I'm confused on how to construct a long short portfolio using strictly options.
If I wanted to hedge stock, I would long stock A and short stock B by making sure that the quantity * price of A = quantity * price of B (excluding beta for simplicity). So total exposure long and short would be equal. Therefore if the price of both A and B increased by 1%, my portfolio wouldn't change in value.
How would I replicate this sort of hedge using a call option on A and a put option on B? I've looked into delta hedging, but that looks like it only works if one side of the hedge is using stock. Otherwise the option with the higher underlying stock price would move the portfolio value more given an equal percent price change in A and B.