The big banks have become more competitive with their fixed-rate mortgage offerings over the past year, while smaller lenders have increased share in the refinance segment, according to the latest AFG Competition Index.AFG's figures, based on sales by affiliated brokers, also show that the big banks have done a lot more business with first-home buyers over the past year.Overall, the big banks and their subsidiaries accounted for 72.2 per cent of mortgages written by AFG brokers in August - little changed from 72.8 per cent a year earlier.However, in the fixed-rate segment big bank share increased from 48.4 per cent to 73.6 per cent over that period.In the refinancing segment the big banks gave up share to smaller lenders, dropping from 66.7 per cent to 63.9 per cent over the 12 months to August.Big bank share of first-home buyer business increased from 73.1 per cent to 78.2 per cent.Among individual lenders, AMP Bank, ING Direct and ME picked up share, while Bank of Queensland, Macquarie and Suncorp lost ground.