Going Beyond Tradition – Reinsurance Treaty Pricing with Piecewise Pareto Distribution Typically, non-proportional treaty pricing of excess layers in P&C reinsurance is performed with well-known frequency and severity-based approaches using historical experience. For severity, it is a common practice to fit a single statistical distribution to historical claims. Fitting a single distribution to claims can be challenging when data is sparse or has outliers. This could lead to underestimating or overestimating claims especially at the tail end of distributions impacting pricing. In a competitive market, pricing anomalies can put reinsurers at a disadvantage against their competitors. Therefore, this article is aimed at showing how a piecewise Pareto distribution can be used for treaty pricing to overcome such difficulties in distribution fitting, leading to better outcomes for reinsurers. Traditional method of treaty pricing Generally, with treaty pricing claims are segregated into more frequent small claims, non-catastrophe large claims and catastrophe claims for their distinctive risk characteristics. Large claims such as large fire losses tend to be infrequent and have high severity. Claims over a selected threshold are considered as large claims and an appropriate statistical distribution is fitted to them. Then the fitted severity distribution and a claim frequency distribution, which comes from number of claims above the selected threshold, are aggregated to provide an aggregate claim distribution for pricing. This method is prevalent in the reinsurance market. We have observed that some reinsurers originating from Asia tend to use it. However, some well established large reinsurers coming from Europe and other parts of the world and even some medium sized reinsurers tend to use piecewise Pareto distribution for pricing potentially being motivated by the advantages Pareto distribution provides, which we discuss later and the straightforward mathematics  that can be used for pricing with piecewise Pareto distribution. Distribution fitting with the traditional method Underwriters and pricing actuaries typically use historical treaty experience to perform pricing. Historical individual claims are trended for inflation and adjusted for structural changes such as change in level of retention over time to reflect projected treaty period. Then distribution fitting is done on claims and a best fit is chosen using one or a selection of statistical criteria such as Least Squares Error, Kolmogorov or Anderson value. The outcome is a single fitted distribution. Difficulties with the traditional method This method of choosing one single distribution comes with its own drawbacks. If claims are not spread out reasonably well, for example, claims with a very few outliers, then distribution fitting becomes difficult. The difficulty stems from trying to fit a single distribution over a wider range often leading to overestimating or underestimating specifically at the tail end of the distribution. In some cases, we only get claims closer to the selected deductible leaving a wider range without any claims. This makes distribution fitting extremely difficult. A certain level of judgement is required with the help of risk profiles and market loss data to form a view on possible claims at the tail. The following graph illustrates the difficulty in distribution fitting with underestimated and overestimated areas in the fitted distribution. Pareto distribution and its popularity The Pareto distribution is named after the Italian civil engineer, Vilfredo Pareto, who came up with the concept of “Pareto efficiency”. The distribution is famously known as the Pareto principle or “80-20” rule. This rule states that, for example, 80% of the wealth of a society is held by 20% of its population. Social, scientific, actuarial and other fields widely use it. The Pareto distribution has two parameters, scale (or threshold) and shape (often denoted as alpha, α). The popularity and wide use of it in the actuarial field, especially with pricing can be attributed to several compelling reasons. Parameter invariance arguably is the most important feature, which implies that as long as we are in the tail the same alpha parameter applies whatever the threshold be . The ease of deriving parameters using empirical data with techniques such as Method of Moment and Maximum Likelihood (MLE). Can be used to represent empirical data fairly well over a wide range of values. Availability of benchmarks for alpha values to help underwriters and actuaries to choose for pricing of different classes of business. Make it easier to explain parameter selections and results. Using one single Pareto distribution to fit can lead to issues mentioned previously. To work around these issues, the article introduces piecewise Pareto distribution. In fact, piecewise Pareto distribution is not new to actuarial practice. Underwriters and actuaries have been using it for a long time but its use has been limited in pricing. The next section of the article delves into treaty pricing with piecewise Pareto distribution. Pricing with piecewise Pareto distribution How this works is best explained with an example. Assume that we are pricing a non-proportional treaty layer with limit of $4 million in excess of $1 million deductible (i.e. 4m xs 1m) for treaty year 2018 having historical treaty results for the period 2010 to 2017. The basic idea of piecewise Pareto distribution is to split the layer being priced into chunks and fit separate Pareto distributions to them. First, we divide the layer limit into equal size chunks called priorities (You may split by a log scale as done in the given example). Second, we determine the number of claims exceeding each priority for each historical treaty year. (This is similar to assuming a large loss threshold and selecting number of claims above it for each treaty year to determine claim frequency with the traditional method). Then average exposure adjusted exceeding frequency for each priority is calculated with some weight assignment. In the example, two weight options have been given to choose from. For example, weight W1 gives equal weight to each historical treaty year whereas weight W2 discards the oldest treaty year giving equal weights to the rest of historical treaty years. The following table shows how the layer starting from the deductible of 1m to the end (i.e. limit + deductible) of 5m […]
In our June 2020 Bulletin number 002/ARB-BULLETIN/06/2020 we reviewed the quarterly financial performance of local professional reinsurance companies (IPR) for 2018 and 2019. Based on their latest published 1st Quarter 2020 results, this Bulletin attempts to further graphically depict the individual financial performance of IPR members, particularly in the wake of the Jakarta floods in early January 2020. In addition to the previous graphs covering: Solvency or RBC Level Investment Funds Equity Guarantee Funds or Assets. we have added two new graphs covering IPR members’ Profitability and Liquidity ratios (measured as Assets / Liabilities) : Solvency or RBC Level Based on OJK regulation the minimum RBC level for a local reinsurance company is 120%. All local reinsurance companies in the panel comply with this requirement Investment Funds Equity Based on OJK regulation No 67/POJK.05/2016 the minimum equity for a local reinsurance company is IDR 300 Billion All local reinsurance companies in the panel comply with this requirement Guarantee Funds or Assets 5. Profitability 6. Liquidity If you have any issues on the above or on any other item please do not hesitate to contact: Bernard Krova – email@example.com Wayan Sumendra – firstname.lastname@example.org Adia Adithiya – email@example.com To the extent this note expresses any opinion on any aspect of risk, the recipient acknowledges that any such assessment is an expression of PT Asia Reinsurance Brokers Indonesia’s opinion only, and is not a statement of fact. Any decision to rely on any such assessment of risk is entirely the responsibility of the recipient. PT Asia Reinsurance Brokers Indonesia will not in any event be responsible for any losses which may be incurred by any party as a result of any reliance placed on any such opinion.
AM Best has downgraded the Financial Strength Rating (FSR) to B++ (Good) from A- (Excellent) and the Long-Term Issuer Credit Rating (Long-Term ICR) to “bbb+” from “a-” of General Insurance Corporation of India (GIC Re) (India). The outlook of the FSR has been revised to stable from negative whilst the Long-Term ICR outlook is negative. These Credit Ratings (ratings) reflect GIC Re’s balance sheet strength, which AM Best categorises as strong, as well as its adequate operating performance, favourable business profile and appropriate enterprise risk management (ERM). The rating downgrades follow a deterioration in AM Best’s view of GIC Re’s balance sheet strength fundamentals. GIC Re’s risk-adjusted capitalisation, as measured by Best Capital Adequacy Ratio (BCAR), declined to the strong level at fiscal year-end 2020, as compared with the strongest level in fiscal year 2019 and prior. This deterioration follows an approximately 30% decline in GIC Re’s reported capital and surplus in fiscal year 2020 due to a significant fall in the market value of its equity investments, as well as from the reporting of a full year operating loss. Unfavourable movements in the fair value of GIC Re’s investment holdings follow global volatility in investment markets in the face of the prevailing COVID-19 pandemic. At the same time, GIC Re’s fast premium growth continues to outpace capital accumulation leading to lower risk-adjusted capitalisation. In addition, GIC Re’s regulatory solvency position at fiscal year-end 2020 was marginally above the regulatory minimum requirement. Positive balance sheet strength considerations include the company’s relatively modest underwriting leverage, its typically liquid investment portfolio and retrocession counterparties of high credit quality. AM Best assesses GIC Re’s operating performance as adequate. GIC Re has reported a five-year average return-on-equity (ROE) ratio of 5% (fiscal years 2016 to 2020), as calculated by AM Best. However, the company posted an operating loss in fiscal year 2020 following weaker-than-expected underwriting performance, emanating principally from its domestic lines of crop, motor, fire and health business, as well as from natural catastrophe events impacting GIC Re’s foreign business portfolio. The company’s combined ratio deteriorated to 106% in fiscal year 2019 and to over 110% in fiscal year 2020. Over the medium term, the negative trend in underwriting performance may be moderated partially by the recent imposition of premium rate increases and changes to reinsurance treaty terms for domestic fire and crop business, and from an increased focus on underwriting discipline. In addition, the company’s exposure to crop business has been reduced significantly starting in fiscal year 2021. Notwithstanding this, competitive market conditions and disruption borne by the COVID-19 pandemic remain key challenges for GIC Re over the near term. AM Best assesses GIC Re’s business profile as favourable. GIC Re is a leading reinsurer in India, with over a 75% market share based on ceded domestic written premiums. The company continues to have close relationships with direct insurers in India, and local regulations provide GIC Re with an advantage in obtaining domestic reinsurance placements. In addition, GIC Re maintains a geographically diversified underwriting portfolio, with approximately 30% of business sourced outside of India in fiscal year 2020. The negative outlook for the Long-Term ICR reflects AM Best’s concern that continued underwriting losses, coupled with the potential for further volatility in India’s investment markets amid the prevailing COVID-19 pandemic, may further pressure GIC Re’s operating performance and balance sheet strength fundamentals. In recent years, the company has relied on investment returns and realised gains to offset the reported underwriting losses and grow its capital base; however, under the current conditions, such a model may no longer be sustainable. Ratings are communicated to rated entities prior to publication. Unless stated otherwise, the ratings were not amended subsequent to that communication. This press release relates to Credit Ratings that have been published on AM Best’s website. For all rating information relating to the release and pertinent disclosures, including details of the office responsible for issuing each of the individual ratings referenced in this release, please see AM Best’s Recent Rating Activity web page. For additional information regarding the use and limitations of Credit Rating opinions, please view Guide to Best’s Credit Ratings. For information on the proper media use of Best’s Credit Ratings and AM Best press releases, please view Guide for Media – Proper Use of Best’s Credit Ratings and AM Best Rating Action Press Releases. AM Best is a global credit rating agency, news publisher and data analytics provider specializing in the insurance industry. Headquartered in the United States, the company does business in over 100 countries with regional offices in New York, London, Amsterdam, Dubai, Hong Kong, Singapore and Mexico City. For more information, visit www.ambest.com. If you have any issues on the above or on any other item please do not hesitate to contact: Bernard Krova – firstname.lastname@example.org Wayan Sumendra – email@example.com Adia Adithiya – firstname.lastname@example.org
As an insurance company in Indonesia you have a vested interest in the financial health of the local professional reinsurance companies (IPR). To help you better understand the financial performance of the IPR members we have extracted relevant data from their published quarterly financial statements relating to: Solvency or RBC Level Investment Funds Equity Guarantee Funds or Assets. The performance of each IPR member over the past two years is graphically shown below: Solvency or RBC Level The graph shows RBC levels on a quarterly basis for 2018 and 2019. Based on OJK regulation the minimum RBC level for a local reinsurance company is 120%. All local reinsurance companies in the panel comply with this requirement Investment Funds The graph shows Investment funds on a quarterly basis for 2018 and 2019 Equity The graph shows Equity on a quarterly basis for 2018 and 2019. Based on OJK regulation No 67/POJK.05/2016 the minimum equity for a local reinsurance company is IDR 300 Billion All local reinsurance companies in the panel comply with this requirement Guarantee Funds or Assets The graph shows Assets on a quarterly basis for 2018 and 2019. We intend to update this on a quarterly basis for your information. If you have any issues on the above or on any other item please do not hesitate to contact: Bernard Krova – email@example.com Wayan Sumendra – firstname.lastname@example.org Adia Adithiya – email@example.com To the extent this note expresses any opinion on any aspect of risk, the recipient acknowledges that any such assessment is an expression of PT Asia Reinsurance Brokers Indonesia’s opinion only, and is not a statement of fact. Any decision to rely on any such assessment of risk is entirely the responsibility of the recipient. PT Asia Reinsurance Brokers Indonesia will not in any event be responsible for any losses which may be incurred by any party as a result of any reliance placed on any such opinion.