I kind of understand how a perpetual futures contract works, but I don't see how it affect the price of the underlying asset, such as Bitcoin.

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The majority of volume is traded via perpetual swaps, hence the majority of belief of the commodity price must lie in those perpetual swaps. For this to be true, it would mean that the perpetual swap affects the spot price in the first place.

As the perpetual swap is a derivative of the actual commodity they share the price changes with each other by the no-arbitrage constraint as per answer here. https://qr.ae/pNaIuG

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