Hamish Ogston, who owns a majority stake in CPP, responded in robust language after action was announced by the Financial Conduct Authority (FCA) over the scandal involving 13 high street banks and credit card companies.
The lenders, together with CPP, have agreed to offer redress for mis-sold credit card and identity theft protection policies. But Mr Ogston declined the opportunity to express regret.
Barclays, HSBC and Royal Bank of Scotland are among those to have signed up to the scheme which will cost up to £1.3bn.
The scandal involved 23 million policies and saw customers given misleading and unclear information about the insurance. CPP has already been fined £10.5 million over the affair.
But Mr Ogston described the £1.3 billion quoted by the FCA as "b******s" and a "ridiculous figure".
Mr Ogston said the scale of overall compensation paid out would be much smaller than the headline figure.
The mis-selling scandal ran from 2005 to 2011, during which time CPP sold 4.4 million policies and renewed almost 19 million.
FCA chief executive Martin Wheatley said: "We believe this will be a good outcome for customers who may have been mis-sold the card and identity protection policies."
Shares in CPP plunged by a quarter on the regulator's announcement.