If Tesla has your car-loving heart, it now wants your auto insurance business, too. The electric auto manufacturer has waded into the insurance business with a program in California — its largest market — and plans to expand to other states in the future. While the company says its rates could be as much as 20% cheaper than other insurers' prices — even 30% in some cases — early reports from Tesla owners suggest that some drivers are getting quotes that are higher than their current coverage elsewhere, experts say. "While it is entirely possible that Tesla can offer significant savings, it's not clear if current [owners] will be able to take advantage of them immediately," said Mark Fitzpatrick, an auto insurance analyst at personal finance website ValuePenguin. "I believe Tesla will continue to tweak its insurance program before rolling it out nationally."

Tesla Model 3 Silas Stein | picture alliance | Getty Images

A Tesla spokesperson said a few bugs were found in the algorithm used to price policies for some customers and that has been fixed. Tesla began offering the new policies in late August through Tesla Insurance Services, which is licensed as an insurance agency in California. Tesla CEO Elon Musk said in an April earnings call that an insurance option through his company would be "more compelling than anything else out there." Current Tesla owners can get a quote online through their existing account with the company. The policy management and claims process will be handled through Tesla Insurance, while State National Insurance is the underwriter — the entity taking on the financial risk of the Tesla policies. Officials at Tesla didn't repond to a CNBC request for specific policy quotes. Tesla Insurance is also taking steps toward becoming a full-blown insurance carrier, which would mean also being able to underwrite its own policies. The Tesla spokesperson declined to comment on the timing or whether it would mean venturing into other lines of coverage, such as home or life.

Teslas tend to be pricier to insure, due largely to the cost of fixing them. Collision coverage accounts for between 57% and 65% of a policy's cost, according to ValuePenguin. In California, the average insurance policy cost for a Model 3 — the least expensive Tesla with a 2019 base price of $35,000 — is $1,913 yearly, with a $500 comprehensive and collision deductible, according to ValuePenguin's survey of three insurers (State Farm, Geico and Progressive). Insurance is higher for pricier models: an average $2,473 annually for the Model X (2019 base price of $81,000) and $2,963 for the Model S (2019 base price: $75,000). Tesla maintains that because it knows more about its cars, technology and repair process, it can offer policies that are less expensive. It also is reducing some costs like commissions that are common with auto insurance policies sold through other insurers. While Tesla policies will be discounted for the car having an autopilot feature, other discounts that may be applied are common in the industry.

Musk has talked about having access to all sorts of data, but right now they aren't really using any of it. Matt Timmons Research analyst at ValuePenguin

"Discounts for multiple policies, or being a good driver or having an anti-theft device — those are not particular to Tesla," said Matt Timmons, a ValuePenguin research analyst. And while anonymous, aggregated data is currently used to help set the price for the California policies, the company does not use or record data from individual vehicles, such as GPS or vehicle camera footage. Regulatory filings and company executive comments suggest Tesla eventually wants to use individual driving data to price policies, if drivers agree to it and a particular state's laws allow it. Where it's permitted, some insurance companies already offer policies that use so-called telematics — direct data from your car about your driving habits through a specialized device or smart-phone app — to potentially offer additional discounts for safe drivers (those who avoid excessive speeds, hard braking, etc.). More from Personal Finance:

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How to break up with your financial advisor The Tesla spokesperson said the company plans to incorporate more types of data into its insurance offerings over time, but declined to provide additional details. After the company's planned move into insurance was announced in April, Warren Buffett, chairman of Berkshire Hathaway, said Tesla would likely struggle as it enters the insurance business — something that Buffett's company invests in heavily. Musk has endorsed the notion that automation in cars would bring insurance prices down. However, in 2017, several insurance companies raised their rates on Tesla cars, saying they generated more claims and were more expensive to repair.