Math 479
Casualty Actuarial Mathematics
Fall 2014
University of Illinois at Urbana-Champaign
Professor Rick Gorvett
Session 8: Ratemaking II
September 18, 2014
1
Last Time
• Ratemaking I
– Overall concept
– Two foundational techniques
• Pure premium method
• Loss ratio method
2
Agenda
• Ratemaking II
– Trend vs development – is there overlap?
– Relativities
– Parallelogram method
3
Loss Trend
vs
Loss Development
4
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
5
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”
6
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
7
Relativities
8
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
9
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
10
a basic limits (and perhaps other limits) basis
Parallelogram
Technique
11
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
12
Parallelogram Method
2008
2009
1.000
1.200
+20% rate change on July 1, 2008
What is the on-level factor to bring 2008 CY EP to a 2009 rate-level basis?
13
CAS Exam 5, May 2007, # 7
14
CAS Exam 5, May 2007, # 8
15
CAS Exam 5, May 2008, # 24
16
CAS Exam 5, May 2008, # 27
17
CAS Exam 5, May 2007, # 34
18
CAS Exam 5, May 2008, # 14
19
CAS Exam 5, May 2007, # 37
20
Next Time
• Ratemaking III
– Exposure bases
– Putting it all together
21