The risk profile and max loss for the two positions are the same - cost of the stock minus commission received, but people use different strike prices for the covered call vs. naked put because generally you want to sell the closest OTM call or put. In almost all cases the closest OTM call is at a different SP than the closest OTM put.I generally choose the first OTM strike price for the call -- BECAUSE it means I can earn more profit if the stock price goes up. An OTM put won't do that -- your only profit is from the option premium.And, in general, I would expect the stock price to go up, because I would only do a CC/CSP on a company I felt is a good one.So I'd rather do the ITM put for the same reason I did the OTM call. It's just that the put gives me the extra money ahead of time, before the (hoped for) price increase.Typically, I put a $0.03 limit order in to buy back the call/put, since there would be no time value left in the option and it would signal it's time to go to different strike price/expiration date.
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