Still working on my master thesis and I have a question I have been looking at for some time but can't find a good reason.

I am looking to follow the steps of Horvath et al. (2019) in order to calibrate the heston model to market data using neural networks. At the moment I am focusing on the creation of my artificial dataset that will be used to train the model, thus trying to get a good understanding of the bounds of the parameters kappa,theta,sigma,rho I am trying to generate.

In his paper, Crisóstomo (2014) gives bounds that allow to avoid possible solutions that while mathematically feasible, are not acceptable in an economic sense. His bounds are:[0,20][0,1][0,1][-1,1]. But in other papers I am reading, they propose the bounds [0.001,15][0.001,6][0.005,4]and [-0.999,0.999]. Is there any specific reasons for this, or else, do you know (or have a reference paper) what bounds should be used and for what specific reasons ?

Thanks a lot in advance



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