is it by market participants like in the equity or is it by exchange, if by exchange then how?
The amount of the premium is determined by several factors - the underlying stock price in relation to the strike price (intrinsic value), the length of time until the option expires (time value), how much the price fluctuates (volatility value), and most importantly demand and supply.
Would recommend you to go through this module on Varsity to learn more.
The Black-Scholes Calculator is also a popular options pricing model that uses these parameters to determine the fair market value of an option.
Check out this article explaining how to use it.
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