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There is an implicit assumption in your model. Namely that the price of the cow is perfectly correlated with the stock: they always move in the same direction. In this case you can indeed hedge your risk using cows. I let you be the judge of the validity of that assumption. More likely the moves of cow prices are independent which means that you should ...


if put call parity seems to be violated there could be things you are ignoring like dividends or hard to borrow fees. Hard to borrow will make puts more expensive

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