API controller passed invalid JSON receives null

I'm using ASP.NET's ApiController class to create a Web API. I find that if I pass invalid JSON, instead of the caller getting a 500, the input parameter is null. As in, if I pass

{ "InputProperty:" "Some Value" }

which is clearly not valid, to this method:

[HttpPost]
public Dto.OperationOutput Operation(Dto.OperationInput p_input)
{
    return this.BusinessLogic.Operation(p_input);
}

I get that p_input is null. I'd rather send something back telling the user they didn't POST valid JSON.

In my WebApiConfig.cs, I have:

config.Formatters.JsonFormatter.SerializerSettings.NullValueHandling = Newtonsoft.Json.NullValueHandling.Ignore;
config.Formatters.XmlFormatter.UseXmlSerializer = true;

Any ideas? I did see this example, but I believe that's ASP.NET MVC, not ApiController.

edit: I've made the output from the class a little more specific and changed the status code. I'd started making these changes and later saw @CodeCaster's second comment.

public class ModelStateValidFilterAttribute : System.Web.Http.Filters.ActionFilterAttribute
{
    /// <summary>
    /// Before the action method is invoked, check to see if the model is
    /// valid.
    /// </summary>
    public override void OnActionExecuting(System.Web.Http.Controllers.HttpActionContext p_context)
    {
        if (!p_context.ModelState.IsValid)
        {
            List<ErrorPart> errorParts = new List<ErrorPart>();

            foreach (var modelState in p_context.ModelState)
            {
                foreach (var error in modelState.Value.Errors)
                {
                    String message = "The request is not valid; perhaps it is not well-formed.";

                    if (error.Exception != null)
                    {
                        message = error.Exception.Message;
                    }
                    else if (!String.IsNullOrWhiteSpace(error.ErrorMessage))
                    {
                        message = error.ErrorMessage;
                    }

                    errorParts.Add(
                        new ErrorPart
                        {
                            ErrorMessage = message
                          , Property = modelState.Key
                        }
                    );
                }
            }

            throw new HttpResponseException(
                p_context.Request.CreateResponse<Object>(
                    HttpStatusCode.BadRequest
                  , new { Errors = errorParts }
                )
            );
        }
        else
        {
            base.OnActionExecuting(p_context);
        }
    }
}

original answer: Thanks to a pointer from @CodeCaster, I am using the following, and it seems to work:

/// <summary>
/// Throws an <c>HttpResponseException</c> if the model state is not valid;
/// with no validation attributes in the model, this will occur when the
/// input is not well-formed.
/// </summary>
public class ModelStateValidFilterAttribute : System.Web.Http.Filters.ActionFilterAttribute
{
    /// <summary>
    /// Before the action method is invoked, check to see if the model is
    /// valid.
    /// </summary>
    public override void OnActionExecuting(System.Web.Http.Controllers.HttpActionContext p_context)
    {
        if (!p_context.ModelState.IsValid)
        {
            throw new HttpResponseException(
                new HttpResponseMessage
                {
                    Content = new StringContent("The posted data is not valid; perhaps it is not well-formed.")
                  , ReasonPhrase = "Exception"
                  , StatusCode = HttpStatusCode.InternalServerError
                }
            );
        }
        else
        {
            base.OnActionExecuting(p_context);
        }
    }
}