[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **On-Level Premium**
## Definition
==On Level Premium== On-level premium is historical earned premium adjusted to the current rate level, eliminating the impact of rate changes during the experience period.
## Purpose
- Match premium to losses at consistent rate level
- Remove distortion from rate changes
- Calculate accurate loss ratios
- Support rate indications
## On-Leveling Process
### Step 1: Identify Rate Changes
```
Document all rate changes during experience period:
- Effective date
- Rate change percentage
- Portion of premium affected
```
### Step 2: Calculate On-Level Factors
```
On-Level Factor = Current Rate / Historical Rate
If rates increased 10%:
On-Level Factor = 1.10 / 1.00 = 1.10
```
### Step 3: Apply to Earned Premium
```
On-Level Premium = Historical Earned × On-Level Factor
```
## Example
```
Calendar Year 2024 Premium:
Written: $1,000,000 (1/1/2024)
Rate change: +10% effective 7/1/2024
Earned premium by rate level:
Jan-Jun (old rate): $500,000
Jul-Dec (new rate): $550,000
Total CY earned: $1,050,000
On-leveling to 12/31/2024 rate:
Jan-Jun: $500,000 × 1.10 = $550,000
Jul-Dec: $550,000 × 1.00 = $550,000
On-level premium: $1,100,000
On-level factor: $1,100,000 / $1,050,000 = 1.048
```
## Parallelogram Method
For accident year premium with mid-year rate change:
```
AY 2024 with 7/1/2024 rate change of +10%:
Premium at old rate:
- 6 months of AY 2024 policies
- 6 months of AY 2023 policies
= 6/12 × 1.00 = 0.50
Premium at new rate:
- 6 months of AY 2024 policies
- 6 months of AY 2025 policies
= 6/12 × 1.10 = 0.55
Weighted average rate level = 1.05
On-level factor to current = 1.10 / 1.05 = 1.048
```
## Related Concepts
- [[Earned Premium]]
- [[Rate Change]]
- [[Loss Ratio Method]]
## References
- Werner & Modlin, Chapter 7