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One of the easiest ways to transform any token into dollar exposure is perpetual swap contracts. For example, Bitmex offers a BTC/USD contract that is margined in BTC. This contract is structured like non-linear inverse future contracts, meaning the contract value is measured in one currency, USD, but the position is margined and settled in a different currency, BTC. If a user opens a 1x short position, this gives the user a dollar exposure with the ability to earn yields from funding payments. This way of hedging is in fact widely adopted by traders to get exposed to dollar exposure.
PIKA achieves its stability in a similar way. To mint a PIKA, a user can simply open a 1 dollar value of short position in any supported token swap markets(e.g., ETH or WBTC).