I am calibrating the Heston model with sequential quadratic programming algorithm. It turns out that the volatility surfaces I am calibrating to can be fit very well with extreme values of mean reversion $\lambda$ and vol of vol $\xi$, such as $\lambda=11000$ and $\xi = 2000$. The values are legitimate since the only constraints are $\lambda > 0$ and $\xi > 0$. If both increase simultaneously, large mean-reversion stretches convexity of the smile and the volatility surface is not that extreme at all.
However, such extreme values of parameters have nothing to do with the actual conditions of the market. I notice that this problem is also not unique to the Heston model. Hence I wanted to ask how to constrain parameters of Heston model during calibration to sensible limits (perhaps penalize large values of parameters might help)?
I see that Madan et. al. (2019, Figure 5b) observed the same behavior ($\kappa$ – mean reversion, $\theta$ – vol of vol):
Thank you in advance.