How can you calculate Pure IBNR and IBNER from the IBNR within 5 minutes?
Calculation of IBNER and Pure IBNR
This article gives a brief about the different
forms of IBNR component and its estimation that we generally come across in the
General Insurance industry.
Hopefully everyone is already familiar with
the other terms of GI before reading this article. It will be useful to familiarize
yourself with the following terms before reading this article any further
(Ultimate Claims, Reported Claims, Incurred, Accident/Underwriting/Reporting
Year Cohort, Chain Ladder Estimate, BF Estimate).
Before we get to the estimation, let us
first clear our understandings of the various terms.
Incurred but not reported (IBNR): For a particular year the actuaries estimate the Ultimate Cost
(generally referred as the Ultimate Claims) for all the business that has been written.
This ultimate cost can be divided into Incurred Claims (Reported claim amount)
and IBNR.
IBNR can be further split down to two
categories:
1)
Incurred but not enough reported
(IBNER): This portion of the IBNR refers to the not reported amount for the
already reported claims. To simply this let us take an example: A company
received a claim for Motor Insurance of Rs. 10,000 which will be recorded as
the Incurred Claim amount. However based on experience the Actuary estimates that
the final cost of the claim would be Rs. 15,000. Hence the difference of Rs.
5,000 is treated as the IBNER component of the claim.
2)
Pure IBNR: This portion of the
IBNR is the component that refers to the claims cost for the claims which have
not been reported till now. We can also understand this as new claims which are
not in the book but are expected to be experienced. For ex – A company has
written some business in an area against which it has received 10 claims.
However based on experience the Actuary estimates these claims to be 15 in
total. Hence the cost of the additional 5 claims is considered as Pure IBNR.
When we estimate the Ultimate Claims for
General Insurance classes on a Reporting Year cohort we will be estimating the
final cost of the Claims which have already been reported to the company. Hence
any IBNR suggested under this methodology would all be IBNER as we would not be
expecting to incur any further reported claims under this basis.
However, when we perform projections on an
Underwriting Year/Accident Year basis we face the issue of IBNER and Pure IBNR.
Please note that in general there is no need for the Actuary to split his
results between IBNER and Pure IBNR but we still need to have an understating
to explain the IBNR component in totally to other stakeholders.
A general method used to separate out the
IBNER and Pure IBNR component can be based on the Average Cost per Claim Method
(ACPC).
When we estimate the ultimate claims based on Incurred/Paid amount in general for a RunOff triangle we do not go into the separation of the Claims Cost by each Claim. We can also estimate the ultimate claims cost by the ACPC method. The estimation would require estimate the ultimate claim count to be the expected and also estimating the ultimate average claim cost expected.
When we estimate the ultimate claims based on Incurred/Paid amount in general for a RunOff triangle we do not go into the separation of the Claims Cost by each Claim. We can also estimate the ultimate claims cost by the ACPC method. The estimation would require estimate the ultimate claim count to be the expected and also estimating the ultimate average claim cost expected.
Let us understand this with an example.
Suppose we have the reported claims and
incurred amounts data for a few Accident Years. Using the standard techniques
we have estimated the ultimate number of claims for each of the AYs. These can
be seen below:
AY

Reported Claims

Ultimate Claims

Unreported claims

2015

140

140

0

2016

150

150

0

2017

140

145

5

2018

135

150

15

2019

100

155

55

Further, based on the Incurred Amounts we
have estimated the current Average Cost per Claim (Incurred Amounts/Reported
Claims). Again using the standard estimation techniques we will estimate the
ultimate ACPC for each of the AYs.
AY

ACPC

Ultimate ACPC

2015

1000

1000

2016

1100

1100

2017

1050

1100

2018

900

1150

2019

700

1145

Based on the above two tables we can
estimate the IBNR component for these claims.
AY

Incurred Amount

Ultimate Amount

IBNR

2015

₹ 1,40,000.00

₹ 1,40,000.00

₹ 

2016

₹ 1,65,000.00

₹ 1,65,000.00

₹ 

2017

₹ 1,47,000.00

₹ 1,59,500.00

₹ 12,500.00

2018

₹ 1,21,500.00

₹ 1,72,500.00

₹ 51,000.00

2019

₹ 70,000.00

₹ 1,77,475.00

₹ 1,07,475.00

Incurred
Amount = Reported Claims * ACPC
Ultimate Costs = Ultimate Claims * Ultimate ACPC
IBNR = Ultimate Costs – Incurred Amount
Ultimate Costs = Ultimate Claims * Ultimate ACPC
IBNR = Ultimate Costs – Incurred Amount
Please note that the IBNR estimated in the
table above is the total IBNR (IBNER + Pure IBNR). Based on the information
above we can estimate the IBNER and Pure IBNR components:
AY

IBNER

Pure IBNR

IBNR

2015

₹ 

₹ 

₹ 

2016

₹ 

₹ 

₹ 

2017

₹ 7,000.00

₹ 5,500.00

₹ 12,500.00

2018

₹ 33,750.00

₹ 17,250.00

₹ 51,000.00

2019

₹ 44,500.00

₹ 62,975.00

₹ 1,07,475.00

IBNER
= (Ultimate ACPC – ACPC) * Reported Claims
Pure IBNR = Ultimate ACPC * Unreported Claims
IBNR = IBNER + Pure IBNR
Pure IBNR = Ultimate ACPC * Unreported Claims
IBNR = IBNER + Pure IBNR
This is the most straightforward method to
estimate the IBNR components. There have been various researches and papers
written to estimate this using other statistical techniques as well. Interested
people can look at the papers available on CAS/IFoA websites or any other
Actuarial Forums.
Follow Writer of this article on LinkedIn : Ujjaval Agarwal
Note: On behalf of Actuary Sense, i would like to thank Ujjaval Agarwal for writing this article in a very easy language which is easily interpreted by our readers. Mr. Ujjaval is an Actuarial Consultant with RSA and prior to that associated with PwC
Follow me on LinkedIn: Kamal Sardana
Nice article, Ujjaval. Keep it up.
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