The given sentence refers to an action that is believed to have happened. Modal verbs such as "must have" in option C are used to make guesses or deductions about an action in the past that we believe has definitely or possibly happened (based on our knowledge, information or evidence or lack of it). It is used in the same way as the present prefect tense (the action being described happened in the past and is still true in the present.
"Must" in option A is just the modal and is incomplete without the verb 'have'. Thus, is incorrect.
"Must be" is used with the present participle and gerund 'happening'. Here, the reference is to an action in the present perfect tense.
"Must have been" is perfect continuous and does not agree with the given context.
Thus, option C is the correct answer.