ASX shares are shaking off the nosebleed inflation figures that came out of the United States yesterday (overnight Aussie time).

The consumer price index in the world's biggest economy leapt 1.3% in June, bringing annual inflation figures to a blistering 9.1%. This was significantly higher than consensus expectations and the highest levels seen in the US in 40 years.

To put the figure in some perspective, if inflation were to continue at this level, prices in the US would double every eight years. That means in just 16 years, one dollar would be worth only 25 of today's cents.

US markets closed only moderately lower, with the Dow Jones leading the fall, down 0.7%. Futures indicate Thursday will see more modest selling.

As for ASX shares this morning, the All Ordinaries Index (ASX: XAO) is up 0.3%.

ASX tech shares are also broadly edging higher, with the S&P/ASX All Technology Index (ASX: XTX) up 0.4% at this same time.

And gold shares are shining brightly amid the soaring US inflation numbers, as witnessed by the 0.8% boost in the S&P/ASX All Ordinaries Gold Index (ASX: XGD).

Here's what investors are considering down the road.

ASX shares and global equities facing hawkish US Fed

With inflation continuing to run hot, ASX share investors can expect more aggressive tightening from the US Federal Reserve in the months ahead. And investors should prepare for continuing volatility in global share and bond markets.

Markets have already widely priced in another 0.50% to 0.75% interest rate rise from the Fed at its 27 July meeting. Now analysts are upping the odds of seeing a historical 1.0% rates boost to tame the inflation beast to which many say the Fed has been too slow to react.

"The Fed is right to worry about the unmooring of inflation expectations. And this report raises the chance of an even larger rate hike than 75 basis points down the line," said Bloomberg economists Anna Wong and Andrew Husby.

"Incoming data suggests the Fed's inflation problem has worsened, and we expect policymakers to react by scaling up the pace of rate hikes to reinforce their credibility," analysts from Nomura added.

Is the US heading for a recession?

If the world's top economy tips into a recession, it will certainly pose headwinds for many ASX shares.

And with the latest round of outsized inflation figures, the odds of that recession are ramping up.

According to Kristina Clifton, senior economist at Commonwealth Bank of Australia (courtesy of Reuters): "Stubbornly high inflation increases the risk that the FOMC [Federal Open Market Committee] continues to hike aggressively and triggers a recession."

"We still don't know what's going to happen but it's most likely we're going to have a recession because the Fed is going to have to act aggressively," added Chris Zaccarelli, chief investment officer at Independent Advisor Alliance.

As for the impact on US stock markets – and by extension the ripple effects that will be felt by ASX shares – Anthony Saglimbene, global market strategist at Ameriprise Financial said: "The Fed is going to continue to be aggressive, and right now, the Fed is not your friend, at least from an investor stand-point and until that changes it's going to be hard for stocks to gain traction."

"We look for further market volatility as investors digest the combination of slowing growth, persistent inflation, and the likelihood that second-quarter earnings season results in downward revisions for margins and profits," John Lynch, chief investment officer at Comerica Wealth Management, added (quoted by Reuters).

Peter Cardillo, chief market economist at Spartan Capital Securities, came in with a glass-half-full approach.

While admitting "the numbers are ugly", Cardillo said, "the hints that inflation might be beginning to decelerate are there".

When US inflation does decelerate, and the Fed can begin easing back on the interest rate hikes, global markets and ASX shares will breathe a sigh of relief.