It is a seller’s market, undeniably. The supply of homes for sale is low, demand is high, and now prices are heating up even more. But sellers today see more reasons to stay put than to profit.

Home prices jumped 7.1 percent annually in May, according to a new report from CoreLogic. That’s the biggest jump in four years. Annual price gains had been shrinking slightly, as mortgage rates rose, but apparently higher rates are not hurting demand. They are, however, exacerbating the already critical supply shortage.

“During the first quarter, we found that about 50 percent of all existing homeowners had a mortgage rate of 3.75 percent or less,” said Frank Nothaft, chief economist for CoreLogic. “May’s mortgage rates averaged a seven-year high of 4.6 percent, with an increasing number of homeowners keeping the low-rate loans they currently have, rather than sell and buy another home that would carry a higher interest rate.”

If mortgage rates were to rise further, fewer homeowners would want to move. In fact, if today’s homeowners just considering a move were faced with a mortgage rate 1 percentage point higher than their current one, 24 percent would not move, according to a survey by John Burns Real Estate Consulting. Thirty-six percent said they “may not” move. The average rate on the 30-year fixed is now slightly more than 1 percentage point higher than the lows following the recession.

The median price of an existing home sold in May was $264,800, according to the National Association of Realtors. Of course, all real estate is local, and certain markets are hotter than others. Seattle, Denver, and San Francisco continue to see some of the biggest price gains, as they also have the leanest supply.

The supply of homes for sale has been dropping on an annual basis for the past 36 months, according to the National Association of Realtors. The shortage is most acute at the lower end of the market, where demand is highest and where investors bought thousands of distressed properties during the housing crash, turning them into lucrative rentals.

Younger potential buyers have already delayed homeownership due to the recession and high levels of student loan debt. They have also been hampered by high rents, making it more difficult to save for a downpayment.

Higher rents, combined with higher home prices, are the number one reason for the decline in young homeowners, followed by lower marriage and fertility rates, according to a recent study by Freddie Mac.

“Historically low mortgage rates and increasingly favorable employment conditions should have generated a far greater number of home purchases by young adults, especially in the last five years,” said Sam Khater, Freddie Mac’s chief economist. “Unfortunately, home-price and rent growth above incomes — driven primarily by a severe shortage of housing supply — have been too high of a hurdle for many would-be buyers to clear.”