Lookbackoptionsarepath-dependentoptions.Ingeneral,thebinomialtreemethods,asthemostpopularapproachestopricingoptions,involveapathdependentvariableaswellastheunderlyingassetpriceforlookbackoptions.However,forfloatingstrikelookbackoptions,asingle-statevariablebinomialtreemethodcanbeconstructed.Thispaperisdevotedtotheconvergenceanalysisofthesingle-statebinomialtreemethodsbothfordiscretelyandcontinuouslymonitoredAmericanfloatingstrikelookbackoptions.Wealsoinvestigatesomepropertiesofsuchoptions,includingeffectsofexpirationdate,interestrateandpidendyieldonoptionsprices,propertiesofoptimalexerciseboundariesandsoon.
