You can access the object by using properties as keys:

    JObject code = JObject.Parse(json);
    string gender = (string)code["value"]["option"];


For your example, try:

    JObject code = JObject.Parse(json);
    var val = code["value"];
    string option = (string)val["option"];

    if (option == "ML")
       val["option"] = "Male";

    if (option == "FM")
       val["option"] = "Female";

    string result = code.ToString();