ASTM, which currently holds 63.4% of SIAS, is 58.8% owned by Nuova Argo Finanziaria, a holding company which is owned by private equity Ardian and Italy's Gavio group.
As part of the deal, ASTM will launch a takeover bid for 5% of SIAS capital at 17.5 euros a share.
SIAS shares closed at 17.23 euros on Thursday.
At the end of the merger operation, and if the takeover bid is successful, Nuova Argo Finanziaria will own 40.56% of the new group's capital.
ASTM was advised by JP Morgan and UniCredit while SIAS was advised by Mediobanca
(This story corrects paragraph 5 to show capital owned by Nuovo Argo after merger will be 40.56% and not 43.598%)
(Reporting by Stephen Jewkes; editing by David Evans)