Combobox binding itemsource to custom list and selecteditem to an instance of that list doesn't work

I tried really different ways to make my combobox working but I'm still stuck :(

Here is a very simplified version of my app : (just edited, sorry for mistakes)

<ListView ItemsSource="{Binding People}" SelectedItem="{Binding SelectedPerson}"/>
<ComboBox ItemsSource="{Binding Grades}" SelectedItem="{Binding SelectedPerson.MyGrade}" 
     DisplayMemberPath="Name"/>

And the code behind :

public class Person
{
    private string name;
    public string Name
    {
        get { return name; }
        set
        {
            if (name != value)
            {
                name = value;
                NotifyPropertyChanged("Name");
            }
        }
    }

    private Grade myGrade;
    public Grade MyGrade
    {
        get { return myGrade; }
        set
        {
            if (myGrade != value)
            {
                myGrade = value;
                NotifyPropertyChanged("MyGrade");
            }
        }

    }

    //-- INotifyPropertyChanged implementation
}
public class Grade
{
    private string name;
    public string Name
    {
        get { return name; }
        set
        {
            if (name != value)
            {
                name = value;
                NotifyPropertyChanged("Name");
            }
        }
    }

    private int prop;
    public int Prop
    {
        get { return prop; }
        set
        {
            if (prop != value)
            {
                prop = value;
                NotifyPropertyChanged("Prop");
            }
        }

    }

    //-- INotifyPropertyChanged implementation
}
public partial class MainWindow : Window
{
    public ObservableCollection<Person> People { get; set; }
    public ObservableCollection<Grade> Grades { get; set; }

    private Person selectedPerson;
    public Person SelectedPerson
    {
        get { return selectedPerson; }
        set
        {
            if (selectedPerson != value)
            {
                selectedPerson = value;
                NotifyPropertyChanged("SelectedPerson");
            }
        }
    }

    public MainWindow()
    {
        InitializeComponent();
        this.DataContext = this;

        People = new ObservableCollection<Person>();
        Grades = new ObservableCollection<Grade>();

        Grades.Add(new Grade() { Name = "Grade 1", Prop = 1 });
        Grades.Add(new Grade() { Name = "Grade 2", Prop = 2 });

        People.Add(new Person() { Name = "guy 1", MyGrade = Grades[0] });
        People.Add(new Person() { Name = "guy 2", MyGrade = Grades[0] });
        People.Add(new Person() { Name = "guy 3", MyGrade = Grades[1] });
    }

    //-- INotifyPropertyChanged implementation
}

The problem is that the combobox is still empty when I select an item in the listview. The itemsource is OK (If I click on the combobox, I can see "grade 1" and "grade 2"). I think there is something missing to tell "the Person.Grade is part of the Grades list" but I cannot find what.

Hope you can help me ;)