Notice Period and Buyout Option
Unless the particular clause pertaining to notice conditions in the contract of employment is presented verbatim, no exact answer can be given. In general, the buyout option of the notice period would be subject to the discretion of the employer only. However, many employers misuse this discretion to discourage the resignation of efficient employees. Some outgoing employees, on their part, treat the buyout option as if it is their right and fail to get sufficient joining time from prospective employers when they switch jobs.
The poster may approach the CEO, politely explain the circumstances under which they are compelled to exercise the option of buyout, and get their nod for early and peaceful relieving.