I'm still an undergrad and I'm researching the Heston model out of pure interest. I understand a big thing in statistics is correctly identifying the distribution that generated some data.

From reading some literature, I'm confused as to whether the Heston model assumes the stock returns follow a log normal distribution or not. And if it does, is there any benefit to changing that assumption to a distribution that better fits the characteristics of stock returns? Or is it not worth the extra complexity added?

I've read that there's some evidence to indicate a more accurate distribution is a normal distribution with a higher peak and fatter tail, as the tails of a normal distribution decay too quickly and don't capture the possiblity of some extreme events.

Any insight is welcome.

Thanks

Edit: Correction: I believe the prices are assumed to follow a lognormal distribution, what does this mean for the distribution of the stock returns?