Prophet Modelling Technique (2): New Business Processing

From my experience working with Prophet users (Valuation Team), most are quite familiar with running in-force projections, such as monthly valuation and embedded value calculations. However, when it comes to new business ("NB") processing, many users find themselves uncertain or confused on how it works. It’s not uncommon for me to receive questions like,

"Why can’t I just use the cross multiplication method?"
"Why does the project method take so much longer to run?"

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In this blog post, I’ll walk through how NB processing works in Prophet, highlight the differences between the two most common methods — cross multiplication and project method — and explain why I often recommend the project method for Prophet users from family takaful operators.

What is NB Processing?

NB processing in Prophet is a technique used to project results for future sales, based on sales volume specified in the Sales File. Prophet offers three methods for new business projection, but in practice, cross multiplication and project method are most commonly used.

To understand how these methods work, it’s important to first break down the two key components involved in NB projection, i.e. NB profile and Sales File.

A. Overall Concept

NB Profile / NB Premium × Sales File = Projected Cash Flows

In essence, Prophet projects new business cash flows by multiplying the NB profile with the monthly sales volumes from the Sales File. To be more specific, the "NB Profile" in the above formula refers to per dollar NB profile.

Let me use an illustration to better explain the above formula:

From the NB profile, the expected premium incomes for policy month 1 and 2 are $100,000 and 95,000 respectively.
The NB profile is generated using a model point file, with annualized premium $1,200,000. The annualized premium is captured under a mandatory variable PREM_AMOUNT. We need to ensure this variable is spelled correctly, as it is Prophet a specified variable.
If expected sales for Jan '25 is $600,000, the expected premium income for Feb '25 is 100,000 / 1,200,000 × 600,000 = $50,000.
Using similar approach, the expected premium income for Feb '25 is $47,500.

Similarly, if expected sales for Feb '25 is $900,000, the expected premium incomes for Feb '25 (policy month 1) and Mar '25 (policy month 2) are $75,000 and $71,250.

To get the expected premium income for Feb '25 on totality basis, we need to add up the results from both Jan '25 block and Feb '25 block of new business, i.e., 47,500 + 75,000 = $122,500.

B. NB Profile

The NB profile is generated from NB model points. Prophet distinguishes these model points by looking at the SPCODE, where values exceeding the "Last Sub-product Code for Existing Business" (as defined in the Structures) are treated as NB model points. In addition, it is important to ensure DUR_M for NB model point is set to 0.

For example, if the "Last Sub-product Code for Existing Business" is set to 50, all model point files with SPCODE = 51, 52, ..., 9999 are treated as NB model points.

You may have another question in mind: "Will my results be better if I use more NB points in the calculations?" In fact, NB model points represent the distribution of the target new business stated in the Sales File.

The most common approach is to use the actual new business acquired by the company. This approach assumes the distribution is the same as the actual new business.
You can also construct the expected distribution using fewer model points.
In simple words, 1 model point and 100,000 homogenous model points produce the same NB profile.

C. Sales File

The Sales File contains monthly sales volumes, organized by Prophet product and SPCODE. For example, if your new business model point file includes SPCODEs 51 and 52, then your sales file should contain columns labeled “PRODUCT#51” and “PRODUCT#52,” representing the expected monthly sales for each SPCODE.

Cross Multiplication vs. Project Method

The key difference between the cross multiplication method and the project method lies in how the NB profile is produced and used over time.

Cross multiplication method - Prophet generates the NB profile once, based on a single starting date. This same NB profile is then multiplied by the sales volumes for each month in the projection period.
Project method - Prophet regenerates the NB profile for every single month. Each month’s projection begins with a new starting date, and a new NB profile is created to match that start date before being multiplied by that month’s sales volume.

In simple terms, you can think of the project method as a series of cross multiplications—each tied to a different starting month.

Why Does This Matter?

You might wonder whether it’s really necessary to regenerate the NB profile each month. The answer depends on whether your model includes calendar date-specific cash flows.

If your projection assumptions are NOT dependent on the calendar—say, if policy events like benefits occur exactly one year from issue regardless of start month—then the cross multiplication method may be sufficient.
However, in Family Takaful, the timing of certain events—particularly profit and surplus sharing—is often tied to the financial year-end. For example, surplus distribution may be performed annually as of 31 December, regardless of when a policy was issued during the year. Unless this has been simplified to a monthly declaration (which is less common), the model needs to reflect this calendar-based timing accurately.

If a user applies the cross multiplication method in this context, Prophet will apply the same NB profile to all sales months. As a result, every new business policy—regardless of its actual issue date—will appear to participate in surplus sharing on the same schedule. This leads to inaccurate results, where surplus sharing seems to happen monthly, simply because the NB profile does not reflect different policy start dates.

To model this behavior correctly, the project method should be used, as it regenerates the NB profile for each month’s batch of new business. This ensures that each policy reflects the correct projection period and aligns with the actual financial calendar.

But What About Performance?

It’s true that the project method is significantly SLOWER than the cross multiplication method. Because Prophet regenerates the NB profile for each month in the sales file, a 3-year projection (i.e., 36 monthly sales points) means Prophet must generate and project 36 separate sets of NB profiles.

As a rule of thumb, you can expect the project method to take roughly 36 times longer than the cross multiplication method for a 3-year horizon. Naturally, this extended run time becomes a key consideration for modelers.

To manage performance while maintaining accuracy, I recommend using grouped model points when applying the project method. By grouping similar model points before generating the NB profile, you can significantly reduce the volume of data while still capturing the essential patterns of new business.

Wrap Up

Choosing between the cross multiplication method and the project method isn’t just a matter of run time—it’s about choosing the right method to reflect your business reality.

For Family Takaful products, where profit and surplus sharing often follow a fixed calendar cycle, the project method is the more accurate approach. While it does come with a performance trade-off, this can be managed with proper grouping techniques.

Ultimately, using the right NB processing method ensures your projections are not only technically correct but also aligned with the true business mechanics of your products.

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