Extractor Fan for Island Hob

We are moving to a house which has a kitchen/dining room/lounge with a vaulted ceiling. The hob is sited in an island unit, but does not have an extractor fan. I am rather concerned about steam and cooking smells. We cannot have an extractor which rises out of the unit because there is not enough room and it cannot be extracted outside under the floor as there is underfloor heating. An extractor above the hob would need a long chimney because of the vaulted ceiling and I wonder if that is possible and if so, presume extremely expensive. There is a window about 2 metres away from the hob and I wonder if it will just be easier to open that slightly when cooking! Any advice would be very much appreciated.