The state has reached an agreement with UBS Securities that allows it to avoid a $71 million payout from a deal entered into by the Massachusetts Turnpike Authority in 2001.

The soon-to-be defunct authority entered into five risky transactions, known as "swaptions," to help cover the cost of the Big Dig highway construction project.

In July, the Turnpike avoided a $261 million payout after lawmakers passed an overhaul of the state's transportation system. The move prevented a downgrade in the authority's bond rating that could have triggered payouts on four of the swaps.

That left a remaining threat of a fifth payout that could have cost the state $71 million.

Under an agreement signed with UBS, however, the July bond rating upgrade is sufficient to avoid that payout.