Illiquidity Premium + Put Option

Can someone please explain the logic behind having the illiquidity premium be the price of a marketable security minus the value of a put option with a strike equal to the price of the marketable security? Is the put option on the illiquid asset or on the marketable security? What is the formula saying?

Let’s say you want to make a riskfree investment. If a security is $10, you would buy a $10 strike put which costs $2 to completely hedge your risk on both upside and downside. So to entice a riskfree investor like you to buy this, they would have to reduce the price to $10-2 = $8

$2 is the illiquidity premium