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Teaching calculator · methodology

How the premium is calculated and where the numbers come from

The calculator follows the classic actuarial scheme: the insurance premium equals the expected loss for each peril plus the insurer's loading. All probabilities are estimated from open data for 2024–2026 and rounded; this is a teaching model, not the tariff of any particular company.

1. Formula

For each selected insured event i:

expected lossi = Pi(V) × max(0, Si × V × krepair − deductible)
net premium = Σ expected losses     gross premium = net ÷ (1 − loading)

Loading is the share of the gross premium that covers the insurer's expenses (acquisition, claims handling, administration) and profit. On the Russian KASKO market it is usually 25–40%; the calculator defaults to 30%.

The simulation “A year in the life of 1,000 cars” rolls every event for every car with probability Pi; the actual loss varies randomly between 50% and 150% of the average. It shows that real payouts deviate from the expectation and why an insurer needs a large portfolio and reserves.

2. Cars and prices

The models are taken from the best-sellers of the Russian market in 2026 according to the Autostat agency: LADA Granta and Haval Jolion top the ranking, LADA Vesta is in the top five, Geely Monjaro is the most popular mid-size crossover, and BMW remains the best-selling premium brand despite parallel import. Prices are the approximate cost of a new car in a typical trim as of September 2026.

ModelSegmentPrice, ₽k theftk repairRationale for the coefficients
LADA GrantaEconomy1,050,0000.61.0Lada is 11% of thefts with roughly 25–30% of the fleet; parts are cheap and available
LADA VestaEconomy1,700,0000.61.0same
Haval JolionComfort2,500,0001.01.1Chinese brands are 8.5% of thefts with a similar share of the fleet; parts cost more and take longer
Geely MonjaroComfort4,100,0001.21.1Growing interest of thieves in expensive Chinese cars
BMW X5Premium12,000,0004.01.3BMW is about 8% of thefts with about 1.5% of the fleet; repairs with parallel-import parts

3. Insured events and probabilities

Probabilities are expressed as the number of events per 1,000 cars per year (per mille, ‰). Where sources give only shares of KASKO claims, they are converted to frequencies through the typical KASKO claim frequency of 25–35% of policies per year.

Dependence on the car's price. Each built-in peril has a range of estimates. Which point of the range is used in the calculation depends on the car's price: a car at RUB 1M or below gets the low end, a car at RUB 12M or above gets the high end, and in between the value is interpolated by the logarithm of the price. For the “minor accident” peril with a range of 47–90 ‰ this gives about 48 ‰ for a LADA Granta, about 63 ‰ for a Haval Jolion and 90 ‰ for a BMW X5. The reasoning is that expensive cars are more often insured under KASKO, are driven more intensively in large cities, are more attractive to thieves and vandals, and their owners more readily report even minor damage. For events added manually the probability is fixed.

Event‰ mid-pointRange of estimatesLoss, % of priceHow the estimate was obtained
Minor accident5047–905RSA: claim frequency under compulsory MTPL is 4.7% of policies per year, 41% are settled via the simplified “Europrotocol” procedure (minor ones). Under KASKO the frequency is higher because it includes at-fault accidents.
Serious accident32–545Traffic police: 117k injury accidents in the first 11 months of 2025 against a fleet of 64M vehicles, about 2 ‰; severe accidents without injuries added.
Theft of the vehicle0.30.2–0.5100Interior Ministry: 10,731 thefts and 3,046 larcenies of cars in 2024, down a further 12–22% in 2025; against roughly 48M passenger cars this is 0.2–0.3 ‰. Multiplied by the model's theft coefficient.
Glass and light damage7050–901.5Rosgosstrakh: every fourth KASKO claim concerns glazing.
Hail, storm, natural disaster53–88Rosgosstrakh: 64% of natural-disaster claims in 2025 were hail; natural disasters are 2–3% of KASKO claims.
Falling tree, snow or objects21.5–3121.8k cases in H1 2026 at one large insurer (+37%), RUB 156M paid, average payout about RUB 87k.
Fire, arson0.30.2–0.480VNIIPO: 19.3k vehicle fires in 2016, 79% passenger cars, declining about 5% a year; now roughly 12–14k a year against 48M passenger cars.
Break-in and theft of property64–103Rosgosstrakh: unlawful acts by third parties are 7–7.8% of KASKO claims; about a third are thefts of parts and belongings.
Vandalism, scratches while parked1410–203The remaining two thirds of third-party-act claims.
Collision with an animal0.50.3–115Ingosstrakh: 418 animal collisions in 2025; other insurers report 18–22% growth year on year. Against a portfolio of about a million cars this is 0.3–1 ‰.

Adjustment coefficients

4. Limitations of the model

5. Sources

  1. Autostat, model sales ranking in Russia, 2026 — autonews.ru, t-j.ru, osnmedia.ru
  2. Premium brand sales, H1 2026 — zr.ru
  3. Prices: LADA Granta — lada.ru; LADA Vesta 2026 — ixbt.com; Geely Monjaro 2026 — ixbt.com; BMW X5 via parallel import — autospot.ru, carto-auto.ru
  4. RSA, MTPL claim frequency 4.7% (Oct 2024 – Sep 2025) — insur-info.ru
  5. Europrotocol: 761.7k applications, 41% of all, 2025 — kommersant.ru
  6. Average MTPL payout RUB 117.6k — autonews.ru
  7. Traffic police, accident statistics for 2025 — kommersant.ru; accident and fleet summary — t-j.ru
  8. Interior Ministry, car thefts and larcenies in 2024 — kommersant.ru; crime statistics, January–November 2025 — mvdmedia.ru; H1 2026 — iz.ru
  9. Most stolen makes (VSK, AlfaStrakhovanie, Ingosstrakh) — finuslugi.ru, ingos.ru
  10. Rosgosstrakh: every fourth KASKO claim is glazing — rgs.ru
  11. Rosgosstrakh: hail as the main natural disaster, 2023–2025 — rgs.ru
  12. Falling trees and objects, H1 2026 — insur-info.ru, rg.ru
  13. VNIIPO, vehicle fires — iprospb.ru; “Fires and Fire Safety in 2023” — VNIIPO (PDF)
  14. Rosgosstrakh: third-party acts are 7–7.8% of KASKO claims — infullbroker.ru
  15. Animal collisions, insurers' data, 2025–2026 — zr.ru
  16. KASKO loss ratio and structure, 2025 — interfax.ru, kommersant.ru