This is CNBC's live blog covering European markets.

European markets on Thursday closed at their highest level since April 2022, despite a choppy afternoon following the release of U.S. inflation data.

The pan-European Stoxx 600 index provisionally closed 0.7% higher, with most sectors and major bourses in positive territory.

Retail stocks led the gains, up nearly 2%, while chemicals and healthcare stocks were both down around 0.1%.

The December CPI report was in line with economist expectations for a monthly dip of 0.1% but a 6.5% rise year-over-year. That compared to a 0.1% monthly gain in November and an annual pace of 7.1%.

U.S. stocks were lower after the open but swung to a gain toward midday, with the Dow Jones Industrial Average up 0.4%.

Huw Roberts, head of analytics at Quant Insight, told CNBC the inflation print had not given any guidance to markets, and investors may look to speeches from Fed officials on Thursday and Friday for further clues.

European markets close 0.6% higher

European stocks ended the day up 0.6%, despite a choppy afternoon following the release of U.S. inflation data.

That took the Stoxx 600 index to its highest level since April 2022. The U.K.'s FTSE 100 index gained another 0.9% after surpassing its 2018 heights in Wednesday's session. At 7794.04 points, the FTSE is inching closer to its all-time high of 7877.45 points.

France's CAC 40 and Germany's DAX were both up 0.74%.

Among sectors, retail stocks led gains as they climbed 1.88%.

— Jenni Reid

Stocks continue moving at market open

The three major indexes jumped around in the first minutes of trading Thursday as investors continued digesting the CPI data.

At 9:35 a.m., the Dow was down 0.1%. The S&P 500 also shed 0.1%, while the Nasdaq Composite lost 0.2%.

All three indexes opened up at 9:30 a.m.

— Alex Harring

U.S. inflation fell 0.1% month on month in December

The U.S. consumer price index fell 0.1% on the previous month in December, in line with the Dow Jones estimate.

It was the biggest monthly decline since April 2020.

Headline CPI was still up 6.5% year on year, but this was the smallest figure since October 2021.

European stocks fell, then rose sharply on the news before trimming gains.

— Jenni Reid

Swiss National Bank says it doesn't need a central bank digital currency

Thomas Moser, alternate member of the governing board of the Swiss National Bank, said he doesn't yet see a need yet to issue a central bank digital currency.

Central banks around the world are exploring the use of CBDCs.

— Arjun Kharpal

Volkswagen Group 2022 sales lowest in over a decade

The Volkswagen Group reported its lowest sales in more than a decade in 2022, according to Reuters, after the company contended with Covid-19 lockdowns in China and with supply chain challenges caused by the war in Ukraine.

The German group said Thursday it delivered 8.3 million vehicles to customers last year, down by 7% compared to 2021.

Weakening global economies and supply chain shortages will continue to cloud the outlook for 2023, according to extended executive sales committee member Hildegard Wortmann.

The sales figures put Volkswagen behind Toyota Group for a third year in a row in terms of production. The Japanese carmaker had already produced 9.5 million cars by November, according to Reuters.

— Hannah Ward-Glenton

European stocks hit highest level since April 2022

European stocks hit their highest level since April 2022 Thursday morning, with all sectors in positive territory.

The Stoxx 600 index was trading around 450.19 at 9:50 a.m. London time. Travel and leisure stocks led the gains, up 1.4%.

The autos, banks, retail and telecoms sectors were also trading over 1% higher.

— Hannah Ward-Glenton

Stocks on the move: Ubisoft down 21%, Logica down 14%, Centrica up 5%

Shares of French video game publisher Ubisoft plunged more than 21% in early trade after the company cut its revenue guidance, postponed the release of its new game "Skull & Bones" and cancelled three unannounced games.

Swiss computer peripherals company Logitech sank more than 14% after missing quarterly earnings expectations and cutting its sales outlook.

At the top of the European blue chip index, British gas owner Centrica climbed more than 5% after raising its full-year earnings forecast.

- Elliot Smith

CNBC Pro: Morgan Stanley names its 'top pick' in Chinese tech — and gives it over 70% upside

China's tech sector has come under pressure in recent years, thanks to a regulatory crackdown and the fallout from the country's zero-Covid policy.

But Wall Street is giving Chinese tech stocks some love again, and Morgan Stanley has named its "top pick" in the sector.

Pro subscribers can read more here.

— Zavier Ong

CNBC Pro: Morgan Stanley says these 3 firms take sustainability seriously — and have upside

As investments in sustainability take off, companies, too, are increasingly adopting sustainable practices.

Morgan Stanley has three European stock picks to help sustainability-focused investors. Those companies not only have solid ESG credentials, but also financial performance to boot.

Pro subscribers can read more here.

— Zavier Ong

Stocks close higher as investors gear up for Thursday's inflation reading

Stocks finished higher Wednesday as investors optimistically positioned ahead of Thursday's CPI report.

The Nasdaq Composite gained 1.8%, notching a four-day streak. A rally with that length has not been seen in the tech-heavy index since September.

The Dow ended up more than 260 points, or 0.8%.

The S&P 500 added 1.3%. All 11 of the broad index's sectors ended the day up, led by real estate with a 3.6% gain.

— Alex Harring

European markets: Here are the opening calls

European markets are heading for a negative open Thursday as investors remain uncertain on the economic outlook, a topic high on the agenda at the World Economic Forum in Davos this week.

The U.K.'s FTSE 100 index is expected to open 37 points lower at 7,793, Germany's DAX 69 points lower at 15,125, France's CAC down 35 points at 7,052 and Italy's FTSE MIB down 77 points at 25,939, according to data from IG.

CNBC will be speaking to a range of delegates at the World Economic Forum on Wednesday, including the CEOs of Enel, Merck, Rio Tinto and leaders of the Netherlands and Ireland, among others.

Follow our coverage here.

— Holly Ellyatt