Author: Mayank Goyal FIA

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The methodology on how to calculate IBNR doesn’t only rely on the Method selected but how the selections of methods take place. You need to understand a few concepts before dwelling into reserving Methods like Chain Ladder, BF Method, and others.

In this Section, we will explain you the process of calculation of IBNR Reserves in General Insurance rather than numerical calculation. That will follow up soon after we understand the process completely.

Applying just the methods wouldn’t give you the IBNR or the outstanding reserves. It is important to understand the complete process.

Below are the steps which are generally been followed for calculation of IBNR reserves. These are explained in simplest terms and keeping in mind your level, the complications have been removed which may include providing a tail factor, age to age factors, weighted average development, interpolating LDFs and many other real life issues.

But still, these exercises will give you the knowledge for the questions asked in an interview up until 0 to 5 years. Yes! you got it right.

The processes are the same every time, methods are tweaked according to situation. Therefore, it becomes important to understand the process.

By an experienced Reserving/ Reinsurance Reserving GI professional

Many methods assume that the future pattern will follow past patterns. So, we will try to find the factor responsible for past incrementation. However, many times there are cases when we particularly do not consider a development year or an accident year due to adversities or change in processes. Simply, wherever the patter is hindered we do not consider that part.

Learning Methodology for IBNR Calculation

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Questions Related to Processes in IBNR Calculation

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Selecting LDFs require some experience and a number of statistical analytics and model distributions can be used to select it for a particular LOB(Line of Business). Each LOB has different features like short tail or long tail, data available, market point of view, and others.

Selecting Loss Development Factors (LDFs)

To select DFs to be used for projecting claims for future years, any of the following can be considered

• average of all the development factors can be taken or
• as a conservative measure, the largest development factor for any development year can be taken or
• the weighted average can be taken.

These all were already explained in the previous exercise.

Selecting loss development factors for unusual cases.

It is also possible that altogether different patterns are selected where they are not applicable. Like a new organization would go for benchmarked factors or may not use any development method at all or a new location for a multinational Insurance company, so they can use development factors of another region with a little tweak or delayed.

You will come to know in upcoming exercises how a new general insurance company usually calculate their IBNR’s when no development factors are available with them.

The selected age-to-age factor (a.k.a. claim development factor or loss development factor) represents the growth anticipated in the subsequent development interval.
Selections are based on a review of the historical claim development data, the age-to-age factors, the various averages of the age-to-age factors, and a review of the prior year’s claim development factor selections.

Selecting Benchmark LDFs

When the credibility of the insurer’s historical experience is limited, there may be a need to supplement the experience with benchmark data.
Possible benchmark includes:

• In case, the insurer is exposed to similar LOBs with matching case handling process
• LDFs from the industry which related to similar products and are comparable
• using LDFs of other geographical location with a delay

When using benchmarks, there may be significant differences between the line of business being analyzed and the benchmark with regard to claims practices, policy coverages, underwriting, geographic mix, claim coding, policyholder deductibles and/or limits, legal precedents, etc.

The following characteristics are considered when selecting DFs for a particular class.

1. Smoothened factors
   There should be a smooth progression of individual Loss development factors and average factors across development periods.
   In case, there is a development period that is adverse, it is generally removed from within the calculation. Refer to Example 2.
   A steadily decreasing incremental development from valuation to valuation
   
   
2. Stability of age-to-age factors for the same development period.
   
   As you see in the example, the development for 2-3 and 3-4 years should be almost the same with a little variance within each development interval (i.e. down the columns).
   
   
3. Changed Patterns and Historical experience
   There can be changes in claims practices, policy coverages, underwriting, geographic mix, claim coding, policyholder deductibles and/or limits, legal precedents in some years. The factors must be adjusted to involve a drastic change in any of these internal or external/ environmental/ regulatory factors.
   
   Has the insurer’s book of business and insurer operations changed over time?
   Have the effects of changes in external factors manifested themselves in the reported claims experience?
   
   
4. The credibility of the experience.
   We have read credibility Theory. There may be a time where we provide weights or use experience for a given AY and age.
   There may also be a time when some Benchmark DFs from the market may also be considered where credibility is lacking.
   
   
   
   

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The ELR method can also be used to set the loss reserve for particular business lines and policy periods.

What Is the Expected Loss Ratio – ELR Method?

Expected loss ratio (ELR) method is a technique used to determine the projected amount of claims, relative to earned premiums. The expected loss ratio (ELR) method is used when an insurer lacks the appropriate past claims occurrence data to provide because of changes to its product offerings and when it lacks a large enough sample of data for long-tail product lines.

The Formula for the ELR Method Is

ELR Method = EP * ELR – Reported Claims

How to Calculate Expected Loss Ratio – ELR Method

To calculate the expected loss ratio method multiply earned premiums by the expected loss ratio and then subtract paid losses.

What Does the ELR Method Tell You?

Insurers set aside a portion of their premiums from underwriting new policies in order to pay for future claims. The expected loss ratio is used to determine how much they set aside. It’s also important to note that the frequency and severity of the claims they expect to experience also plays a role. Insurers use a variety of forecasting methods in order to determine claims reserves.

In certain instances, such as new lines of business, the ELR method may be the only possible way to figure out the appropriate level of loss reserves required. The ELR method can also be used to set the loss reserve for particular business lines and policy periods. The expected loss ratio, multiplied by the appropriate earned premium figure, will produce the estimated ultimate losses (paid or incurred). However, for certain lines of business, government regulations may dictate the minimum levels of loss reserves required.

• Used to determine the projected amount of claims, relative to earned premiums.
• Insurers set aside a portion of premiums from policies to pay for future claims—the expected loss ratio determines how much they set aside.
• ELR is used for businesses or business lines that lack past data, while the chain ladder method is used for stable businesses.

Example of How to Use Expected Loss Ratio (ELR) Method

Insurers can also use expected loss ratio to calculate the incurred but not reported (IBNR) reserve and total reserve. The expected loss ratio is the ratio of ultimate losses to earned premiums. The ultimate losses can be calculated as the earned premium multiplied by the expected loss ratio. The total reserve is calculated as the ultimate losses less paid losses. The IBNR reserve is calculated as the total reserve less the cash reserve.

For example, an insurer has earned premiums of $10,000,000 and an expected loss ratio of 0.60. Over the course of the year, it has paid losses of $750,000 and cash reserves of $900,000. The insurer’s total reserve would be $5,250,000 ($10,000,000 * 0.60 – $750,000), and its IBNR reserve would be $4,350,000 ($5,250,000 – $900,000).

The Difference Between the ELR Method and the Chain Ladder Method (CLM)

Both the ELR and the chain ladder method (CLM) measure claim reserves, where the CLM uses past data to predict what happens in the future. While the expected loss ratio (ELR) is used when there’s little past data to go off of, CLM is used for stable businesses and business lines.

Limitations of Using the ELR Method

The amount of claims reserves that an insurer should set aside is determined by actuarial models and forecasting methods. Insurers often use the expected loss ratio on the amount and quality of data that is available. It is often useful in the early stages of forecasting because it does not take into account actual paid losses, but in later stages, this lack of sensitivity to changes in reported and paid losses makes it less accurate and thus, less useful.

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Bornhuetter-Ferguson (aka BF Method) combines features of the chain ladder and expected loss ratio methods and assigns weights for the percentage of losses paid and losses incurred

What is Bornhuetter Ferguson Technique

The Bornhuetter Ferguson technique (BF Method) is a method for calculating an estimate of an insurance company’s losses. The Bornhuetter Ferguson technique, also called the Bornhuetter Ferguson method (BF Method), estimates incurred but not yet reported (IBNR) losses for a policy year. This technique was created by two actuaries, Bornhuetter and Ferguson, and was first presented in 1975.

BREAKING DOWN Bornhuetter Ferguson Technique

Bornhuetter-Ferguson is one of the most-widely used loss reserve valuation methods, second only to the chain ladder method. It combines features of the chain ladder and expected loss ratio methods and assigns weights for the percentage of losses paid and losses incurred. Unlike the chain ladder method, which builds a model based on past experience, the Bornhuetter-Ferguson technique builds a model based on the insurer’s exposure to loss.

The chain ladder method examines the point over a period in time in which a claim is reported or paid. Insurers use this to “budget” for future losses, with the sum of all of the future losses equaling the IBNR. Claim estimates from past time periods are made concrete, based on loss experience. This means that the actuary swaps past estimates with actual claims.

The Bornhuetter-Ferguson technique estimates IBNR during a period of time by estimating the ultimate loss for a particular risk exposure, and then estimating the percent of this ultimate loss that was not reported at the time. Bornhuetter-Ferguson calculates the estimated loss as the sum of reported loss plus IBNR, with IBNR calculated as the estimated ultimate loss multiplied by the percentage of loss that is unreported. Loss estimates use priori loss estimates.

Bornhuetter Ferguson (BF Method) may be the most useful in cases where actual reported losses do not provide a good indicator of IBNR. This is more likely to be an issue when losses are low frequency but high severity. Severity refers to the amount you have received Insurance claim for. Average Severity would be the loss associated with an average Insurance claim., a combination that makes it more difficult to provide accurate estimates. It is easier for an insurer to predict what will happen with high frequency, low severity. Severity refers to the amount you have received Insurance claim for. Average Severity would be the loss associated with an average Insurance claim. claims.

The Bornhuetter Ferguson Calculation

There are two algebraically equivalent methods for calculating loss, according to the Bornhuetter-Ferguson technique. In the first approach, undeveloped reported (or paid) losses are added directly to expected losses (based on an a priori loss ratio), multiplied by an estimated percent unreported.

BF=L+ELR∗Exposure∗(1−w)

In the second calculation method, reported (or paid) losses are first developed to ultimate using a chain ladder approach and applying a loss development factor (LDF). Next, the chain ladder ultimate is multiplied by an estimated percent reported. Finally, expected losses multiplied by an estimated percent unreported are added (as in the first approach).

BF=L∗LDF∗w+ELR∗Exposure∗(1−w)

The estimated percent reported is the reciprocal of the loss development factor. IBNR claims are then figured by subtracting reported losses from the Bornhuetter-Ferguson ultimate loss estimate.

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The claims projections in this method is done using the past experience of how the claims have developed. The principle of this method is that historical loss development patterns (called development factor) are indicative of future loss development patterns.

The chain ladder or development method (CLM) is a method used to calculate IBNR reserves as a part of claims reserves estimate by insurers for reporting on their financial statements.

This method assumes that the future pattern will follow past patterns. So, we will try to find the factor responsible for past incrementation. However, many times there are cases when we particularly do not consider a development year or an accident year due to adversities or change in processes. Simply, wherever the patter is hindered we do not consider that part.

Learn Chain Ladder Method (CLM)

The chain ladder method calculates incurred but not reportedIncurred But Not Reported or IBNR reserves are a part of claims reserves estimated by insurers for reporting on their financial statements. Claims reserves are estimates of claims that have occurred on or before the financial statement report date but which have yet to be paid. This a current lia… (IBNR) loss estimates, using run-off triangles of paid losses and incurred losses, representing the sum of paid losses and case reserves. Insurance companies are required to set aside a portion of the premiums they receive from their underwriting activities to pay for claims that may be filed in the future. The amount of claims forecasted, along with the amount of claims that are actually paid, determine how much profit the insurer will publish in its financial documents.

Reserve triangles are two-dimensional matrices that are generated by accumulating claim data over a period of time. The claim data is run through a stochastic process to create the run-off matrices after allowing for many degrees of freedom.

At its core, the chain ladder method operates under the assumption that patterns in claims activities in the past will continue to be seen in the future. In order for this assumption to hold, data from past loss experiences must be accurate.

Several factors can impact accuracy, including changes to the product offerings, regulatory and legal changes, periods of high severity. Severity refers to the amount you have received Insurance claim for. Average Severity would be the loss associated with an average Insurance claim. claims, and changes in the claims settlement process. If the assumptions built into the model differ from observed claims, insurers may have to make adjustments to the model.

The calculation takes place completely using the age to ultimate factors, the factors which were selected in earlier exercises and we simply multiply the reported/incurred to those factors. You’ll be able to understand from the below exercise.

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