The first parameter to the Html.DropDownList needs to be a name that does not match the name in your model. Below I used "OptionId" instead of "Options".
View
<%= Html.DropDownList("OptionId",Model.Options) %>
Controller
SelectListItem item1 = new SelectListItem();
item1.Text = "Red";
item1.Value = "Red";
item1.Selected = false;
viewModel.Options.Add(item1);
SelectListItem item2 = new SelectListItem();
item2.Text = "Green";
item2.Value = "Green";
item2.Selected = true;
viewModel.Options.Add(item2);
SelectListItem item3 = new SelectListItem();
item3.Text = "Blue";
item3.Value = "Blue";
item3.Selected = false;
viewModel.Options.Add(item3);