How can I configure Ninject to inject my DbContext for use with ASP.NET Identity Framework?

I'd like to use Ninject to inject my DbContext ASP.NET Identity Framework.

At the moment I have the following line in my web.config file:

<appSettings>
    <add key="owin:appStartup" value="OwinTest.Identity.OwinStart, OwinTest.Identity" />
</appSettings>

This causes the Configuration() method on class OwinStart in my OwinTest.Identity project to be called.

Here's my OwinStart class:

public class OwinStart
    {
        public void Configuration(IAppBuilder app)
        {
            app.CreatePerOwinContext<IMyContext>(this.GetDbContext);
            app.CreatePerOwinContext<ApplicationRoleManager>(ApplicationRoleManager.Create);
            app.CreatePerOwinContext<ApplicationUserManager>(ApplicationUserManager.Create);

            app.UseCookieAuthentication(
                new CookieAuthenticationOptions()
                {
                    AuthenticationType = DefaultAuthenticationTypes.ApplicationCookie,
                    LoginPath = new PathString("/Login")
                });
        }

        /// <summary>
        /// Gets an instance of the DbContext for OWIN
        /// </summary>
        /// <returns></returns>
        private IMyContext GetDbContext()
        {
            // Create dbcontext instance
            return new MyContext();
        }
    }

As you can see, I create an instance of my DbContext using the new keyword, when I really want to be making use of Ninject to inject my DbContext in.

Is it possible for me to wire up Ninject to inject my database context in within OWIN?