The government has directed the nation's spy agency, the Government Communications Security Bureau, to help resolve the problem.
Stubbs said if the Exchange stayed down for a couple more days it would be difficult to fairly price investments.
The attacks had been a wake-up call and lessons needed to be learned from them, Stubbs said.
"These attacks come from anywhere in the world, they travel at the speed of light," he said.
"New Zealand is not immune from it, and I think this is a very salient lesson to everybody: we are not being ignored, we are clearly being targeted."
Last Friday, the Stock Exchange suffered its fourth day of offshore cyber attacks, overwhelming the NZX website.
Share trading was temporarily put on hold, because investors could not see up-to-date company announcements, leading to an uninformed market.
After trading resumed, the benchmark NZX-50 index was down about 40 points or 0.4 per cent at 12,012, about 100 points shy of a record high.
The ZDNet technology website said the cyber attacks had occurred around the world over the past two weeks, but the NZX was among the hardest hit.
Other financial service companies affected by the attacks include the global payments company, PayPal, and money transfer companies Braintree and Worldpay.
- RNZ