„Underwriting vs. Accident year“

In our current setup loss events are simulated with respect to calendar time.

In the easiest case, the exposures causing all these loss events lie in the same year and were also written in that year.

Things tend to be a little more complicated in real life.

The exposure is often contracted for a period  that does not fully match the calendar year in which it was contracted, e.g. one year from the time of inception (underwriting year - UWY).

Such exposure will have some properties related to its UWY, like the premium level,  as well as some related to the year(s) for which the exposure exists ("accident year", AY), for example inflation.

Note that even a company only writing policies valid until the end of the calendar year is affected by the problem, as soon as there is a tacit renewal clause. Example: in Switzerland some motor TPL insurers write all their policies until end of year („Hauptverfall") regardless of the inception, automatically renewed for one year if neither side gave a one month notice prior to end of year.

Problems linked with UWY affect both input and output of internal models. Typical examples are:

• How is written exposure split over the affected calendar years?
• How is unexpired exposure accounted for at end of calendar year?
• Provide performance measurement by UWY
  

One of the bigger issues related to UWY is accrual.

It is mainly an accounting issue, both in real life and simulation. The  difficulties arise from the requirement to provide estimates of assets and liabilities at a given point in time where not all risks of the underwriting year have yet expired.

Typical figures to be estimated include:

• estimates of earned and unearned premiums
• estimates of earned and unearned expenses (deferred acquisition costs)
• estimates of earned ultimate losses
• estimates of deficiency reserve
• estimates of unearned profits (IFRS 4, economic valuation)

Accounting standards, supervisory bodies, economic valuation concepts etc. define these numbers in various ways.

Note: the complexity of all these tasks considerably increases for assumed reinsurance on a risk attaching basis. Since it refers to the underwriting of a cedant, such business is always UWY based.

An essential part of modeling is simplification and focus on the essential.

On the other hand, oversimplification is bad thing, especially when it is imposed by restrictions of a software. So how sophisticated should we get here?

What are your requests in the categories "must have", "nice to have" , and "modeller's heaven"?

All your feedback is welcome, whether from a business perspective or a more technical/algorithmic oriented perspective.

Fundamentally, any model is an abstraction of some process or system of interrelated processes.  Successful models significantly simplify the processes being modelled while continuing to capture the essential behaviour and results of the systems they represent.  Modelling of general insurance is no different.  Insurance company financial performance is the result of numerous processes, some initiated by and managed to varying degrees by the enterprise, others more exogenous.  Certain processes are related serially or in some other simple manner; others are more intricately intertwined.

As a starting point, one might outline the life of a single policy by identifying the basic processes and any relationship they might have:

Issue the policy on a known date (its “effective date”), specifying an expiry date.  Premium is specified on this date, and paid in one or more instalments over the duration of the policy.

Between the effective and expiration dates, exogenous insured events will occur on identifiable dates (“accident dates”).  Concurrently, the premium is “earned” by the company; i.e., exchanged with finality for the promise of indemnity and defence, and therefore recognised as revenue on the company books.

At some point subsequent to the occurrence of each insured event, the company will learn that the event has occurred, again on an identifiable date (the “report date”).  Additional information may emerge subsequent to the initial report date.

Once reported, the company may make payments, either honouring their obligations to indemnify the policyholder (“indemnity payments”) or to defend the policyholder and the company against liability for indemnity (“claim adjustment expense payments”).  Such payments may occur on one or several occasions (“payment dates”).

In addition to the occurrence of the insured events themselves, other external processes affect the eventual cash flows and reported revenues and expenses from this policy.  For example, the policy might cover a type of legal liability which is adversely or favourably affected by a landmark court ruling (an accident date effect).  General economic inflation might affect claim amounts, based on price levels prevailing at the time that the event occurs, and to varying degrees price levels prevailing when claim payments are eventually made. Exogenous factors may attach closely to particular dates or processes or may be less clearly related to the “primary” processes.

Once a basic process model is identified, a modeller of a financial services enterprise typically needs to address the fundamental question of whether the model can be simplified without sacrificing an unacceptable degree of accuracy.  It is not uncommon, for example, for life insurance modellers to use a policy-by-policy “seriatim” approach to modelling, as the prevalence of policyholder options in most life insurance policies is exceedingly difficult to approximate in the aggregate.  General insurance policies, on the other hand, provide many fewer policyholder options, and lend themselves well to aggregation.  Fundamentally, groups of related items are collected into indivisible aggregations (“model points”) and modelled as single abstract entities.  A modeller would typically try to segregate a portfolio of insurance policies into as few groups as possible while ensuring an acceptable level of homogeneity within each group.  Some factors for “bucketing” policies are fairly obvious – such as line of business and time of issue (“underwriting period”); others are useful for some types of policies and not for others – such as distribution channel and policy duration.

While premium in any model where events (policy issuance and claims) are grouped by period is nearly always organised primarily by underwriting period and secondarily by calendar period, a foundational question that invariably must be addressed in any model is whether claims should be grouped by accident year or by underwriting year (certainly there are other options; however, here we will limit consideration to these two choices).

There is no unilateral advantage to one grouping or the other – each has certain advantages in certain situations.

If reinsurance is in place on a risks-attaching basis, or if the model is intended for an underwriting-period-based analysis, claims organised by underwriting period are essential.  One would expect that it would be easier and more accurate to generate claims directly by underwriting period than to simulate by accident period and subsequently re-organise them.  Conversely, for losses-occurring reinsurance or accident-year-oriented analysis, it is preferable to generate claims directly by accident year.

Because groups of policies are underwritten at the same time, covering similar business in similar environments, underwriting periods are more easily separated into underwriting-period-by-accident-period subgroups than are accident periods.  It tends to be easier to divide an underwriting period “forward” into accident periods than to divide an accident period “backward” into its constituent underwriting periods.

However, in most jurisdictions, actuaries are required to report claims by accident period and conventionally use that basis for much of their analysis.  Even if not the most convenient model, it may be more accurate to generate claims by accident period using high-confidence parameters and then re-organise the claims by underwriting period than to fit lower-confidence parameters to a “direct” underwriting period model.

Finally, in many situations, both bases may be desirable – for example, reinsurance might not always “follow form”, or there may be risks-attaching reinsurance where the wealth of the company’s knowledge is oriented by accident year.

Based on experience, I would rate several alternatives as follows:

“Essential” – any model needs to allow the option to generate claims either on a “direct by underwriting period” or “direct by accident period” basis.  A model point either has claims by underwriting period or by accident period, but not both.

“Nice to Have” – allow either basis to be the primary generation basis, and add an option for a secondary subdivision to the other basis.  A model point has claims by underwriting period only, accident period only or underwriting period by accident period.

“Modeller’s Heaven” – add the option to generate claims directly by underwriting and accident period.

Any of these options should still reflect the underlying core processes and the appropriate influence of exogenous effects.