If I am short both a call and a put with the same strike on the same security, what happens if I let this position expire in-the-money?
How much, if any, cash would I need to have liquid at expiration to settle?
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If you do not wish to exercise the option you can give your broker a 'contrary exercise advice' which is an instruction for them not to exercise the option at expiration (normally in the US, the OCC will automatically exercise any option that expires in-the money by a penny or more)
Otherwise you have to have sufficient margin available to complete the exercise of the in-the-money leg. If you have insufficient margin, your broker may elect to give contrary exercise advice on your behalf rather than allowing you to exercise and them being forced to liquidate.
You will likely need whatever margin would be necessary to purchase the underlying stock at the specified exercise price.