What is a "quasi closed form solution"?

[Aber]

Several times in research paper and books I have stumbled upon the word/phrase: quasi-closed form solution. An Example:
"The great difference between the Heston model and other (potentially more realistic) stochastic volatility models is the existence of a fast and easily implemented quasi-closed form solution for European options" - The Volatility Surface, Jim Gatheral

My question is when exactly is a solution considered as "Quasi form"?

Let's for instance look at the SABR model and the closed form solution for black's volatility. Is that also a quasi form. I don't think so

 

[Daniel Duffy]

Many of these terms are ill-defined, ambiguous and redundant. And everyone has idiosyncratic views on the issues. The exception being rigorous mathematicians who define every term before using them.

"quasi-form" makes no sense. Heston himself 1993 calls it 'closed form'.

You need to ask what you want to do with the formula.

Just make everything explicit!

1, what is closed solution? 2. how do I compute a closed solution? 3. what kinds of closed solution? 4. Variations/what kind of. 5. Why closed solutions. 6. Advantages and disadvantages. 7. What if I can't find a closed solution(or there isn't one).

?? there is no closed form for a non-perpetual American option price.

// Quote

His suggestion also gives a few clues about why closed-form solutions may not be as useful as you might think:"What is the added value of closed [-form] solutions if 1) they are based on an ANSATZ and 2) they are incredibly difficult to solve numerically? Example: The Heston 1993 paper 1) he assumes solution in a special form and 2) brittle complex integral"P

 

[Daniel Duffy]

A related remark is that closed/exact solutions are for 95% non-existent in real life (although certain branches of physics would have us believe otherwise) and numerical method are needed. An example is ODE ... looking for exact solutions and theory of ODE is cute but IMO you need to know how to solve ODE and use them in many kinds of situations. An excellent example is MOL == ODE meet PDE. Then ODE solvers are needed, i.e. a must.

I thought it was worth a mention.

http://www.pdecomp.net/Scholarpedia/MOLfinal.pdf