smoothing methodology extracting forward forward volatilities tanya exponentials tried earlier bexp cx etc fit well gave negative numbers bootstrapping tried b c 1 standard power law accompanying graph shows 12 months fits quite good case ffvols become negative believe corresponds 0 beta would preferred exp variants explain owing mean reverting vols power law might practical alternative implementation standpoint naveen tanya tamarchenko ect 11 17 2000 02 59 pm naveen andrews corp enron enron alex huang corp enron enron cc vince j kaminski hou ect ect vasant shanbhogue hou ect ect vladimir gorny hou ect ect subject smoothing methodology extracting forward forward volatilities following discussions implemented one method creating forward forward curve implied vol curve sorted 12 forward curves original forward vol curve 12 curves corresponding certain month fitted 12 curves function power x b beta figured beta 0 5 function suitable performing bootstrapping routine deriving ff vols implied x x x x x tx 0 x double check also beta 0 5 combinations parameters b beta equality holds even restriction beta class functions represents quite variety shapes see example fitting well example ff vol curve constructed implied vol curve ng try power well comments