Zero clauses insure banks and financial institutions against reductions in benchmark interest rates, usually the Euribor.
These changes directly affect variable-rate mortgages, so the bank shields itself with a minimum level of profitability if these rates are negative. In other words, with zero clauses, if interest rates are negative the bank can ensure that the interest rate does not fall below 0%, as we would find ourselves in the paradoxical situation of the bank paying its customers to lend them the mortgage money, if interest rates are negative and the 0% clause is not applied.
Zero clause example
You have bought a home with a variable-rate mortgage. Let's imagine that the Euribor (the daily benchmark mortgage rate reflecting the interest rates at which leading banks lend money to each other in the interbank market in the EU) is at the fictitious and difficult level of -1.2%.
In this case, the bank charges a spread of 1% over the Euribor, which is currently -1.2%. Adding these figures together gives an interest rate of -0.2%. As you can see, the bank would have to pay the customer for having the mortgage, as the interest rate is negative. If this example were real, banks and financial institutions would not dare to lend money because of the high risk that fluctuations in the Euribor entail.
Zero clauses were created for this reason, to guarantee to the bank that the minimum interest rate it would receive is 0%.