Interest rate proportional to house value

We have a variable interest rate of 4.95% on our PPR with Ulster Bank.
We have €59,000 left on the mortgage and as the balance outstanding is than 1/2 of the value of our house (the house is valued at €265,000),is it true that the lender should give us the ECB rate + 0.5%? Ulster Bank have said the best rate that they'll give is 4.75%

Are you talking about different tracker rates/margins for different LTV (Loan To Value) ratios? Some lenders offer lower margins for lower LTVs. See this thread for example:

Best Home Loan Deals

theoaks said:

We have €59,000 left on the mortgage and as the balance outstanding is than 1/2 of the value of our house (the house is valued at €265,000),is it true that the lender should give us the ECB rate + 0.5%? Ulster Bank have said the best rate that they'll give is 4.75%

Click to expand...

No-any lender is free to set their own rate. NIB will give you ECB + 0.5% as far as I know.

There is some advice in this thread that may be of interest.