Corelogic: There is no housing bubble

David Paul Morris | Bloomberg | Getty Images

Contractors raise a wall while working on a new home under construction in Dublin, California.

Home prices are up over 12 percent nationally from a year ago, and limited supplies of homes for sale continue to push that number higher. Demand is coming back, home builder sentiment is at a seven-year high and real estate agents are reporting bidding wars. None of this means housing is heading back to the bubble, according to economists at CoreLogic.

(Read more: Home builder confidence soars despite rising rates)

"The fundamentals are there right now, and the market is responding," said Mark Fleming, chief economist at CoreLogic.

Even in the fastest growing markets, where prices are up around 20 percent from a year ago, Fleming pointed to still near-record affordability. For housing price affordability to return to the average level that we saw in the years between 2000 and 2004, he said, either home prices would have to rise an additional 47 percent or interest rates rise to 6.75 percent. Only Washington, D.C., and Hawaii are "technically unaffordable," according to CoreLogic.

Rising mortgage rates will help to temper the possibility of a bubble as well, but they will not cut into demand dramatically, as some have predicted, according to Fleming.

"Buyers buy based upon payment, and those payments are still highly affordable relative to their incomes," he said. "Even with 100 basis point swing, there's still plenty of room in that [affordability] index."

The concern, however, has been that as mortgage rates rise, home prices would necessarily fall, as buyers lose purchasing power. That may not be the case, according to a new analysis.

(Read more: Map: Tracking the US real estate recovery)

"History shows that a rapid rise in interest rates tends to have little correlation with home prices. Rather, rising rates are more likely to contribute to a decrease in home purchase volume and an increase in the market share of adjustable-rate mortgages," wrote Mark Palim in a Fannie Mae commentary.

Home prices are determined more by income and employment than anything else. That is why prices cannot continue to rise at the current rate. Incomes are not keeping pace, and affordability will therefore suffer.

"If prices were to continue to rise at 12, 15, 20 percent in some markets, then we are talking about a different scenario," said Fleming. "We have room to grow, but it can't grow indefinitely."

—By CNBC's Diana Olick. Follow her on Twitter @Diana_Olick.

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