You can access the object by using properties as keys:
JObject obj = JObject.Parse(json);
string gender = (string)obj["value"]["option"];
For your example, try:
JObject obj = JObject.Parse(json);
var val = obj["value"];
string option = (string)val["option"];
if (option == "ML")
val["option"] = "Male";
if (option == "FM")
val["option"] = "Female";
string result = obj.ToString();