What Was Probably True
Modal Verbs of Probability - Past
Modal verbs of probability express an opinion based on what a speaker knows about a situation at the moment of speaking. The following forms are used to speak about past situations.
Example:
The bank guarantee could have been available last week.
A commercial loan can't have been given to that builder.
I could have been rich if I had done a better job with managed liabilities.
'Must' plus the perfect form (must have done) expresses the idea that you are almost 100% sure of your opinion about a given situation which took place in the past.
Subject + must + have + past participle + objects
Example:
I must have been confused with the particular policies of that bank branch.
He must have been aware the endorsement would reflect poorly on the candidate.
'Might' or 'could' plus the perfect form of the verb (could / might have done) expresses an opinion that you think was probably true at a past moment in time.
Subject + might / could + have + past participle + objects
Example:
David might have kept the expense receipt.
The funds in your account may have been insufficient to cover this purchase.
'Can't' plus the perfect form of the verb (can't have done) expresses the idea that you are almost 100% sure that something was not true at a past moment in time. Note that the form is 'can't have done' NOT 'couldn't have done'.
Subject + can't + have + past participle + objects
Example:
A commercial loan can't have been given to that builder.
He can't have been able to know that the value of the company common stock price would fall so much.