interval of 2 values (t1 and t2) is:
P(t1
the Terms used are confusing in the Definition of marginal probability it says it may be considered an unconditional probability. Marginal means unconditional. What we find here (1.98%) is definitely unconditional - it does not Change year to year, whereas what is called "unconditional" does Change.
@haoxue3 "instantaneuous" = "in any given instant" or arbitrarily small amount of time. This is just the core concept underlying calculus. The point in using "instantaneous" here is to distinguish it h(t) from a discrete measure (failure between two distinct points in time). In moving from discrete to continuous time we imagine the limit as del_t tends to 0 (or again, an arbitrary small fraction of time), so that h(t) can be said to occur in an instant rather than over a period.
Can you explain hazard rate in detail? What does "instantaneous" mean?
I believe hazard rate is derived from survival analysis in statistics, if so, hazard rate is the same as conditional PD, but why one is 2% and the other is 1.98%?
I don't quite get it.
Shouldn't the conditional prob be cumulatuve survival*uncoditional? Why do you divide it? The chance that it survives the first year and defaulting in the second should be a multiplication in my opinion. What am I missing here?
Your question is exactly why I am on this page now. Saw that in Schweser and couldn't fathom the why behind it. And what you have suggested should be done is what was done when mortality tables were considered in Chapter 2 of Book 3 in FRM Part 1.
According to Malz: the difference between the two- and one-year default probabilities-the probability of the joint event of survival through the first year and default in the second-is 1.94% above which is Unconditional or also called Joint PD = Conditional PD x Cum Survival.
Thanks for the vid. I guess what is missing , is a video which could explain intuitively the difference between uncdonditional and conditional default probability. When to use the unconditional and when to use conditional pd. Why would we want to condition the default pro in year 4 on the company having survived til the end of year 3 ? ... I need to think about this ;-)
why is the conditional prob not just = Cumulative Survival Previous Year * Unconditional PD, since Unconditional PD was explained as PD in a given year. The default in a given year can only happen with survival in the previous year, right?
In other words the term unconditional is very confusing since the condition is that the item did survive in the previous years.
I know it is and old video but could I obtain the spreadsheet? thanks!
This is fine but what if i want to predict the number time to failure..Not like this...trial and error..what is the prob of failure in 1,2,3,4,5...but directly a final number days the subject will survive..can I do that?
A couple things that were somewhat confusing to me here has to do with the concept of conditionality. When something is conditional, I'd expect for it to change depending on the condition. When something is unconditional, I'd expect for it remain unchanged regardless of the condition. You know... like uncontional love (a little joke).
Here we see the opposite behaviors for the following PD's: The unconditional PD & conditional PD. The unconditional PD keeps changing. The conditional PD seems as though it is fixed.
How could we explain this? Was there a typo in the spreadsheet? Like was it supposed to be the other way around?
Thanks
the whole concept of 'condition PD' is quite amusing to me. So, you basically say that conditional PD in year 3 = probability of the company defaulting in year 3, provided that it survived up until year 2. I mean, how can I company default in year 3, if it had not survived up until year 2. Why is that even a condition?
it is like saying: the probability that mr. Ben is alive in his 40th year provided that he did not die up until he is 40. Why would there ever be a question of Ben being alive or not when he is 40, if he is already dead before that. Why should that even be a condition?
Best example