The Options Clearing Corporation (OCC) is the entity that ensures the writer of an option fulfills the obligations determined under the terms of the option. The OCC acts as a guarantor, ensuring that the obligations of the contracts they clear are fulfilled. It operates as a clearinghouse for futures markets, providing a system of guarantees that reduces the risk of default. The OCC works with its members, who are required to maintain a specific amount of capital and a special fund that can be used in case of default. This structure ensures the integrity of the options market by guaranteeing the performance of every option contract.

Choice A is incorrect. While the exchange provides a platform for trading options, it does not ensure that the obligations under the terms of an option are fulfilled by the writer of the option. This responsibility lies with another entity.

Choice B is incorrect. The market maker's role is to provide liquidity in the market by buying and selling securities, including options, but they do not guarantee that obligations under an option contract will be fulfilled by its writer.

Choice D is incorrect. The buyer of an option has no obligation to ensure that terms of an option are fulfilled by its writer. Their only obligation is to pay for and accept delivery if they choose to exercise their right under the contract.