R – DDD: subclasses & root entities

Let's say I have the typical entity Car

class Car : Entity
{
    public double MaxSpeed { get; set; }
    public Color Color { get; set; }
    /* ... */
}

This entity, in my domain model, would be the root entity of an Aggregate.

Now let's say I specialize cars. I create a Ferrari, and the happy owners of Ferraris like to call them by a nickname:

class Ferrari : Car
{
    public string Nickname { get; set; }
}

Let's say I have another entity, the Company entity. It would be the root entity of another Aggregate. There are many people working on a company, represented by the entity Person. Persons may have cars. But the President of a company is usually very rich and this kind of people, they have Ferraris:

class President : Person
{
    public Ferrari Ferrari { get; set; }
}

In this situation, I have the entity President, who is inside the Company Aggregate, that is holding a reference to a Ferrari, an specialization of the root entity of another aggregate.

Is this correct in view of DDD? Can/should I consider the specialization of root entities themselves as root entities of the same aggregate? I mean, in the domain I described, is the entity Ferrari also the root entity of the Car Aggregate (since Ferrari is also a Car)?

Now let's say I have to persist this model to a Database. I think that my question does not depend on the OR/M framework I will use.

How should I build the table holding Cars? Should I build a single table Cars, with a "CarType" column (possible values: "Car", "Ferrari"), and a nullable Nickname column?

Or should I build a table for Cars and a table for Ferraris, the latter one having its PK a FK of Cars?

Thanks!