To pay or not to pay is the question now facing some homeowners. Not because they can’t afford their mortgage, but because they don’t want to keep paying on a home that’s lost value. But even as they gain popularity, strategic defaults are highly controversial — some might say immoral. But about a quarter of American homeowners took out loans that are bigger than their homes are now worth and some of them say it’s simply irrational for them to keep paying the mortgage. Grace Chen and her husband, Antonis Orphanou, have this debate about their own home. From the outside, there is nothing to flag them as troubled homeowners. They haven’t lost their jobs. Their interest rate has stayed the same. And they are not counted among the legions headed to foreclosure. In fact, they haven’t even missed a single mortgage payment.