using the dot notation only works if the base is already an option, ie:

var foo.bar = "baz"; // fails
var foo = {};
foo.bar = "baz"; // succeeds 

Each option property that is, in an of itself an object, must be declared 
as an object, so your options should look like this:

var options = {
    width: 410,
    height: 260,
    areaOpacity: 1,
    backgroundColor: '#4d4d4f',
    series: [{
        color: '#000',
        visibleInLegend: false
    }],
    hAxis: {
        baselineColor: 'red',
        gridlines: {
            color: 'red',
        }
    },
    vAxis: {
        gridlines: {
            color: 'red'
        }
    }
}; 

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