I have to estimate the effort required for a project and I have no historical data. In college I learned these methods, but I have the feeling that they have been replaced by new approaches such as story points (which need historical data such as velocity of iteration) in agile projects, for example.
These older estimation methods have not been 'deprecated'
- Object Point and Function Point: Function Point is a better developed process than Object Point. For Function Point there are multiple professional organizations such as IFPUG, COSMIC and ISO/IEC industry standards developed by them. Here is a recent review: 40 Years of Function Points: Past, Present, Future. However, to count Object Points or Function Points, your client should have signed off on requirements and you need to have your high-level design done (to be able to count objects/functions).
- COCOMO and COCOMO II: When I search for articles/blogs published within the last couple of years on this topic, I see many. However, this model is based on lines of source code. You will have to make a judgement call whether lines of code is at all a relevant metric for your project.
you didn't mention the purpose of the estimate. e.g. for a new project approval, or for hiring/allocating resources or on-going monitoring and control.
This makes a lot of difference as to what accuracy might be required, and hence the method.
It might still be useful to use what you now consider to be a somewhat obsolete method, particularly if the results will be compared with a previous project that used the same method. Sometimes comparability is at least as important as absolute accuracy.