1. 1 Math 479 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 8: Ratemaking II September 18, 2014

2. 2 Last Time Ratemaking I –Overall concept –Two foundational techniques Pure premium method Loss ratio method

3. 3 Agenda Ratemaking II –Trend vs development – is there overlap? –Relativities –Parallelogram method

4. 4 Loss Trend vs Loss Development

5. 5 Relationship to Reserving Developing losses to their projected ultimate values is a core concept But now, we add consideration of trend Why? –Historically, suppose that AY 2010 claims will develop for (let ’ s say) ten years –Suppose that for ratemaking purposes, we are estimating AY 2015 –Note: AY 2015 may also be expected to develop for ten years, but starting 5 years later

6. 6 Loss Trend In our example, if we use AY 2010 losses as a basis for our “ what if ” scenario ( “ what if 2010 losses are representative of what losses might occur in 2015 ” ), we must acknowledge that, in 2015, they will occur at a cost level that applies 5 years later Use historical patterns of losses (e.g., frequency and severity) to estimate and project loss “ trend ” or “ inflation ”

7. 7 Trend vs Development Is there “ overlap ” here? Are the trend and development processes somewhat redundant? Answer: No. There are two “ time periods ” in the ratemaking process –(1) Average accident date for the experience period, to average accident date for the future policies which will be written under the new projected rates –(2) From the occurrence period of the losses to their final ultimate values

8. 8 Relativities

9. 9 Ratemaking “ Relativities ” Three main kinds of relativities –Classification –Territorial –Increased limits Classification ratemaking –One class is the “ base class ” (relativity = 1.00) –Rates for other classes are keyed off of the base class rate Class rate = base rate × class relativity factor –More on this in the “ Risk Classification ” section

10. 10 Ratemaking “ Relativities ” (cont.) Territorial ratemaking –Very similar to classification ratemaking, conceptually and procedurally Increased limits factors –Basic limits premium or loss cost E.g., $100,000 per occurrence limit –Calculate premiums or loss costs for higher policy limits by multiplying the basic limits value by the appropriate increased limits factor (ILF) –Often, trending and/or developing is performed on a basic limits (and perhaps other limits) basis

11. 11 Parallelogram Technique

12. 12 Key Concepts Written premium: booked at policy issuance Earned premium: applying to coverage provided Rate changes: +/- change in rate per exposure unit Benefit changes: change to benefits provided (possibly to in-force policies, as well as new policies) On-level factors: bring CY EP to “ current ” rate level On-level premiums: brought to “ current ” rate level

13. 13 Parallelogram Method 20082009 +20% rate change on July 1, 2008 What is the on-level factor to bring 2008 CY EP to a 2009 rate-level basis? 1.000 1.200

14. 14 CAS Exam 5, May 2007, # 7

15. 15 CAS Exam 5, May 2007, # 8

16. 16 CAS Exam 5, May 2008, # 24

17. 17 CAS Exam 5, May 2008, # 27

18. 18 CAS Exam 5, May 2007, # 34

19. 19 CAS Exam 5, May 2008, # 14

20. 20 CAS Exam 5, May 2007, # 37

21. 21 Next Time Ratemaking III –Exposure bases –Putting it all together