1 WELCOME PRICING AND MODELING OF THE PERSONAL AUTO INSURANCE
2 INDEX 1. INTRODUCTION 2. MAINTARGET INPRICING 3. RATE / PREMIUM 4. FREQUENCY / SEVERITY & NRP 5. NET PREMIUM METHOD 6. LOSS RATIOMETHOD 7. GLM
3 INTRODUCTION Insurance is aform of risk management primarily il used to hedge against the risk of a contingent, uncertain loss. Insurance is defined as the equitable transfer of the risk of a loss, from one entity to another, in exchange for payment.
4 In non life insurance sector, increasing costs and nearly stopping the growth of insured ratio make the competition more difficult. Free tariff system in auto insurance ( Own Damage OD ) sector has caused big problem. This competition has engendered decreasing the companies profit and huge differences among the premiums. The essence of this competition is the application of the different criteria in tariffs and differences in the premium accordingly. While determining the rates in OD actuarial analysis are made considering the risk factors The aim of the modeling method is to determine expected cost in the future. Through the past data, the efficient premium is determined to reach the expected profit. The logic in calculating the premium depends on expected loss. IBNR ( Incurred But Not Reported ) is being evaluated separately in calculation of expected loss.
5 Success in Pricing Sell the right product to the right customer at the right time at the right price
6 The Right Pi Price Meets the objectives primarily financial secondarily volume, mix, brand etc. of all interested parties
7 MAIN TARGET FOR PRICING : In conjunction with given coverage the aim is to reach up to expected profitability. ( The more efficient pricing for the company, the greater is its profitability ) To determine adequate premium and rates align with competition in the sector EXPRESSING WITH ADEQUATE PREMIUM Premium should be able to cover both indemnities and other business expenses accordingly, Each coverage should be priced separately,
8 IN PRICING WORK ; Average prices are set per companies Average prices are set per sectors Regional differences are determined Risks are segmented
9 RATE Rate consists of a lot of elements. These are Cost of Claim + Cost of Production + Operating Expense + Profit In addition to that ; Improvements in the insurance market, Pricecompetition with the other insurance companies, Growth Strategy are the some other factors which play roles in forming the rate.
10 Components of Premium Profit Technical Epenses& Expenses Premium Loads Profit Load General Expenses Allowance for Reinsurance Acquisition Expenses Levies Risk Premium Cost Expected Claims Cost
11 The organizations and managers most of the times are interested in and worried about the costs. The control of the costs of the past, present and future is part of the job of all the managers in a company. In the companies that try to have profits, control the costs. Knowing the cost of the product is essential for decision making regarding price and mix assignation of products and services. What is the cost of insurance?
12 EVALUATION PARAMETERS 1 Written Premium 2 Earned Premium / Unearned Premium 3 Risk Premium 4 Cancellation Rate 5 Average Written Premium 6 Frequency 7 Severity 8 Net Loss Incurred 9 Loss Ratio
13 PREMIUM The amount to be charged for a certain amount of insurance coverage is called the premium It can be grouped as Written Earned and Unearned. Written premium :The amount of premium an insured agrees to pay for specified coverage over and agreed length of time. Earned premium : The portion of written premium for the protection and insurance company has actually provided. For example, an insured prepays $ for a oneyear policy which is effective January 1 st. On July 1, the company providing coverage has earned 50 % ( or $ 500 ) of the written premium. Because it has provided coverage for half of the year. Unearned premium : Not provided coverage for the rest of the year
14 The essence of the premium is formed by the risk premium. The risk premium is the level that equalize the expected loss expenses, The claims / losses are the cost for the insurance. In order to be able to calculate the risk premium we need two main ratios Frequency, Severity Frequency and severity are derived from the claims. Expected value derived from loss allocation determines the premium applied to the portfolio. The size of the standard deviation regarding loss allocation identifies the defect / error / deviation in the premium. Small deviation points out that the risk over the company is less.
15 Frequency : Frequency is the number of occurrences of a repeating event per unit time. There is a relation between the policies issued and the count of claims. Count of Claim Files f : Count of Policy Example :3.000 / = 30% Severity : Severity impliesthe averageclaim li Total Amount of Claims s: Total Count of Claim Files Example : / = In the meantime Paid Incurred Reported claims canbe defined under the claim terminology
16 Net Risk Premium ( Cost of Claim ): The risk premium is the level that equalize the expected loss expenses. The main point in calculation of the net risk premium is to know frequency (exposure of making claims ) and severity ( average claim amount ) NRP is calculated by Count of Claim Files f : Count of Policy Total Amount of Claims X s: Total Count of Claim Files
17 Expenses, Commission, Profit : Expenses ( cost ) are grouped as fixed costs and variable costs Some costs tend to remain the same even during busy periods, unlike variable costs, which rise and fall with volume of work. Over time, the importance of these fixed costs" has become more important to managers. Examples of fixed costs include the depreciation of equipment, and the cost of department such as employee salaries software license. Commission is the amount that is paid to producers ( agents, brokers ) Variable costs are expenses that change in proportion to the activity of a business. Variable cost is the sum of marginal cost over all units produced. It can also be considered normal costs. Fixed costs and variable costs make up the two components of total cost. These variables ibl are used to dt determine the rate.
18 NRP + Fixed Costs R = = = ( Variable Cost + Profit ) 1 ( 20% +10% ) 0,70
19 Loss Adjusted Expenses ( LAE ): Expenses incurred in the process of adjusting claims either allocated or unallocated ( These expenses are the out of indemnity payments ) Allocated Loss Adjustment Expenses ( ALAE ) : Includes all loss adjustment expenses that can be directly applied or allocated to claim file number. ( expenses for the claim file such as outsource of legal advisory ) Unallocated Loss Adjustment Expenses ( ULAE ) : Includes all loss adjustment expenses that can not be directly applied or allocated to a claim file number, such as claim department salaries and operating expenses. LAE = ALAE + ULAE
20 PRICING METHODS : There are different type of pricing methods. Net Premium Method and Loss Ratio Method are the basic methods. Net Premium Method : In this methodology, average premium for each risk, loss adjusted expenses and fixed costs in accordance with insurance period are included in calculation. The total amount of this parameters are confronted with variable costs and expected profit.
21 NtP Net Premium Method Mthd: Count of Policy = X Premium = P Premium with existing rate = Pe Average Premium with existing rate = APe Average Premium = AP Incurred dloss = L Loss incurred per risk = Lr Loss Adjusted Expenses = LAE LAE per risk = LAEr Fixed Costs = F Fixed Costs per risk = Fr Variable Costs = V Variable Costs per risk = Vr Variable cost ratio = VR ( V is divided by premium ) Expected profit = P
22 Net Premium Method : Price is formulated as, Net premium ( LAE included ) + Fixed Costs Rate = 1 ( Variable costs + expected profit ) Count of Incurred Loss In net premium calculation Count of Policy x s ratio is taken into account Incurred loss covers paid and outstanding losses within the related period Rate formula can be re written below according to risk based P = [Lr + LAE + Fr ] / [ 1 VR P]
23 Net PremiumMethod : P = [Lr + LAE + Fr ] / [ 1 VR P] Conformity with this formula an example can be given as ; Losses and LAE are 650 TL per risk Fixed costs are 100 TL Variable cost ratio is 20 % Expected profit is 10 % P = [ ] / [ 1 0,20 0,10] P = TL
24 Loss Ratio Method : In generally It is defined as loss ratio is calculated to earned premium. This method confronts with incurred loss and expected loss. Incurred loss covers paid and reserved losses while the expected loss is loss level for being profitable LR method = Incurred Loss Ratio / Expected Loss Ratio ILR = 85 % ELR = 70% 0,85 / 0,7 =1,21 As a result of this ratio average premium level is insufficient with existing rates and need to be increased 21 %.
25 GLM ( Generalized Linear Modeling ) In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the varianceof each measurement to be a function of its predicted d value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as awayof unifying i various other statistical ti ti models, They proposed an iteratively reweighted least squares method for maximum likelihood estimation of the model parameters. Maximum likelihood estimation remains popular and is the default method on many statistical computing packages.
26 GLM is a predictive modeling involves using historical data to construct a statistical model that will be predictive of the future. Each observation in the historical dataset contains information or data elements that are essential in building a predictive model. There are three types of elements in the historical dataset. First, there will be a dependentd variable ibl which h is what htyou are trying to predict. For example, when modeling severity, the dependent variable is the loss amount.
27 Second, there will be a weight associated with each observation. When modeling severity, the weight is the number of claims associated with ihthe loss amount of theobservation. Finally, there are independent variables. These are the characteristics of each observation that are being studied to ascertain whether a variable has any predictive power. Actuaries uses the historical data to build a statistical model. The majority of companies using predictive modeling are building such models to identify new rating variables and to better quantify the relationships between these new variables and existing rating variables.
28 GLM explains the relation between dependent variable. variable and independent For example frequency or severity can be accepted as dependent variable whereas those factors such as ; Client ( Age, Gender, Driving license year, Loss history ) Vehicle ( Vehicle age, Sum Insured, Type of usage, make&model, ) Region, city are independent factors This model works on multiple varied analysis. GLM is a statistical / actuarial method which is widely used in Global insurance
29 VEHICLE BRAND Row Number Level 1 Description Exposure 95 % Confidence Interval 1 KIA , VOLVO , NISSAN , PEUGEOT , BMW , HONDA , CITROEN , TOYOTA ,047 9 VOLKSWAGEN , MERCEDES HYUNDAI , FORD , RENAULT , AUDI , OTHERS ,10097 According to segmentation these factors are taken into account in terms of brands
30 VEHICLE REGISTERED CITY Row Number Level 1 Description Exposure 95 % Confidence Interval 1 CITY A , CITY B CITY C , CITY D , CITY E , CITY F , CITY G , Those cities type of usage are also determined. 5 CITY E % confidence interval results are shown USAGE OF THE VEHICLE Row Number Level 1 Description Exposure 95 % Confidence Interval 1 PERSON COMPANY ,224877
31 NO CLAIM DISCOUNT LEVEL Row Number Level 1 Description Exposure 95 % Confidence Interval , , , , The numbers in the 95% confidence level show coefficient of the factors. These coeffcients are showing reduction orloading ratios.
32 The numbers in the 95% confidence level show coefficient of the factors. These coefficients are showing reduction or loading ratios. Adding 1 with these coefficients you can reach to the risk premium
33 VEHICLE BRAND Row Number Level 1 Description Exposure 95 % Confidence Interval 1 KIA , VOLVO , NISSAN , PEUGEOT , BMW , HONDA , CITROEN , TOYOTA ,047 9 VOLKSWAGEN , MERCEDES HYUNDAI , FORD , RENAULT , AUDI , OTHERS ,89903 USAGE OF THE VEHICLE Row Number Level 1 Description Exposure 95 % Confidence Interval 1 PERSON COMPANY , NO CLAIM DISCOUNT LEVEL Row Number Level 1 Description Exposure 95 % Confidence Interval , , , , VEHICLE REGISTERED CITY Row Number Level 1 Description Exposure 95 % Confidence Interval 1 CITY A , CITY B CITY C , CITY D , CITY E , CITY F , CITY G ,645242
34 Example = Insured is a person and living in city A His car is 2012 model Honda He has got no NCD The risk premium is = 1, x 1, x 1,46789 x 1 =2,278 Than you make necessary loadings over the risk premium
35 THANK YOU