How do I convert a System.Type to its nullable version?

Here is the code I use:

Type GetNullableType(Type type) {
    // Use Nullable.GetUnderlyingType() to remove the Nullable<T> wrapper if type is already nullable.
    type = Nullable.GetUnderlyingType(type) ?? type; // avoid type becoming null
    if (type.IsValueType)
        return typeof(Nullable<>).MakeGenericType(type);
    else
        return type;
}