Pricing Basis & Reserving: Key Components

The Components of a Pricing Basis

A pricing basis is the complete set of assumptions an actuary uses to calculate the premium for an insurance product. These assumptions project future cash flows associated with a policy, allowing the insurer to determine a price that meets its objectives.

A comprehensive guide from Milliman provides an excellent, structured overview of these components. While it focuses on a microinsurance product, the categories of assumptions are universal.

As you've seen, the pricing basis can be organized into several key categories. Let's walk through them, using the cancer insurance model from our last lesson as a practical example.

Here are the core components of a pricing basis:

1. Demographic Assumptions (Risk Assumptions): These relate to the policyholder's behaviour and risk profile.

   • Mortality/Morbidity Rates: The probability of death or sickness. For the cancer product, the model uses separate incidence rates for mortality (death from any cause) and morbidity (cancer diagnosis).
   • Lapse/Persistency Rates: The probability that a policyholder will cease paying premiums and let their policy lapse. This is a critical assumption as it affects the duration of expected cash flows.

2. Financial Assumptions (Economic Assumptions): These relate to the economic environment.

   • Investment Return / Discount Rate: The expected rate of return the insurer will earn on the premiums it invests. This rate is also used to discount future cash flows (like claims and expenses) to their present value.
   • Expense Inflation: The rate at which expenses are expected to increase over time.

3. Expense Assumptions: These cover the costs of selling and administering the policies.

   • Acquisition Expenses: One-time costs incurred at the start of a policy, such as commission paid to a sales agent, underwriting costs, and marketing.
   • Maintenance/Renewal Expenses: Ongoing costs to administer the policy, such as processing premiums, handling customer service, and maintaining systems.
   • These are often expressed as a percentage of premium, a fixed amount per policy, or a combination. In the cancer model video, you'll note the actuary assumes expenses as a percentage of premium based on clues from the product's design.

4. Profit and Contingency Assumptions:

   • Profit Margin: An explicit loading to ensure the product meets its profitability target. This can be a percentage of premium, a return on capital, or another metric.
   • Contingency Margin: An additional buffer included in the premium to account for uncertainty and the risk of assumptions proving incorrect. This is also known as a Margin for Adverse Deviation (MAD).

Putting all these assumptions together allows the actuary to project all future income (premiums, investment returns) and outgo (claims, expenses, taxes), and solve for a premium that achieves the desired profit margin.

The Relationship Between Pricing and Reserving

Once a policy is sold, the insurer has a legal obligation to pay future benefits. It must hold a liability on its balance sheet to represent the value of this promise. The process of calculating this liability is called reserving, and the assumptions used are the reserving basis.

The fundamental question is: how does the pricing basis relate to the reserving basis?

The functions of pricing and reserving are distinct, which often leads to different, though related, sets of assumptions.

This difference in purpose—pricing to win business profitably versus reserving to value existing obligations prudently—is the main driver of differences in assumptions.

• Pricing assumptions are typically best-estimate. They represent the most realistic expectation of the future, set at a level that balances profitability with market competitiveness.
• Reserving assumptions are often more prudent or conservative. They include an explicit or implicit margin to provide a buffer against adverse experience and ensure the company can meet its obligations even if the future is worse than expected.

Let's see this in action. The actuary in the cancer product video explicitly discusses how and why his reserving assumptions differ from his pricing assumptions.

The example from the video is key. For a cancer insurance product where a benefit is paid on diagnosis but not on death:

• Pricing Mortality: A best-estimate assumption is used.
• Reserving Mortality: A lower mortality rate is assumed. Why? If fewer people die from other causes, more people remain in the pool who are eligible to be diagnosed with cancer and claim the benefit. A lower mortality rate is therefore more prudent from the insurer's perspective as it leads to higher expected claim costs and a higher reserve.

This illustrates the principle of prudence: for reserving, you adjust assumptions in the direction that results in a higher liability.

Reconciliation and Feedback

Although the assumptions may differ, they cannot exist in isolation. A robust actuarial framework requires a clear and logical connection between them.

The key takeaways from this are:

1. Consistency: The reserving basis should be recognisably related to the pricing basis. For example, the reserving basis might be defined as "pricing best-estimate + a specific margin."
2. Reconciliation: Companies must be able to explain and justify any differences between the two bases.
3. Feedback Loop: The actual experience that emerges from a block of business (monitored by reserving and valuation actuaries) must be fed back to the pricing actuaries. If claims are consistently higher than priced for, future premiums must be adjusted. This is a core part of the Actuarial Control Cycle.

Conclusion

We have now established the specific "ingredients" required to calculate a premium and have explored the crucial, nuanced relationship between pricing and reserving.

The pricing basis is the set of best-estimate assumptions covering demographics, economics, expenses, and profit, designed to create a competitive and profitable product.

The reserving basis uses these assumptions as a starting point but typically incorporates a level of prudence or conservatism to ensure the company's solvency and its ability to meet all promises to existing policyholders. The direction of this prudence depends on the specific product design.

While the two sets of assumptions serve different masters—market demands for pricing, regulatory and solvency needs for reserving—they are two sides of the same coin and must be actively reconciled through a robust feedback loop.

In our next lesson, we will examine the "recipes" that use these ingredients. We'll explore the main pricing methodologies—from simple formulas to complex cashflow models—that turn the pricing basis into a final premium.

Key Takeaways & Cheatsheet