Exotic options

There are three generations of exotics.

1st gen: These are "vanilla" derivatives, things with linear/almost linear payoffs in the contract like max(spot - strike, 0} that you can price with black scholes pretty comfortably. This includes call options, put options, European and American. I'd throw digital/binary options in there as well. As another commenter has pointed out, the prices for vanillas are often readily available on exchanges, or their prices may be inferred directly from such data.

2nd gen exotics are things that can be priced with some mathematics to manipulate black scholes into closed form solution, but which maybe you shouldn't (though a local vol will help). This is stuff with more elaborate less-linear payoffs like Asian options, barrier options, lookbacks, cliquets, var swaps*. The payoffs for these things are relatively simple in that they are x + y + z and maybe with a max or a min. Maybe two maxes, maybe two mins, or both. They will only be traded OTC.

Then you have 3rd gen exotics, which we often call structured products. These are much more complicated payoffs and they can have several layers of functions. They can have complex baskets underneath where assets can drop out and come in over the lifetime of the option. They are often attached to an interest rate leg for funding and they should really only be priced with stochastic volatility models using Monte Carlo or Finite Difference, or an ML model to reproduce the same. These are also only traded OTC.