Home mortgage rates took a sharp nosedive last month, falling to their lowest levels in six years, the government reported yesterday. The Federal Home Loan Bank Board said fixed-rate mortgages for new homes dropped to an average of 12.08 percent in early December, down by some 0.3 percent from the 12.39 percent average in early November.

The bank board survey found that rates on the most popular adjustable-rate mortgage dropped to 10.45 percent from 10.52 percent in November.

Warren Lasko, executive vice president of the Mortgage Bankers Association, said fixed-rate mortgages had declined to between 11.5 and 11.75 percent, driven down by a big rally on bond markets in late December.

The rates from the bank board survey are for loans on new homes where the mortgage covers at least 75 percent of the purchase price of the home. The rates are also the effective interest rate, which includes any fees, or "points," that lenders tack on to the quoted mortgage rate.

The Federal Home Loan Mortgage Corp., which does a weekly survey of mortgage rates, found that fixed-rate loans, without taking into account add-on fees, had dropped to 11.09 percent for the week ending Dec. 27 from 11.14 percent the week before. The bank board survey said mortgage rates have been declining fairly steadily since reaching a peak of 15.24 percent for a fixed-rate loan in July 1984.