Tom Ridge, the first homeland security chief under President George W. Bush, says companies face more risk of cyber attacks similar to those that struck JPMorgan Chase & Co., Home Depot Inc. and Target Co.

Speaking at a briefing in London today, Ridge whose new company has teamed up with Lloyd’s of London to offer cyber attack insurance, said the risks had been accentuated by the “extraordinary breaches” at JPMorgan and two of America’s largest retailers.

“What we have seen is the sophistication of these attacks continue to elevate,” said Ridge, 69, chairman of Ridge Insurance Solutions Company. “Who would have thought that JPMorgan with its security budget could be hacked into. Now a lot of people are thinking if it could happen to them, it could happen to us too.”

JPMorgan last week outlined the scope of the previously disclosed data breach, revealing that 76 million households and 7 million small businesses had been affected in one of the largest cyber-attacks on record. Home Depot confirmed a security breach in September that compromised 56 million payment cards, while an attack on Target last year affected as many as 110 million shoppers.

“It takes companies some time before they know the depth of an invasion,” said Ridge, who was appointed by former President Bush to oversee U.S. domestic security after the terrorist attacks on Sept. 11, 2001. “After Home Depot and Target a lot of the companies are starting to look at cyber very differently.”

Ridge approached Lloyd’s in February to offer the insurance product that he says is unique to the market by providing both cyber assessment and insurance.

The company is initially targeting businesses with market value of as much as $500 million that represent about 80 percent of all U.S. publicly listed companies and that he says are most vulnerable to attacks. Insurance policies of as much as $50 million each are available from today, according to a statement. The company expects to generate $40 million in premiums in the first 18 months.