Speaking publicly for the first time about the scandal, Hildebrand told media in Zurich that he had complied with all the regulations of the central bank.
"I acted correctly on every count," he said, following days of media speculation over allegations of insider trading.
It emerged last month that his wife Kashya Hildebrand profited after buying $504,000 in August, just weeks before an intervention by the SNB to halt the rise of the franc -- a move that saw the dollar rise significantly against the Swiss currency.
The purchase, which investigators said appeared to have been carried out without her husband's knowledge, was deemed "sensitive" by auditors who nevertheless cleared the couple of any wrongdoing.
"I immediately allowed an investigation and allowed the investigators to look at all my records," Hildebrand said.
Bank Sarasin in Basel this week dismissed an employee who allegedly transmitted transaction details to a lawyer close to the far-right Swiss People's Party whose chief Christoph Blocher is a Hildebrand critic.
Zurich prosecutors have launched a criminal case against a 39-year-old former bank worker.