Notice Period Buyout

Hi, I have resigned from my current company and I have a notice period of 60 days. I am ready to serve four weeks and buy out the remaining notice period. But my current employer is not ready for my notice period buyout saying that I will have to serve the entire 60 days. In the agreement (appointment letter) that I have signed, has the following clause: "After your confirmation, the Management may terminate your employment, by giving two month’s written notice or basic salary in lieu thereof without assigning any reasons. Similarly, you can leave service of the Company by giving two months’ notice in writing or basic salary in lieu thereof after your confirmation." Although on talking with the HR, they are quoting that the appointment letter is an interim document and I have to follow the process as per the company's exit policy (which have been revised very recently and after my confirmation). How do I go about this situation and is it possible for me to buyout notice period. Please reply.