[hippich]

From my (a very layman) understanding, the price of the security is stochastic can be assumed only during a very short period, which does not include major moves. If this is correct, does it mean all these models are useful only for market makers earning money from the spread, or they can be useful for retail traders?

[backlash875]

There are other models that take into account jumps in the prices/market. As for retail traders using these models, I think it is not recommended and not practical.

[hippich]

Any names/links/etc to learn more about such models?

[backlash875]

The Heston model has stochastic volatility. You can add jumps to this: https://en.wikipedia.org/wiki/Stochastic_volatility_jump