Eligibility to buy out notice period

My Termincation of Employment is as follows: "During the probationary period, either party will be entitled to terminate the contract of employment by giving six months' notice in writing to the other. After confirmation, termination of employment by either party will be by giving six months' notice writing to the other or salary in lieu there of. In the event of your giving a notice of termination shorter than the above period, the company shall have its own discretion to adjust any leave due to you or recover from you such amount from your dues towards the shortfall in the notice period. In addition to this, you are liable to pay 50% of the salary received as liquidated damages, if you resign from the service before completion of Three years from the date of joining. The Company may at its sole discretion terminate the Contract of Employment without notice and / or salary in lieu of notice, if in the opinion of the Company; the continuance of your employment is detrimental to the interest of the Company. Provided that, in the event of termination as provided hereinabove, all benefits / perquisites / allowances shall stand forfeited immediately, and you will only receive any statutory benefits as applicable to you on the date of your termination" I have completed 3 years and I'm not a probationary employee. I have given notice of termination. I wish to serve 3 months' notice and buy out left over 3 months' as total is 6 months' notice. But, my company is not accepting buy out offer. Neither they are letting go early. According to above stated clause, do the company have discretion to deny my buy out option ? am I eligible to get relieved early ? What are my options other than serving 6 months' notice ?