Need early relieving from my current organization but not able to get it

Situation: I have received an offer from a Global Technology company and their global policy is to give 30 days’ time to all future employees to join their organization. My current organization which is an Indian Private Sector bank has a notice period of 90 days and it allows notice period waiver by paying the basic salary of notice period shortfall, subject to discretion of the competent authority at the bank (exact clause mentioned below). I have submitted my resignation to the bank and requested them to release me in 30 days given the constraints of the new job offer that I have received and considering that it will be a livelihood / financial insecurity risk for me if I lose the opportunity. However, the business head is not agreeing to release me earlier than 90 days. I have tried explaining the entire situation to the HR as well but no one seems to be providing any resolution. I wanted to understand what options do I have in a situation like this. Bank Separation verbatim clause: a. On account of Resignation: After confirmation, you may resign from the Bank’s service, subject to acceptance of your resignation by the competent authority, for which you will be required to mandatorily serve a notice period of 90 days. You will not be permitted to adjust any accumulated leave at your credit including accruals against the notice period. However, waiver of the notice period (if any), will be at the discretion of the competent authority. In such an event, the basic salary equivalent of the notice period shortfall (if any), after adjusting with privilege leave / surplus privilege leave (if applicable), will be recovered from employee. b. On account of Termination: Notwithstanding what is provided in the Staff rules, and the above paragraphs, your services, after confirmation, may be terminated by the Bank by giving 30 days’ notice or payment of 30 days’ salary in lieu thereof without assigning any reasons thereof.