In pursuing its mandate, a central bank assumes financial risks through its monetary policy operations. Central bank capital is a critical tool in mitigating these risks. We investigate the concept of central bank capital as a mechanism for risk sharing with its shareholder. Adopting an option pricing framework, we explore the setting where the central bank commits to distributing dividends when its capital is robust, while the shareholder may be called upon to recapitalize the bank during adverse economic conditions when its capital is negative. Our analysis dissects the trade-offs inherent in these options, seeking a mutually beneficial agreement that disincentivizes deviation for either party. This equilibrium is essential for safeguarding the independence and credibility of the central bank in executing monetary policy effectively.