This article will concentrate on highlighting a number of key considerations to be taken by reinsurers when pricing for reinsurance especially for small and national reinsurers that generally lack the skills available to global multinational reinsurers. The approach taken is to focus on the fundamentals as sophistication that divorces from fundamentals (Mortgage Backed Securities, 2008 crisis) merely drowns us in the ‘unintended’ consequences of such complications.

Reinsurance is priced around two methodologies:[1]

1. experience rating

2. exposure rating

A lot has been said on these two measures in a lot of publications but we will highlight only some key points here. There is normally no homogenous class of risks that can be collectively priced and each treaty and proposal for facultative coverage has to be assessed on its own. The burning cost shows the average cost to settle claims for a particular reinsurance arrangement. Loss ratio is simultaneously analyzed to corroborate the burning cost as it will need explanation if a treaty has high burning cost but low loss ratio.

Exposure rating sees the exposure that is at risk instead of historical experience. It takes a forward-looking approach rather than the historical approach of experience rating. However as best to our knowledge, there are very few ILFs to guide quantitative exposure rating specific to developing countries. Relationship building, qualitative market assessment and reinsurance cycles are the bread and butter of how reinsurance is performed, especially in developing countries.

Reinsurers in developing countries should be cautious when using Generalized Linear Modeling (GLM) for emerging markets at this stage for most of reinsurance pricing as there is little data available, the data is heterogenous and not credible enough to sufficiently train and test the GLM model in most cases. GLM is extensively used in personal lines like motor and medical pricing because of large data and relatively homogenous risks as compared to commercial insurance and truncated & layered reinsurance data.

Insurers buy reinsurance to stabilize results, reduce volatility in results and reduce peak risk. What this does basically is that reinsurance swaps underwriting risk with credit risk of the reinsurer, which is normally lower. This swapping benefit along with commissions make reinsurance more capital efficient.

Ultimately, the uncertainty surrounding reinsurance pricing cannot be eliminated or even minimized, it can only be contained. This is because while insurers take on tail risks for consumers, reinsurers take on tail risks of insurers and hence by definition is in the business of extremes and tail risk management. Moreover, if reinsurance losses were known with certainty, there would be no need for reinsurance in the first place.  

Value at Risk is a useful tool for management of downside risks. It shows how much we stand to lose at a minimum over a specified confidence and time interval. For instance, motor bodily injury VaR is $250,000 (with 95% confidence interval over 1 year) which means that this $250,000 is the minimum floor which will be exceeded for the 5% worst case losses. However, this floor tells us nothing about how much the losses will go once it exceeds the minimum floor value. For better assessment of tail risks, VaR should be complemented with Tail Value at Risk see how worse can large losses really go when they exceed the minimum VaR floor. For instance, the TVaR for motor bodily injury is $3 million which shows that when 5% worst cases losses will occur and exceed the VaR floor, the average value of such claims will be AED 3 million.

It is important not to take confidence and comfort in precision and quantitative assessments. VaR has become famous for inducing a false sense of security by for instance implying that 95% claims will occur within $250,000 amount. This is dangerous because when tail events do occur, they are more than capitalization of the whole company in question. A case in point in is the 63 floors luxury Address Hotel in Dubai which burnt in new years’ eve and lead to extremely massive clash cover claim which is still under development. Companies had hardly ever seen such event before.

Some products do not have maximum liability and are unlimited like motor bodily injury, workmen compensation’s bodily injury and certain umbrella terms. Hence the reinsurer should carefully evaluate experience to form realistic expectations of such losses. Moreover, even when there are very high but maximum limits, actual losses can still be higher due to Extra Contractual Obligations. Emerging liabilities like liability catastrophes and mass torts like asbestos highlights these points accurately.

Commercial general liability, product liability and all risks products are especially vulnerable to such emerging liabilities. It is of no importance that previous mass liabilities are excluded in today’s contracts as no one emerging liability is the same. The next major liability catastrophe will be mostly covered in today’s benefits in one form or the other.

Inflation is also a far more important consideration in reinsurance than insurance. This is because many trends like health insurance, tort and legal claims are not following the economic inflation and is in most cases much higher than the economic inflation. Moreover, inflation is not constant over all sizes of claims. For claims with larger amounts, inflation is greater relative to small claims. This means that inflation is superimposed inflation for reinsurance, especially for facultative and excess of loss which absorbs only large claims.

The insurer has to be holistic as well and see the aggregate Reinsurance protection instead of seeing only by lines of business. This is because CAT, aggregate XOL and whole account treaties are also there that takes aggregate loss experience of many lines of business into account.

Reinsurance is effective for both life and general insurance. For life, reinsurance builds protection against new business strain. For general, reinsurance builds capacity for underwriting capacity and economies of scale.

Two other important factors for reinsurance are capital fungibility and loss absorbing capacity. Capital fungibility means surplus capital can be transferred from one country, client, geography etc. to another without hurdles. Regarding loss absorbing capacity, Clash covers has the effect of accumulating and losses. Short tailed liabilities and losses are better absorbed than long tailed which can be more extensive and long term.

Correlation is very important to take into account for reinsurance. Think what the key correlations might be and try to model these explicitly. For example, if pricing is needed for a whole-account treaty that covers six lines of business, two of which are correlated to, say, stock market performance – in the simulation model these can be treated dependently.

Fat tails represent correlation that has not been recognized. Fat tails are much more prevalent in large losses and reinsurance as reinsurers are harbinger of tail liabilities. Two approaches are suggested to take these into account. Firstly, deep underwriting experience and market intuition as well as expert opinion should not be discarded. This qualitative input can be as important as quantitative, if not more. Secondly, complexity science is a whole field dedicated to handling the complexities of reality but it is not expected that this emerging field will be practically implemented by companies in emerging markets. Hence, for the foreseeable future, the main recourse should be on integrating expert opinion to understand correlations better.

Due to the lack of data, it can be difficult to model correlation rigorously. Even the covariance of 2 variables is often difficult to estimate. It may be that a simple model of linear correlations makes more practical sense that a more complex method (copulas etc.). The time saved with the simplified modelling can be used to test the model. The reinsurance actuary in collaboration with underwriters should try correlating a minimal number of variables with crude correlation coefficients, such as by restricting the choice of correlation to one of:[2]

o 0% No correlation

o 30% Weak correlation

o 60% Reasonable correlation

o 90% Strong correlation

When doing this, remember that 30% correlation for example really is weak and will not have a dramatic impact.

Another factor that can significantly skew rate level indices is what we would call “cycle spikes” i.e. chunks of opportunistic business written at appropriate times in the underwriting cycle. When markets are hard, the underwriter may write an extra-ordinary category of business at exceptional rates. When markets soften, they will rapidly ditch this same block of contracts. Such behavior can lead to exaggerated swings in the rate level index that are actually not reflective of what is happening in the “core” business. Applying this to price core reinsurance can be misleading.[3]

For the actuary, given the cyclical nature of market rates, it is worthwhile tracking the technical rates as a consistent benchmark against which to monitor. It is hard to infer anything from individual risks deviating from benchmark, but observing an entire portfolio moving up or down can be very instructive.[4]

Due to the limited amount of data available, it is often quite difficult to accurately price a Clash cover. Actuarial judgment and market knowledge are necessary and so are discussions with the underwriter. Sometimes the source of a potential clash will be obvious (e.g. medical malpractice, where there are often several doctors and a hospital all named in the same lawsuit, a fire in building triggering multiple other insurances as well) and in other cases it might be less obvious (e.g. cat reinsurance in non-cat prone zones).

How does the insurer then monitor its accumulations? Sometimes this simply is not possible, for example Marine Hull and Cargo classes obviously clash but it isn’t feasible to monitor the contents and exact whereabouts of every container throughout the year. If the accumulations are not properly monitored, we should not rely exclusively on the available information as it probably underestimates the risk. Building in a margin for the unreported accumulations can help reduce such potential accumulations.[5]

There are material differences even between distributions that are similar. For instance, data can be fit using Lognormal or Pareto distribution with similar moments and goodness of fit. Both of these can have similar aggregate expected losses but the recoveries on high level layers of excess of loss can be significantly different and hence will materially change the evaluation on the adequacy of the depth of aggregate reinsurance coverage. [6]

If there are no large losses above high excess layers, the Monte-Carlo or stochastic model should avail market knowledge that are deterministic such as using ILFs to assess these higher layers. While ILFs are mentioned in reports in developed countries and can be easily bought by insurers, there appears to be no market wide initiative for GCC markets to make ILF curves or yield curves that national insurers and reinsurers can avail.

Flat rates must be avoided as they are not sustainable for the relationship between reinsurer and insurer over the long term. If insurer has good loss ratios, it will resent the lower commissions given to reinsurer and will cite that most of the profit from the portfolio is being taken by the reinsurer and vice versa when loss ratios are high. Sliding scale commission and swing rates avoid this contention over equity and induces better sense of fairness in business relationship between insurer and reinsurer.

Insurance companies do not become insolvent due to having vulnerable balance sheets. As insurance is the business of risk taking so there are always vulnerabilities that have the potential to cascade and develop into a larger crisis. This vulnerability is kept in balance by risk management and market confidence.

This is why stress testing should be performed regularly by insurance and reinsurance companies. The realistic side of stress testing also shows that practically stakeholders do not withhold action until the entire share capital has evaporated to react to an insurance company under stress. Their actions are preemptive while they can still reclaim some of their investments. So, despite the stress testing showing insolvency in for example, 4 years, the realistic bankruptcy will usually likely occur much sooner.

It must be emphasized that assumptions are not static quantitative undertakings that occur and impact in silos but rather they form an interesting pact with other assumptions and the broader economic and social context. 

Based on stress testing assumptions, the company’s management should understand the insurance business as the specificity of the insurance-related-reverse production cycle (collecting premiums first, paying out claims later and accumulating assets to cover future payouts) and the requirement to control and mitigate operational risks that are generated everywhere in the insurance value chain. [7]Future claims payments are effectively pre-funded by premium income.

Finally, since they are funded long term, insurers are essentially “deep-pocket” investors which can act counter-cyclically. This makes insurers react very differently to downward market pressure compared with a short-term bank and allows them to still maintain focus on the long term.[8]

Moving on, reinsurers are not first risk takers at the same level of front-line insurers but act as backstop. This means that they are not transmitters but absorbers of risk materialization. But as such they have their own limits to risk absorbing and this will determine the reinsurer credit risk level for the insurer.[9]

The results of stress tests and the interpretation of associated findings are heavily influenced by data availability/granularity, the scope and calibration of macro-financial risks, and the assessment of vulnerabilities to these risks. In particular, these difficulties relate to the following issues:[10]

  1. The risk factors are bound to change over time, which can affect the robustness of stress test results.
  2. The impact of shocks depends on valuation methodologies, whose robustness may be undermined by the very stress events the methodologies are designed to measure. Systemic risks affecting financial stability generally arise from uncertainty, that is, rare and non-recurring events rather than repeated realizations of predictable outcomes. This reality might limit the usefulness of certain (quantitative) measures and actuarial valuation models based on robust statistics (which tend to rely on the convergence of prices and parameters to long-term expectations).
  3. The interpretation of macro-financial shocks and their impact on capital adequacy involves a trade-off between accuracy and timeliness. The historical sensitivity of sample firms to macro-financial shocks is essential to assessing the combined impact of selected risk factors over a pre-defined forecast horizon of stress. While reliance on past experiences enhances confidence in the predictability of how shocks impact capital ex ante, it may also make it difficult to interpret signals and provide early warnings without hindsight bias.

Insurers resemble financial corporations as they leverage themselves by issuing risky debt, i.e. insurance policies. Insurers have competitive advantage in creating value by borrowing in insurance (not capital) market. Also, Insurers are financed by their principals (shareholders).[11]

Analyzing reinsurance in such ‘financial market theory’ means that there is tradeoff between the purchase of reinsurance and the risk capital required to maximize shareholders’ value. Reinsurance creates an additional layer of synthetic equity capital to mitigate expected financial distress costs. Hence, the decision to reinsure can be treated as both a risk-management and a capital-structure tool for creating shareholders’ value.[12]

Practical Reinsurance Reflections

Lloyd’s report[13]  on reinsurance pricing highlighted two over-arching beliefs that are relevant to us as well which are “intelligent execution” and “communication”. Intelligent Execution means remembering the context of the information and environment and focusing most of the time on getting a solid grasp of the key dynamics involved, rather than spending too much time worrying about theoretical purism around the edges. Communication is as much about convincing people of what we do not know and what you cannot infer, as it is about what we do and can.

Reinsurance arrangements are required to have protection against severe or multiple occurrence of losses. Assuming that business is being written on profitable terms the transfer of risk to reinsurers also shrinks the profit margins of primary insurers as obviously, reinsurers would also seek to make profits. Therefore, any reinsurance arrangement needs to be optimized so as to retain the maximum levels of risks accepted by the company’s capital structure and the risk profile of its portfolio and thus enjoying maximum return.

Any difference in the level of profitability between the risk retained by the company and that reinsured could result from either:

  • discrepancies in the effective rate at which risks are ceded to reinsurers and that charged by the company to clients; or
  • the company’s pricing mechanism not having adequate loadings to meet commissions and expenses.

Assuming that business is being written on profitable terms the transfer of risk to reinsurers also shrinks the profit margins of primary insurers as obviously, reinsurers would also seek to make profits. Therefore, any reinsurance arrangement needs to be optimized so as to retain the maximum levels of risks accepted by the company’s capital structure and the risk profile of its portfolio and thus enjoying maximum return.

An insurance company can feel the requirement to reinsure certain risks on a facultative basis rather than cede it under a treaty.

  • Coverage is required against the exclusions of the treaty
  • Coverage is required for the cases where MPL is breached (treaty capacity)
  • Cases cannot be priced due to underwriting capacity (i.e., underwriters feel that they do not have the experience to underwrite specific risks)
  • Cases of fronting arrangement

Although the cases which require facultative cover are few in numbers than those covered by the treaty, but due to their significant share in terms of premium volume they need to be carefully assessed.

For reinsurance, the market rate can be quite different to actuary’s technical rates, for a number of reasons[14]:

  • The lead underwriter(s) might have made a different assessment of the risk based on their own knowledge and experience.
  • This might be cycle related: in a hard market, the underwriter is taking advantage and writing for abnormal profits, or in a soft market the main focus is on client retention instead of sound pricing
  • Sometimes there will be significant terms and conditions or other more qualitative features of the risk that are factored in to the market rate (up or down), but which do not feature in the actuary’s technical calculations;
  • There may be commercial considerations at play, such as writing one contract at an expected underwriting loss (or minimal profit) in order to access other contracts that generate sufficient expected profits that it makes good sense to write the full set. This can happen quite frequently on a reinsurance program where one broker is placing several layers of reinsurance for the same client at the same time and the broker will only allow a market to participate on the attractive layers if they also take a share in the more competitively priced layers. Insurance companies also sometimes write medical insurance at a loss and medical acts as a loss leader because once it is sold, a relationship can be developed and clients can be potentially sold other lines of insurance.

Reinsurance is all about peak risks or risk volatility on Severity, frequency or both (Aggregate loss amount). Mathematics and Statistics help to decompose information available and to analyze each component, to recompose results into a synthesis and translate results into economic and business interpretations[15].

Whatever the reinsurance actuary is doing, it must be kept in context. What metrics are being used by reinsurance management to allocate capital, measure underwriting returns and remunerate the underwriting team? It is very important to align risk loading methodologies with these metrics.[16]

It is important to remember not to over-complicate matters. This is not personal lines or life insurance where the actuary can accurately quantify and evaluate much of the risks.  There will usually be significant uncertainty around the expected recoveries from a reinsurance layer, so a complex risk load that takes a lot more effort to calculate and communicate than a simple approach, but which offers only a small increase in “theoretical robustness”, may not be the best one to use. It could also undermine actuary’s credibility with the underwriter if they struggle to understand and accept the actuary’s approach.[17]


[1] Reinsurance Pricing: Practical Issues & Considerations, 8th Sep 2006; 2006 GIRO Reinsurance Matters! Working Party, Mark Flower et al.

[2] Ibid

[3] Ibid

[4] Ibid

[5] Ibid

[6] Ibid

[7] Hans Willert; Dec 2014: The role of governance in Solvency II.

[8] The Geneva Papers; 2015; Thimann; Systematic Features Of Insurance And Banking, And The Role Of Leverage, Capital And Loss Absorption.

[9] Ibid

[10]  IMF: July 2014; Macroprudential Solvency Stress Testing of the Insurance Sector.

[11] Enhancing Insurer Value Through Capital, Dividends And Reinsurance Optimization: Something Old, Something New: Yuriy Krvavych, PhD – Insurance Australia Group (IAG), Sydney. ASTIN Colloquium – Orlando FL, June 2007

[12] Ibid

[13] Reinsurance Pricing: Practical Issues & Considerations, 8th Sep 2006; 2006 GIRO Reinsurance Matters! Working Party, Mark Flower et al.

[14] Ibid

[15] Reinsurance Pricing: Dr. Michael Frohlich 3 Sep 2014. DEUTSCHE AKTUAR AKADEMIE GmbH

[16] Reinsurance Pricing: Practical Issues & Considerations, 8th Sep 2006; 2006 GIRO Reinsurance Matters! Working Party, Mark Flower et al.

[17] Ibid