Uses of models: pricing, capital, provisions, options

Introduction: Why Do We Use Models?

Welcome! In earlier chapters, you learned how to build a model and what goes into it. Now, we are going to look at the "Why." In the world of CP1, models are not just mathematical exercises—they are the primary tools actuaries use to help businesses make massive financial decisions.

Think of an actuarial model as a sophisticated "flight simulator" for a business. Before a company launches a new product or decides how much money to keep in the bank, they run the scenario through a model to see if they might "crash." In this chapter, we focus on four critical uses of models: pricing, capital, provisions, and options.

1. Pricing and Financing Strategies

The most intuitive use of a model is deciding what to charge for a product. In actuarial terms, we call this pricing or setting future financing strategies.

Setting the Price

When an actuary prices a financial product, they use a model to project future cash flows. The model helps determine a price that is high enough to cover:

• The expected cost of benefits payable on contingent events (e.g., a death claim or a car accident).
• The expenses of running the business.
• The cost of capital (the "rent" paid for using the company’s money).
• A margin for surplus/profit.

Financing Strategies

For some products, like pension schemes, we don't just set a "price"; we set a financing strategy. This is a plan for how much money needs to be contributed over time to ensure there is enough to pay benefits in 30 or 40 years. The model helps us see the impact of changing contribution rates today on the stability of the fund tomorrow.

Quick Tip: Don't forget that pricing isn't just about the math. Models also help us see if a price is competitive. If the model says we need to charge \$100 but the market price is \$80, the model has identified a commercial problem!

2. Capital Requirements and Risk Management

Capital is the extra money a provider holds to ensure it can survive even if things go very wrong. Models are essential for calculating how much of this "buffer" is needed.

Regulatory vs. Economic Capital

Models help calculate two main types of capital:

• Regulatory Capital: The minimum amount of money the law (the prudential regulatory regime) says you must hold. If you fall below this, the regulator might shut you down.
• Economic Capital: The amount of money the company thinks it needs based on its own risk appetite. This is often calculated using internal models that look at the specific risks the company faces.

Return on Capital

Companies want to make sure they are using their money efficiently. A model can calculate the return on capital. If a specific product requires a huge amount of capital but only produces a tiny profit, the model tells the business that it might be better off selling a different product instead.

Analogy: Think of capital like the life jacket on a boat. You hope you don't need it, but you use a "model" (safety regulations) to decide how many you need to carry based on how many passengers are on board and how rough the seas might be.

3. Assessing Provisions

A provision (sometimes called a reserve in other contexts, but remember to use the syllabus term provisions) is a liability on the balance sheet. It represents the money the company needs to set aside now to pay for existing commitments.

Why use a model for provisions?

We use models to estimate the present value of these future commitments. This involves:

• Projecting when benefits payable on contingent events will occur.
• Estimating how much those benefits will be.
• Discounting those future values back to today's terms.

Important Distinction: While pricing looks at future business we might write, provisioning looks at business we have already written. The model helps ensure that the company remains solvent and can meet its promises to stakeholders.

4. Pricing and Valuing Options and Guarantees

This is often the most complex part of actuarial modelling. Many financial products come with "extras" that can be very expensive for the provider.

What are Options and Guarantees?

• A Guarantee: A promise that a benefit will not fall below a certain level (e.g., "Your pension will pay at least 3% more each year, no matter what inflation does").
• An Option: A choice given to the customer (e.g., "At age 60, you can choose to take your benefit as a lump sum or a monthly income").

Why they need special models

You cannot value an option or a guarantee using a simple "best estimate" average. Why? Because the cost to the provider is often asymmetric. If the stock market goes up, a guarantee costs the provider nothing. If it crashes, the guarantee could cost millions.

To value these, actuaries often use stochastic modelling. This involves running thousands of different "what if" scenarios to see how often the guarantee gets "triggered" and how much it costs in those specific cases.

Common Mistake: Students often forget that options and guarantees have a cost even if they aren't currently "in the money." A model helps put a price tag on that potential future cost.

5. Summary of Model Uses

To help you remember, here is a quick summary table of how models are used across the business:

Key Takeaways for the Exam

• Models are Decision Tools: Always link the model output back to a business decision (e.g., changing the price, withdrawing a product, or increasing capital).
• Risk Management: Models are central to Enterprise Risk Management (ERM) because they quantify risks that are otherwise just "guesses."
• Different Models for Different Goals: The assumptions used for a pricing model (where you might be optimistic to get sales) might be different from a provisioning model (where you might be prudent for safety).

Don't worry if the distinction between provisions and capital feels a bit blurry at first. Just remember: Provisions are for the expected claims; Capital is for the unexpected disasters.

Quick Review: Can you explain why a simple "average" might not be enough to value a guarantee? If you mentioned that guarantees only cost money in "bad" scenarios and are worth zero in "good" ones, you're exactly on the right track!