You can use .index(), it searches for a given element from among the matched elements.
$('#next').on('click', function () {
var selected = $('select option:selected');
var index = $('select option').index(selected);
var value = $('select option').eq(index + 1).val();
$('select').val(value);
});
$('#prev').on('click', function () {
var selected = $('select option:selected');
var index = $('select option').index(selected);
var value = $('select option').eq(index - 1).val();
$('select').val(value);
});