Pay-As-You-Drive Insurance and Usage-Based Insurance: A Look at Two Recent Articles in the NAAJ
By Anthony Cappelletti
I regularly read articles from a variety of actuarial journals to stay informed of developments in general insurance and actuarial science. It’s a good source of self-study credit for SOA CPD requirements. I always include the SOA’s North American Actuarial Journal (NAAJ) as part of my readings. A couple of recent articles in the NAAJ explored Pay-As-You-Drive (PAYD) insurance and Usage-Based-Insurance (UBI). Automobile insurers are quickly shifting from traditional rating factors to using PAYD and UBI for rating. These two papers look at how PAYD/UBI affect the general insurance industry.
In this article, I’ll give a non-technical review of the main concepts presented in each of the following NAAJ articles:
Jiang Cheng, Frank Y. Feng & Xudong Zeng (2022): Pay-As-You-Drive Insurance: Modeling and Implications, North American Actuarial Journal
Xin Che, Andre Liebenberg & Jianren Xu (2022) Usage-Based Insurance—Impact on Insurers and Potential Implications for InsurTech, North American Actuarial Journal, 26:3, 428-455
Before I get into these two articles, I’ll give a brief overview of PAYD and UBI for insurance rating. When considering PAYD and UBI, one should give some consideration to the issue of insurance discrimination. I recommend reading the following NAAJ article on insurance discrimination issues:
Edward W. (Jed) Frees & Fei Huang (2021): The Discriminating (Pricing) Actuary, North American Actuarial Journal
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The NAAJ is the official journal of the SOA and is published by Taylor & Francis Online. SOA members have access to all NAAJ articles. Click on the link SOA Member Access to explore the NAAJ. After clicking on this link and logging in to your SOA account, the following links will work to access the NAAJ articles referenced in this article:
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Background
By now, everyone has heard of InsurTech. InsurTech generally refers to the use of innovative technologies to increase efficiencies in the business of insurance. Telematics, in the most general sense, is the combination of telecommunications technology and informatics (i.e., computerized data). However, telematics in the insurance industry refers to the use of a device or devices that collect risk data from policyholders and transmit this information to the insurer so that it can be used to determine an individualized rate, or rate adjustment, for the policyholder.
While UBI does not actually require the use of telematics, UBI for automobile insurance usually refers to UBI through telematics. PAYD insurance is a subset of UBI whereby the information transmitted is mileage[1] driven. When more types of information are captured (e.g., instances of hard braking, rapid acceleration, time of day vehicle is driven), the UBI system may be referred to as Pay-How-You-Drive (PHYD). UBI provides a means for insurers to shift away from using non-causal factors (e.g., age, sex, marital status), that may be viewed as unfair discrimination, to using casual factors captured by telematics.
The use of UBI for automobile insurance is becoming more prevalent as most large automobile insurers now offer a UBI product to consumers. Actuarial articles examining UBI systems are most welcome to the GI actuarial community.
Payd Insurance: Modeling and Implications
In “Pay-As-You-Drive Insurance: Modeling and Implications,” Cheng et al. focus on the development of a dynamic theoretical PAYD model. They then use their model to produce results that provide insight into some features of PAYD insurance. Specifically, they look at decision-making of an individual as to when it’s optimal to choose PAYD insurance over traditionally rated insurance.
The PAYD model developed by Cheng et al. is dynamic. That is, the premium is adjusted at various points during the annual policy period to reflect the policyholder’s actual mileage driven during that period. It is common for PAYD insurance policies to have premium adjustments monthly. A dynamic model is necessary to reflect the reality of insurance industry practice.
The model assumes that the frequency of accidents in a time period follows a Poisson process. The Poisson rate is modeled as a continuous and increasing function of mileage. The function is left general so that it may be a linear function or a concave function depending on parameter selection. Research has produced mixed results on whether the function is linear or concave. Cheng et al. focus on the concave relationship (i.e., the frequency of accidents increases at a decreasing rate with respect to mileage). The PAYD premium function should be concave with mileage because of competition with traditional insurance for high mileage drivers.
When a policyholder drives less in a time period, the premium rate will be reduced so there is an incentive to drive less. However, the policyholder gains value by driving their vehicle. There is a benefit to the policyholder in driving one’s vehicle. The optimization considers the total utility of the policyholder that consists of the utility of using the vehicle and the utility of the terminal financial wealth of the policyholder. The wealth function in the models uses income less expenses. The components of expenses that vary with mileage are the cost of gas and PAYD insurance premium. Because this is a non-technical review, I won’t cover all the functions derived and used in their model. Those interested in the technical components are invited to read the article by Cheng et al.
With this function, Cheng et al. investigated two implications regarding PAYD insurance. The first implication concerns the relation between fuel costs and PAYD insurance. The second implication concerns the mileage cutoff below which a driver with traditional insurance will be motivated to make the switch to PAYD insurance.
With respect to the first implication, the utility of terminal wealth may be increased by lowering PAYD insurance premiums (a function of mileage) and lowering fuel costs (a function of mileage and the price of fuel). Under traditional insurance, the utility of terminal wealth may be increased by lowering fuel costs because insurance premium is fixed. This relation is important because public policy legislators use fuel taxes, in part, to incentivize a reduction in the overall amount driven. They determined that “PAYD insurance is less efficient than fuel price in reducing mileage for high-mileage drivers.” However, they note that for lower-mileage drivers, the answer depends on “the exact curvature of the premium function.” They go on to note that for these drivers, “PAYD insurance may work more efficiently than [a] fuel tax” in reducing mileage.
Regarding the second implication, they note that a driver that “pays less with PAYD insurance than with traditional insurance … is not sufficient to determine who should switch to PAYD insurance due to utility loss resulting from the reduced mileage.” They deal with this by using the concept of “optimal mileage” rates for each insurance system. These optimal mileage rates may be determined by the set of preferences for the individual regarding utility for wealth, utility for mileage, and cutoff wealth.[2] Using this, they then provide the condition under which the individual will switch from traditional insurance to PAYD insurance. This yields a formula for the mileage cutoff.
Cheng et al. apply the formulas they developed in quantitative illustrations using selected model parameters. These selections were based upon their consideration of real conditions. It’s an interesting exercise that shows the application of their approach.
After their quantitative illustrations, Cheng et al. conclude that “PAYD insurance can reduce mileage driven more efficiently than increasing fuel prices, and this is relevant to the broader corporate social responsibility in the climate change literature.”
They do note that their model could be extended to incorporate additional policy features and a “time-varying fuel price.” They leave this for future research.
I suggest that anyone working in automobile insurance rating try out these formulas with their own real-world parameter selections. Perhaps it could provide some additional insight into rating, underwriting and marketing policies.
UBI—Impact on Insurers and Potential Implications for Insurtech
In “Usage-Based Insurance—Impact on Insurers and Potential Implications for InsurTech,” Che et al. investigate how an insurer’s adoption of UBI for private passenger automobile liability (PPAL) will affect its underwriting results for that line of business. They applied a fixed-effects multiple regression model to data from U.S. insurers for the period from 1995 to 2018. The dependent variable is the PPAL loss ratio, and the independent variables include a binary indicator if UBI is offered by the insurer for a given year, insurer size, insurer capitalization, line of business diversification, geographic diversification, year fixed effects and insurer fixed effects. Those interested in the technical details of the data sources and the model selection process are invited to read the article by Che et al.
In the article, the following hypotheses were tested:
- Hypothesis 1: UBI adoption is associated with better underwriting performance.
- Hypothesis 2: UBI programs benefit early adopters but not late adopters.
- Hypothesis 3: The benefits of UBI programs are not immediate but are experienced when the programs mature.
Regarding Hypothesis 1, Che et al. found this relation to be insignificant on average.
For testing Hypothesis 2, the UBI variable was split into Early UBI Adopter and Late UBI Adopter. Results of this revised model showed a statistically significant improvement in PPAL loss ratios (lower by 2.8 percent) for early UBI adopters. For late UBI adopters, they found the relation to be insignificant.
For testing Hypothesis 3, the Early UBI Adopter and Late UBI Adopter variables were further refined to include the maturity of the UBI program. This confirmed UBI programs only benefit early adopters and that for early UBI adopters, “each additional year of the UBI adoption on average reduces the insurer’s PPAL loss ratio by 0.30 percent.”
Since some insurers adopted their UBI program as a pilot project, the authors of the article further refined the UBI variable for UBI adopters into four binary variables as follows: Early UBI Adopter Pilot, Early UBI Adopter Post-Pilot, Late UBI Adopter Pilot, and Late UBI Adopter Pilot. This resulted in only Early UBI Adopter Post-Pilot firms showing a statistically significant improvement in PPAL loss ratios.
Che et al. then go on to use a more refined dynamic model to investigate potential flaws in their analysis (e.g., missed variables, inherent bias in the data) and the associated results of it. Their analysis didn’t indicate any flaws (for the ones they tested against) and confirmed the results from the fixed-effects model. Additional analysis by Che et al. showed that “only early UBI adopters are able to garner additional market share, while late UBI adopters are not.”
I found this article to be quite interesting. The conclusion that only early UBI program adopters show improved financial results is important. Insurers should pay close attention to developments in InsurTech so that they will have a chance to be an early adopter.
Final Thoughts
Telematics, UBI, PHYD and PAYD are important to the business of insurance. These programs can alter driving habits and may improve insurer results. Use of these programs will help insurers move away from using traditional non-causal variables (e.g., sex and age of driver) to variables that are directly linked to loss exposure (e.g., amount driven, safe versus aggressive style of driving). This will be seen as a fairer method of insurance discrimination by most policyholders and legislators. Furthermore, programs that entice people to drive less improves society as a whole by reducing congestion on roadways, reducing pollution, reducing greenhouse gas emissions and reducing the frequency of accidents by rewarding safe driving habits.
Having said that, one must think about potential unintended consequences for UBI programs. PHYD systems determine safe driving habits and aggressive driving habits by looking at actions like hard braking or hard acceleration. But there are times when hard breaking or fast acceleration is required for safety. For example, hard breaking may be necessary to avoid potential accidents and fast acceleration may be necessary to safely merge onto a highway. Drivers may try to improve their safer driving score by avoiding hard breaking or fast acceleration even when it’s a safer action.
There is also the question of protection of privacy regarding all the telematics data that is being collected from policyholders. Insurers need to ensure that their data cannot be accessed by hackers.
Then there is the question regarding ownership of a driver’s data. Should it be portable (i.e., a driver can submit their data as proof to other insurers of their safe driving habits) or is the data strictly for use by the insurer that collected it?
Another factor to consider is the improvement in automobile technology that is rapidly occurring. Newer vehicles have many safety features that aid in accident avoidance (when they are activated). The downside is that drivers may be too reliant on these safety features and be less focused on driving in the belief that the automobile will take care of things. But these safety systems are not foolproof. Drivers still need to be focused on driving even when using adaptive cruise control, accident avoidance and lane keeping systems.
And what about vehicle manufacturers being the insurer for the vehicles they sell? And then at some point we’ll be seeing more and more autonomous vehicles in the road. How will this affect insurance pricing models?
We live in interesting changing times. If there is one certainty, it’s that general insurance actuaries must be informed on technological developments and how it will affect insurance.
Statements of fact and opinions expressed herein are those of the individual authors and are not necessarily those of the Society of Actuaries, the editors, or the respective authors’ employers.
Anthony Cappelletti, FSA, FCIA, FCAS, is a staff fellow for the SOA. He can be contacted at acappelletti@soa.org.