In Credit Risk terminology, is the Exposure at Default(EAD) the same thing as the total Credit LIMIT amount on the Loan? Because if Bank gives a loan with a limit of 10,000$ and the borrower has a balance of 2000, at default, he will probably max out the loan; So should the EAD not be the same as the limit amount?
The short answer is that EAD is different from the credit limit and in many cases would be lower. For example if a corporate credit line is used for working capital purpose, the EAD might be much lower as the borrower would eventually stop using the line.
From mathematical perspective, EAD is the sum of contingent limit amount multiplied by cash conversion factor and cash and non cash exposures (all type of loans that is already allocated to the client)
EAD can also be higher than credit limit because of adding the costs of collection activities, noting that these can take a long time. As you mention, the credit limits will tend to have been maxed out, but also missed payments and accruing interest may have increased the exposure before the point in time at which the default is established (definitional issues become relevant here).
Credit limit is the maximum amount of credit an institution will extend to the client. it is a maximum risk measure.
Exposure at default is a current risk measure. The amount of of credit that is extended to a client at any given time will generally be less than the credit limit. It is more of a current state snapshot of the exposure or risk the institution has to the client should the client default at that moment.
As a market risk measure, it is also driven by market rates and credit spreads (in addition to amount of credit that is drawn by the client and the amount that is paid back by the client). Since a lender is long the debt of the client if rates fall and/or credit spreads tighten on a net basis, the exposure at default will go up and may exceed the credit limit. Conversely, the exposure at default may drop if rates and/or credit spreads rise on net despite the client maximizing the use of the credit limit.