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Yep, that's one of the sensitivities of Options in general...

Maybe a hint for some of you how to remember this connection.

The Call Writer (Short Call) is obliged to sell the Share at epiration to the call buyer (Long Call). In order to hedge himself, the Seller of the Call buys the Share in the market which he may deliver to the buyer at expiration. Therefore, when interest rates rise, the opportunity costs for the hedge (i.e. buying the share in exchange for cash) rise.

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