While closed form solutions 'can' be difficult, one of their advantages is thatthey are usually 'easy' to implement.If you are going to first study stochastic volatility, where do you start?If you are going to add price jumps to that, where do you start?If you are going to add volatility jumps to that, where do you start?If you are going to test a numerical or approximation method, what do you test it against?If you are going to try a calibration against 100+ options, using models with a half dozen or more parameters, how do you get it working?The answer is usually to start with a model that has a so-called closed-form or exact solution. Need I remind that the first closed-form model that attracted alot of attention was the Black-Scholes model. The many advantages of exact solutions seem obvious to me. Having said all that, I would acknowledge that one has to be quite carefulwith the Heston '93 model, especially at relatively large 'volatility of volatility'.There are several reasons to be careful. First, there are branch-cut crossings associated with a logarithm.But these can be dealt with or avoided. Second, one has to avoid 'over-reliance'on closed-form models just because they can be solved. This is true forany model. After all, you expect the model tobe 'wrong' quantitatively, but it may also be wrong/misleading in some qualitative way.Again, large vol. of vol. is an issue with the particular model in the examplebecause it makes the volatility reflect off the origin. In my opinion, this is 'bad'.But that is another story.