Peter attended Babson College in Wellesley, MA and the Berkshire School in Sheffield, MA. He is the son of James Crane Kellogg, III of Wall Street specialist firm Spear, Leeds & Kellogg; he joined his father's firm in 1967 after working at Dominick & Dominick. His fortune is primarily from his successful leadership of Spear, Leeds & Kellogg in the 1980s through to its sale in 2000 to Goldman Sachs for a reported $6.5 billion. Kellogg attended Babson College, but later dropped out.

Spear, Leeds was fined $1 million in 2002 by the AMEX and ordered to conduct a review of the supervision of its clearance and specialist operations on the AMEX floor. This came in the wake of a violation of AMEX trading rules in the mid-1990s by a Spear Leeds employee who the AMEX found was not properly supervised by the firm. The employee, who was fined $100,000 and barred from the industry, was reported in the news media to have testified that his actions were known to senior Spear Leeds officials, including Kellogg.

The NASD had publicly announced on November 3, 2003 that it “filed a disciplinary action against Peter Kellogg alleging that he directed fraudulent wash trades and matched trades between four accounts he controlled”. Wash sales are trades of securities without a real change in ownership of the securities traded. Matched orders are orders to buy or sell securities that are entered with knowledge that a matching order on the opposite side has been or will be entered.

The NASD subsequently announced on August 6, 2004 that an NASD panel convened to hear the case dismissed this complaint against Kellogg alleging that he engaged in fraudulent wash and matched trades during August 2001. The public notice stated that "The Hearing Panel found that there was no evidence that Kellogg carried out the four transactions at issue with the intention to defraud, manipulate or deceive. Rather, the panel found that Kellogg conducted the transactions for legitimate Business and tax purposes.”