Investors on Thursday continued their search for safety and flooded into bonds as the relentless selling persisted in the stock market, pushing Treasury yields lower.

The yield on the benchmark 10-year Treasury note dropped nearly 5 basis points to 2.866% after rising to its highest level since 2018 earlier in the week. The yield on the 30-year Treasury bond moved lower to 3.034%. Yields move inversely to prices and 1 basis point is equal to 0.01%.

As the sell-off in equities continued, investors moved back into bonds in search of safety. The shift further pushed up bond prices while lowering yields, which move inversely to one another.

April's consumer price index, released Wednesday, rose 8.3% year-on-year. That was higher than the anticipated 8.1% growth in inflation, but was below March's 8.5% CPI reading.

The 10-year Treasury yield climbed back above 3% following the release of the report, but then eased back.

The latest inflation reading supports the Federal Reserve's plans to more aggressively hike interest rates to combat persistent pricing pressures, fueling recession fears.

Bob Parker, investment committee member at Quilvest Wealth Management, told CNBC's "Squawk Box Europe" on Thursday that the "risk of the global economy going into recession obviously is still an outside risk."

However, Parker believed the chances of a recession had risen from between 10% and 15% a few months ago, to close to 30%, with a 1-2 year time horizon.

"So if you call that stagflation, yes we have it," he said.