Does a derivative's price follow it's underlying even if the derivative isn't trading?

Does a derivative’s price rise even if no contracts are changing hands? Let’s say, an institutional investor buys a stock in huge quantity at market price and the price shoots up. Then, does it’s derivative price too rise even if no contracts are changing hands?

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No. Even if the underlying stock rises, if there is no liquidity in that derivative contract that is no trade happening, there wont be any effect on the derivative contract price.

@Karthik sir can explain this

Well, if no contracts are traded in derivatives which is a hypothetical case but still if that is the case then the SELLERS will also start quoting higher price in derivatives in anticipation to the spot price.
But since the buyers are not willing to pay higher price, so the trade wont take place & the LTP will not get updated until a buyer & a seller is matched at a price in response to the spot.

This type of situation does happens actually in few options contracts where due to lack of liquidity there is a delay until the LTP of respective strike price gets updated even though the underlying has changed in response to the spot.

Some times, clever institutions, traders do buy/sell only 1 contract inorder to quickly update the LTP so the traders which follow will automatically start quoting prices near to LTP.

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Well, then, what does it exactly mean when they say derivative means it’s price is derived from the underlying?

Theoretically yeah, derivative is supposed to be derived from the underlying. But in reality it is usually the other way. Since trading on derivatives are so much more, they move first and underlying follows.

In the example you have quoted though, the stock will move first as the institution would maybe have no interest in trading the F&O.
There are professional traders called arbitrageurs who jump in anytime there is an opportunity to make risk free returns. They ensure that the prices of stock and derivative goes hand in hand. Most of these professionals are trading from the exchange colocation using HFT algos and are so quick that you can’t spot such opportunities by your naked eye.

So for example, if an insti is buying say 100 crores of Infosys. Say Infy stock was at 960 and futures at 962. As soon as this buy order started execution, assume the stock moved to 970. Immediately the arbitrageurs would jump in short the stock and buy the futures. They will keep doing until this gap between spot and futures reduce to normal. The same algo’s would execute strategies on all option strikes. All of these will be happening in micro seconds. So we’d never be able to spot these.