# What is the name of this product?

Consider the payoff =$S_T1_{S_T>K}$ where $S_T$ is the asset price at maturity.

What is this type derivative called?

and is it a liquid option?

This looks like a binary option. Following this wikipedia article it is called an "asset or nothing call". The pricing formula in the Black-Scholes world is

$$S e^{-q T} \Phi(d_1),$$ where $S$ is the current spot price, $q$ is the dividend yield, $\Phi$ the cdf of a standard normal and $d_1$ is as usual in BS.

To my knowledge such options are much less liquid than there plain vanilla counterparts.

I don't think that it has a name on its own, but you can write $$(S_T - K + K)\,1_{S_T>K} = (S_T-K)_+ + K\,1_{S_T>K}$$ so it's a 1 call plus K binary calls.

Binary are hard to hedge, the payoff looks like _|‾, going sharply from out-of-the-money to in-the-money. The delta changes fast and it's difficult to hedge the position.

In practice, you give yourself some cushion by approximating the binary by a call spread with small spread (buy an amount of calls struck at a lower strike, sell the same amount of calls struck at a higher strike). The payoff looks like _/‾.

Its a payoff for asset or nothing call, this option is an OTC derivative (more specifically an exotic option) thus relatively illiquid compared to plain vanilla option. Its payoff, with exercise price ($K$), is $S_t$ if $S{t}>K$ and 0 otherwise and $1_{S_t>K}$ is an indicator function which takes value 1 if $S_t>K$ and 0 otherwise. And that's why it is known as binary option.