Developing an IBNR Model

[RANGERS684]

I'm in the procees of trying to develop an IBNR model and I was hoping you could provide me with some help. I am trying a couple different methods and getting some vastly different results.

In the first method, I am building completion factors by looking at the incurred/paid patterns of historical months which have already matured (i.e more than 12 months old) and averaging their collective first months' completion factors, second months' completion factors ... I then take these average completion factors and apply to my most recent months - so I divide the most recent month by the avg 1st month completion factors, divide the second most recent month by the average 2nd month's completion factors...in order build the incurred amounts for my recent months. The problem I have with this method is that I am essentially taking old completion factors, because in order for me to calculate the historical months' completion factor in my triangle it has to be mature or over 12 months old. The claims systems may have sped up in the last 12 months.

In the second method, I look at any incurred month which has at least 2 months of runout and I'm taking the cumulative paid claims through the 2nd month and dividing it by cumulative paid claims through 1 month. I did the same for 3rd month over 2nd month and so on. I then average the cumulative increases over one another for each month (2 over 1, 3 over 2..) over the last 12 months for which such experience is available and apply that to my most recent months experience to develop their cumulative incurrals. The problem with this method is that one month may have a 1.6 factor of 2nd month over 1st whereas another has a 3.7 factor. Then, I get very different results based on which months are included in my average factors.

The swings are much more sensitive to the cutoff point in the second method than in the first but the first uses old data to calc completions whereas the second uses recent development factors. Are either of these approaches the right method for calculating IBNR? How can I refine these methods to get a more consistent and current result?

Thanks for your help.

[life_actuary_student]

Originally Posted by RANGERS684

I'm in the procees of trying to develop an IBNR model and I was hoping you could provide me with some help. I am trying a couple different methods and getting some vastly different results.

In the first method, I am building completion factors by looking at the incurred/paid patterns of historical months which have already matured (i.e more than 12 months old) and averaging their collective first months' completion factors, second months' completion factors ... I then take these average completion factors and apply to my most recent months - so I divide the most recent month by the avg 1st month completion factors, divide the second most recent month by the average 2nd month's completion factors...in order build the incurred amounts for my recent months. The problem I have with this method is that I am essentially taking old completion factors, because in order for me to calculate the historical months' completion factor in my triangle it has to be mature or over 12 months old. The claims systems may have sped up in the last 12 months.

In the second method, I look at any incurred month which has at least 2 months of runout and I'm taking the cumulative paid claims through the 2nd month and dividing it by cumulative paid claims through 1 month. I did the same for 3rd month over 2nd month and so on. I then average the cumulative increases over one another for each month (2 over 1, 3 over 2..) over the last 12 months for which such experience is available and apply that to my most recent months experience to develop their cumulative incurrals. The problem with this method is that one month may have a 1.6 factor of 2nd month over 1st whereas another has a 3.7 factor. Then, I get very different results based on which months are included in my average factors.

The swings are much more sensitive to the cutoff point in the second method than in the first but the first uses old data to calc completions whereas the second uses recent development factors. Are either of these approaches the right method for calculating IBNR? How can I refine these methods to get a more consistent and current result?

Thanks for your help.

There are "a lot" of resources about developing claim triangles, although, as you point out if the claims process is significantly different now than it was early in the data, the results will be inconsistent. Whenever I see actuary, art and science in the same sentence, I immediately think of claim triangles.

The new idea I'll throw out there is total incurred costs--are there pmpm charges that look consistent?

[MarsLasar]

Originally Posted by RANGERS684

I'm in the procees of trying to develop an IBNR model and I was hoping you could provide me with some help. I am trying a couple different methods and getting some vastly different results.

In the first method, I am building completion factors by looking at the incurred/paid patterns of historical months which have already matured (i.e more than 12 months old) and averaging their collective first months' completion factors, second months' completion factors ... I then take these average completion factors and apply to my most recent months - so I divide the most recent month by the avg 1st month completion factors, divide the second most recent month by the average 2nd month's completion factors...in order build the incurred amounts for my recent months. The problem I have with this method is that I am essentially taking old completion factors, because in order for me to calculate the historical months' completion factor in my triangle it has to be mature or over 12 months old. The claims systems may have sped up in the last 12 months.

In the second method, I look at any incurred month which has at least 2 months of runout and I'm taking the cumulative paid claims through the 2nd month and dividing it by cumulative paid claims through 1 month. I did the same for 3rd month over 2nd month and so on. I then average the cumulative increases over one another for each month (2 over 1, 3 over 2..) over the last 12 months for which such experience is available and apply that to my most recent months experience to develop their cumulative incurrals. The problem with this method is that one month may have a 1.6 factor of 2nd month over 1st whereas another has a 3.7 factor. Then, I get very different results based on which months are included in my average factors.

The swings are much more sensitive to the cutoff point in the second method than in the first but the first uses old data to calc completions whereas the second uses recent development factors. Are either of these approaches the right method for calculating IBNR? How can I refine these methods to get a more consistent and current result?

Thanks for your help.

Is your block fairly stable?

[RANGERS684]

Block is very stable. I understand the need for art but I am a bit unsure as to whether I'm even using the appropriate methodologies.

Which one (if either) of these two are considered the standard approach?

[Polly Nomial]

I like method 2 better since it uses more recent data. You might try looking at each group of factors e.g. 6 occurrances of 2 over 3's. Perhaps the average is not the best choice. Can you see a trend? If not, perhaps throw out the high and low before averaging. Also, if your most recent months are far from complete, you might skip the completion factors altogether and find a pmpm to use for the assumed complete claims. Hope this helps.

[Dr T Non-Fan]

Originally Posted by RANGERS684

Block is very stable. I understand the need for art but I am a bit unsure as to whether I'm even using the appropriate methodologies.

Which one (if either) of these two are considered the standard approach?

Either is equally fine. The choice hinges more on the block of business than the myth that there is one standard approach. Oh, and neither is the standard approach.

What I would like you to do is determine your first-month completion factor's STANDARD DEVIATION and decide whether the average is reasonable estimate of that month's ultimate completion factor. You can also check your history's estimates of first-month completion factor based both on estimates you had at the time and on what you have now.
After this, I hope you will realize that you might need a different method for estimating the IBNR than by estimating completion factors.

What you might want to try is to estimate the completed incurred claims of the most recent months by trending forward and seasonalizing estimates of past completed (and normalized) incurred claims.

If your block of business has a substantial running inventory, you might want to create a model that estimates separately the IBNR from the RBNP, especially if the substantial inventory fluctuates wildly.

Lastly, you could also look at the pattern of completion as a PMPM instead of a ratio. The major assumption for this idea is that IBNR claims are not a function of what has already been paid, something most actuaries are adverse to believing. I mean, a change in claims processing speed would invesely affect IBNR -- if more were paid early, then less would be paid later, and vice versa. Of course, someone in claims processing should be able to tell you whether the processing speed has increased or not. Emphasis on "should."

[JMO]

Always trust health insurance techniques from DTNF.

[Dr T Non-Fan]

Originally Posted by JMO

Always trust health insurance techniques from DTNF.

Ain't nothing there that no one shouldn't know.

[G.O.A.T.]

I didn't see the product mentioned, but gap products (Medigap) cause signficant seasonality.

If that comes into play, also consider that.

[Dr T Non-Fan]

Originally Posted by G.O.A.T.

I didn't see the product mentioned, but gap products (Medigap) cause signficant seasonality.

If that comes into play, also consider that.

More importantly, they cause inverse-like seasonality relative to Individual products with a deductible. Someone choosing one set of seasonal factors for all products might find themselves in a bit of hurt during the pricing exercise.