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