Telematics and the natural evolution of pricing in motor insurance

Telematics and the natural evolution of pricing in motor insurance Montserrat Guillén University of Barcelona www.ub.edu/riskcenter Workshop on data sciences applied to insurance and finance Louvain-la-Neuve, September 15, 2017 1 / 33

1 Introduction and background 2 Research milestones 3 Transition to a pricing based on telematics 4 Going forward to optimal pricing 2 / 33

The concepts in telematics insurance Pay-As-You-Drive (PAYD) automobile insurance is a policy agreement tied to vehicle driven distance. Pay-How-You-Drive (PHYD) considers driving patterns. The permission of the driver for monitoring data from the vehicle and the Global Positioning System (GPS) is required. Telemetry provides the insurer with detailed information on the use of the vehicle and the premium is calculated based on usage. Usage-Based-Insurance (UBI). Distance and driving skills of the drivers are considered (speed, type of road and part of the day when the car is most frequently used,...). These new factors improve the rating system, because they can explain the risk of accident (Litman, 2005; Langford et al., 2008; Ayuso et al., 2010; Jun et al., 2007 and 2011; Verbelen et al., 2017; Henckaerts et al., 2017). 3 / 33

What we do We present methods to quantify risk with application to usage-based motor insurance. We analyse mileage and explore the way exposure to risk is considered in generalized linear models. We include other driving patterns in predictive models. We show illustrations from a pool of young drivers with telematics insurance. Why? Strong evidence exists that information on mileage and driving habits improves the prediction of the number of claims. Our question is: How can telematics information be useful in motor insurance pricing? 4 / 33

What we do How do telematics data look like? Source: Jim Janavich ideas.returnonintelligence.com 5 / 33

Telematics in motor insurance The evolution of motor insurance: How do we implement a PAYD-PHYD-UBI pricing? How do we live with traditional and modern telematics pricing? How do we combine the best of the two? 6 / 33

Telematics in motor insurance If we seek to evaluate the driver s risk: Can we eliminate measurement error? Can we combine information from many sources to assess risk? How can we update price dynamically? 7 / 33

The advantages of selling UBI Advantages for insurance companies: each driver s exposure to the risk of being involved in an accident can be measured more accurately, thus enhancing the actuarial fairness of premiums. Moreover, the insurer can also obtain a more sophisticated segmentation of the market, Hultkrantz et al. (2012) claim that PAYD helps the insurance industry to target risk classes more effectively. Advantages for the insurer: It makes insurance more affordable and it also offers rewards for careful driving. Actually, there are evidences of the changes in the driving patterns of individuals who want to get a better premium under a PAYD/UBI system. Buxbaum (2006) observed that, under this system, drivers have an incentive to drive less and Toledo et al. (2008), Bolderdijk et al. (2011) and Lahrmann et al. (2012) observed a reduction of speed. 8 / 33

Knowledge on telematics pricing 1 The relationship between the distance run by a vehicle and the risk of accident has been discussed by many authors, most of them arguing that this relationship is not proportional (Litman, 2005 and 2011; Langford et al., 2008; Boucher et al., 2013). 2 There is evidence of the relationship between speed, type of road, urban and nighttime driving and the risk of accident (Rice et al., 2003; Ayuso et al., 2010; Laurie, 2011; Ellison et al, 2015; Verbelen et al. 2017). 3 Telematics information can replace some traditional rating factors and provide a pricing model with the same performance (Verbelen et al. 2017; Ayuso et al., 2017). Gender: discrimination that turns out to be a proxy Gender can be replaced by: km/day (Barcelona approach) or km/trip (Leuven approach) 10 / 33

Scor Actuarial Prize for Spain and Portugal, 2016 Risk exposure: contract duration vs. travelled Km We analyse the simultaneous effect of the distance travelled and exposure time on the risk of accident by using Generalized Additive Models (GAM). We carry out an empirical application and show that the the expected number of claims: (1) stabilizes once a certain number of accumulated kilometers is reached and (2) it is not proportional to the duration of the contract, which is in contradiction to insurance practice. Finally, we propose to use a rating system which takes into account simultaneously exposure time and distance travelled in the premium calculation. 11 / 33

Scor Actuarial Prize for Spain and Portugal, 2016 GAM with interaction between duration and kilometers - Predictions surface. 71,489 policies in Spain (2011) 12 / 33

Scor Actuarial Prize for Spain and Portugal, 2016 The effect of kilometers and duration on claim occurrence Big Brother s effect? 13 / 33

Scor Actuarial Prize for Spain and Portugal, 2016 PAYD price structure based on GAM. (Km; d) Relativity (Km; d) Premium (3500; 0.35) 0.7904 0.0510 (4500; 0.50) 1.0691 0.0690 (9000; 0.65) 1.4564 0.0940 (15500; 0.90) 2.2103 0.1427 (19000; 1.00) 2.3428 0.1513 14 / 33

Submitted work Telematics information as complement/substitute of traditional risk factors In Ayuso, Guillen and Nielsen (2016c) we propose a method for assessing the influence on the expected frequency of usage-based variables which can be viewed as a correction of the classical ratemaking model. Given x i, the dependent variable Y i follows a Poisson distribution with parameter λ i, which is a function of the linear combination of parameters and regressors, β 0 + β 1 x i1 +... + β k x ik. E(Y i x i ) = exp(β 0 + β 1 x i1 +... + β k x ik ) (1) The unkown parameters to be estimated are (β 0,..., β k ) 16 / 33

Submitted work Telematics as a correction A two-step procedure: Step 1: Let Ŷi be the frequency estimate obtained as a function of the classical explanatory covariates x i = (x i1,..., x ik ). Step 2: Let Y UBI ˆ i be the prediction from usage base insurance information z i = (z i1,..., z il ). The, let us specify E(Y UBI i z i, Ŷ i ) = Ŷ i exp(η 0 + η 1 z i1 +... + η k z ik ) (2) The parameter estimates can now be obtained using Ŷi as an offset. 17 / 33

Submitted work Empirical application based on 25,014 insureds with car insurance coverage throughout 2011, that is, individuals exposed to the risk for a full year. 18 / 33

Submitted work Poisson model results. All types of claims. 19 / 33

Submitted work Concordant predictions of all models (in percentages). Poisson model results. All types of claims Poisson model results with offsets (Log of Km per year in thousands). All types of claims Poisson model results. Claims where the policyholder is guilty Poisson model results with offsets (Log of Km per year in thousands). Claims where the policyholder is guilty All variables Non-telematics Telematics Telematics with offsets 62.28 55.91 61.34 62.10 62.15 58.60 61.18 62.05 62.70 57.72 61.13 62.65 62.38 58.96 60.89 62.43 20 / 33

Submitted work 21 / 33

Submitted work In Ayuso et al. (2016c) we also propose to include the distance travelled per year as an offset in a Zero Inflated Poisson model to predict the number of claims in Pay as You Drive insureds. The Poisson model with exposure: Let us call T i the exposure factor for policy holder i, in our case T i = ln(d i ), where Di indicates distance travelled, then: E(Y i x i, T i ) = D i exp(β 0 + β 1 x i1 +... + β k x ik ) = D i λ i (3) 22 / 33

Submitted work The ZIP Poisson model: Now the probability of no suffering an accident is P(Y = 0) = p + (1 p)p(y = 0) (4) where p is the probability of excess of zeros. Y follows a Poisson distribution with parameter exp(β 0 + β 1 x i1 +... + β k x ik ), and p may depend on some covariates. 23 / 33

Submitted work A ZIP Poisson model with exposure We assume that p is the probability of an excess of zeros, and it is specified as a logistic regression model such that p i = exp(α 0 + α 1 ln(d i )) 1 + exp(α 0 + α 1 ln(d i )) (5) The Poisson model for Y is specified as follows, with an exposure E(Y i x i, T i ) = D i exp(β 0 + β 1 x i1 +... + β k x ik ) = D i λ i = exp(ln(d i ))λ i where T i = ln(d i ). The expectation of the Poisson part is where D i = D i E(Yi 1 x i, T i ) = 1 + exp(α 0 + α 1 ln(d i )) D iλ i = Di λ i (6) D i 1+exp(α 0+α 1ln(D i )) is a transformation of the original exposure 24 / 33

Submitted work Accidents impact the average speed of the driver Mean (standard deviation) of excess speed and driving intensity (km/day) before, during and after the claim depending on sex and claim type. 25 / 33

Submitted work Linear Regression model for estimating average speed after the accident Variable Parameter Estimate Standard Error t Value Pr > t Intercept 2.31589 0.32346 7.16 <.0001 Speed before 0.46675 0.03111 15.00 <.0001 Bodily injury cost 0.00025 0.00008 3.08 0.0021 Speed before Bodily inj cost -0.00003 0.00001-3.68 0.0002 Male -1.01172 0.44887-2.25 0.0244 Male Speed before 0.18074 0.03950 4.58 <.0001 The speed after the accident is explained by speed before, sex and bodily injury cost of claims. Property damage cost of claims do not explain the speed after the accident. Higher Bodily injury costs are associated with larger average speed reductions. 26 / 33

... and then correct premium 28 / 33

In dependent modelling price, lapse and usage are all interconnected 29 / 33

30 / 33

Further research The past is modelling number of claims and severity and the future is scoring the driver based also on detailed information (breaks, abrupt accelerations, traffic environment and driving style). Telematics makes real time dynamic pricing possible. With our proposal, daily estimates of usage correct the insurance premium and work effectively as a modern version of experience rating. 31 / 33

Our list of papers Ayuso, M., Guillen, M. and Pérez-Marín, A.M. (2014) Time and distance to first accident and driving patterns of young drivers with pay-as-you-drive insurance, Accident Analysis and Prevention 73, 125-131. Ayuso, M., Guillen, M., Pérez-Marín, A.M. (2016a) Telematics and gender discrimination: some usage-based evidence on whether men s risk of accident differs from women s, Risks, 2016, 4, 10. Ayuso, M., Guillen, M., and Pérez-Marín, A.M. (2016b) Using GPS data to analyse the distance travelled to the first accident at fault in pay-as-you drive insurance, Transportation Research Part C 68 (2016) 160-167. Boucher, J.P., Coté, S. and Guillen, M. and Pérez-Marín, A.M. (2016). Exposure as duration and distance in telematics motor insurance using generalized additive models, submitted. Ayuso, M., Guillen, M. and Nielsen, J.P. (2017) Improving automobile insurance ratemaking using telematics: incorporating mileage and driver behaviour data, UB Riskcenter Working Papers Series 2017-01. Ayuso, M., Guillen, M. and Nielsen, J.P. (2016c) Distance travelled as a risk factor when predicting motor insurance claims. In progress. 32 / 33

Our list of papers Telematics and the natural evolution of pricing in motor insurance Montserrat Guillén University of Barcelona www.ub.edu/riskcenter Workshop on data sciences applied to insurance and finance Louvain-la-Neuve, September 15, 2017 33 / 33