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Math 479 Casualty Actuarial Mathematics. Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 8: Ratemaking II September 18, 2014. Last Time. Ratemaking I Overall concept Two foundational techniques Pure premium method Loss ratio method. Agenda.
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Math 479 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 8: Ratemaking II September 18, 2014
Last Time • Ratemaking I • Overall concept • Two foundational techniques • Pure premium method • Loss ratio method
Agenda • Ratemaking II • Trend vs development – is there overlap? • Relativities • Parallelogram method
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
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”
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
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
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
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
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?
Next Time • Ratemaking III • Exposure bases • Putting it all together
