Integration type lambda: how to send json object in request body

Hi all
I’m learning serverless framework and I would like to know how to send a json object in the body of a PUT request with integration type lambda. Bellow is the object (my language is java, but I guess it doesn’t matter):

public class Product {
    private Long id;
    private String name;
    private Double value;
    private String description;
    //getters & setters

I did try many ways around this in my serverless.yml to map this request correctllly, but no success:

handler: com.serverless.requests.UpdateProduct
role: arn:aws:iam::42424242424242:role/DBA
  TABLE_NAME: Product
  - http:
      path: product
      method: put
      integration: lambda
                    "id": "$",
                    "name": "$input.params(''name'')",
                    "value": "$input.params(''value'')",
                    "description": "$input.params(''description'')"

The lambda function should look like this:
public class UpdateProduct implements RequestHandler<Product, ApiGatewayResponse> {

   public ApiGatewayResponse handleRequest(Product input, Context context) {

So how can I send the product object in the request body and retrieve it in the lambda function?