Motor Pure Premium Modeling with D d Deductible: The Indian Context tibl Th I di C t t Biresh Giri Consulting Actuary, Milliman India 11 th GCA February 13, 2009 February 13, 2009
Risk averse Vs Risk loving customers g “I haven’t had any claims on my motor insurance for the past 4 I haven t had any claims on my motor insurance for the past 4 years. Should I have a policy with high deductible next year? It must be a lot cheaper!” Low risk Vs High risk customers Low risk Vs High risk customers “I had one accident each year two years in a row. And have had to “I h d id t h t i A d h h d t pay Rs 5000/- from my pocket. Gosh! I am ready to pay a higher premium if a company is ready to cover this 5000 too!” premium if a company is ready to cover this 5000 too! 2 June 28, 2011
Presentation Flow Allowed deductibles: The past and present scenario p p Effects of increasing deductible Methods of premium rating with deductibles The Indian context The way ahead 3 June 28, 2011
Presentation Flow Allowed deductibles: The past and present scenario p p Effects of increasing deductible Methods of premium rating with deductibles The Indian context The way ahead 4 June 28, 2011
Allowed deductible: Past scenario TYPE OF VEHICLES COMPULSORY COMPULSORY Passenger carrying DEDUCTIBLE (Rs) Goods carrying Vehicles Commercial Vehicles Vehicles (other than vehicles rateable under Class ‐ rateable under Class ‐ GVW < 7500 Kg GVW GVW < 7500 Kg. GVW # Passengers < 17 # Passengers < 17 500 500 D,E,F and G of CVT) 7500 Kg.<= GVW < 16500 Kg. 17 <= # Passengers < 36 1,000 GVW >= 16500 Kg. # Passengers >= 36 1,500 Max (0.5% of IDV of the ( V hi l Vehicles rateable under Class D of the Commercial Vehicles Tariff (CVT) bl d Cl D f h C i l V hi l T iff (CVT) vehicle, 2,000) Rs.50 for two ‐ wheelers Vehicles rateable under Class E, F and G of the Commercial Vehicles Tariff (CVT) and Rs. 500 for others Taxis and Three Wheelers rated as Commercial Vehicles (Not exceeding 1500cc) 500 Taxis and Three Wheelers rated as Commercial Vehicles (Exceeding 1500 cc) 1,000 Private Cars including three wheelers rated as Private Cars(Not exceeding1500cc) 500 Private Cars including three wheelers rated as Private Cars (Exceeding 1500 cc) 1,000 Motorized Two Wheelers. 50 Source: Tariff Advisory Committee (Indian Motor Tariff 2002) 5 June 28, 2011
Allowed deductible: Present scenario IRDA relaxed the condition of fixed deductible by vehicle class IRDA relaxed the condition of fixed deductible by vehicle class effective 1 Jan, 2009 • So, you have already started with the deductible rating If not you better start soon If not, you better start soon • • 6 June 28, 2011
Presentation Flow Allowed deductibles: The past and present scenario p p Effects of increasing deductible Methods of premium rating with deductibles The Indian context The way ahead 7 June 28, 2011
Effects of increasing deductibles g Frequency per policy decreases: Lesser claims burn through Frequency per policy decreases: Lesser claims burn through deductible Claim cost per claim # decreases: Net claim is lower as deductible p is higher SO SO Claim cost per policy decreases But by HOW MUCH? y #: Taken over all claims not just the claims reported 8 June 28, 2011
Effect of increasing deductible A proportion of claimants p p will not claim for amounts just above 1000. The proportion decreases as the amount gets higher t t hi h Pseudo-Deductible Effect 9 June 28, 2011
Presentation Flow Allowed deductibles: The past and present scenario p p Effects of increasing deductible Methods of premium rating with deductibles The Indian context The way ahead 10 June 28, 2011
Methods of premium rating with deductibles p g Traditional Methods Traditional Methods – Loss elimination ratio (LER) – Loss distribution adjustment L di t ib ti dj t t GLM Methods – Fit GLM using other variables then adjust estimates for deductibles o deduct b es – Use deductible as a rating variable in GLM 11 June 28, 2011
Loss elimination ratio Total claim cost at deductible X (current) = Rs 10 lacs Total claim cost at deductible X (current) Rs 10 lacs Total claim cost at deductible Y (new, higher deductible) = Rs 8 lacs Loss elimination ratio = 20% Loss elimination ratio 20% If Z x = Net claim amount at deductible X and Z Y = Net claim amount at deductible Y Then Z Y = Max (Z x + X – Y, 0) 12 June 28, 2011
Loss elimination ratio Frequency/ Severity Estimates Frequency/ Severity Estimates – This method calculated the pure premium directly – No Frequency/severity estimates are calculated q y y Advantage g – Simple and fast ball-park calculation Disadvantage – Doesn’t use the claims data at new deductible for calculations 13 June 28, 2011
Loss distribution adjustment j Fit a statistical distribution to the truncated # claims data 1 1. Fit a statistical distribution to the truncated claims data 2. Find best fitting statistical distribution and parameter estimate estimate #:Claims data will be truncated at the existing deductible 14 June 28, 2011
Loss distribution adjustment j Past scenario: Past scenario: – Data deductible: 500 # – New policy deductible: 500 p y New scenario – Data deductible: 500 Data deductible: 500 – New policy deductible: can be higher than 500. Or lower. Earlier one could work with the parameter estimates of the net distribution Now, parameter estimates of gross distribution will be needed; These will then be adjusted as per the new deductible value #: For private car with capacity < 1500 cc 15 June 28, 2011
Loss distribution adjustment j Comparative graph of the empirical and two statistical CDFs for truncated data 16 June 28, 2011
Loss distribution adjustment j 3 3. Find frequency and expected claim amount at new Find frequency and expected claim amount at new deductibles Effect of increasing deductible on the claim probability distribution 17 June 28, 2011
Loss distribution adjustment j Say the claim amount random variable is Z with CDF F Say the claim amount random variable is Z, with CDF F z Old deductible = X Old deductible = X Claim Frequency = Freq X, (known, from the data) Expected claim amount = E (Z | Z > X) = Exp X p ( | ) p X Expected claim per policy = Freq X * Exp X New deductible = Y (>X) Claim frequency for deductible Y, Freq Y = Freq X *(1-F z (Y)) /(1-F z (X)) q y q Y q X ( z ( )) ( z ( )) Expected claim amount = E (Z | Z > Y) = Exp Y Expected claim per policy = Freq Y * Exp Y 18 June 28, 2011
Loss distribution adjustment j Frequency/ Severity Estimates Frequency/ Severity Estimates – Frequency estimate calculated based on exceedence probability – Severity estimate is the limited expected value at the deductible y p Advantage – Simple Si l – Smooth results Disadvantage – Doesn’t use the claims data at new deductible for calculations – Doesn’t account for pseudo-deductible – A suitable distribution fit may not be found – Doesn’t account for rating variable effects Doesn’t account for rating variable effects 19 June 28, 2011
Fit GLM without deductible as a rating variable g For claims modeling, rating variable information should be used as mush as possible So the GLM modeling framework should be used g The model should be able to produce gross parameter The model should be able to produce gross parameter estimates (May not be possible using standard statistical tools) # tools) #: Guiahi, 2001 has prescribed a method for such parameter estimation. Needs coding in S-Plus, R 20 June 28, 2011
Fit GLM without deductible as a rating variable g Deductible adjustment to parameters can be done subsequently for the desired deductible This method is best suitable and will give most accurate results in the current Indian market scenario 21 June 28, 2011
Fit GLM without deductible as a rating variable g Frequency/ Severity Estimates Frequency/ Severity Estimates – Frequency estimate calculated based on exceedence probability – Severity estimate is the limited expected value at the deductible y p – The estimates can be calculated for each combination of rating variables Advantage – Uses the GLM framework. More accurate and segment-wise estimates Disadvantage – Doesn’t use the claims data at new deductible for calculations – Doesn’t account for pseudo-deductible – A suitable distribution fit may not be found – Severity distribution used to derive frequency; may be inaccurate Severity distribution used to derive frequency; may be inaccurate 22 June 28, 2011
Fit GLM without deductible as a rating variable g Disadvantage Disadvantage Mean claim amount Mean claim amount Gross claim = Net and frequency claim + DEDUCTIBLE depend on deductible People with bigger car may be richer and may want x = 0 + 1 X 1 + 2 X 2 + x 0 1 1 2 higher deductible higher deductible 2 Rating variables are Choice of deductible Choice of deductible used to model mean d t d l depends on other claim amount and rating variables frequency To accurately model frequency and severity at a deductible, policy and claim data AT that deductible is required Deductible can then be used as a rating variable Deductible can then be used as a rating variable 23 June 28, 2011
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