Understanding　the　stochastic　nature　of　emissions　allowances　is　crucial　for　risk　management　in　emissions　trading　markets.　In　this　study,　we　discuss　the　emissions　allowances　spot　price　within　the　European　Union　Emissions　Trading　Scheme:　Powernext　and　European　Climate　Exchange.　To　compare　the　fitness　of　five　stochastic　differential　equations　(SDEs)　to　the　European　Union　allowances　spot　price,　we　apply　regression　theory　to　obtain　the　point　and　interval　estimations　for　the　parameters　of　the　SDEs.　An　empirical　evaluation　demonstrates　that　the　mean　reverting　square　root　process　(MRSRP)　has　the　best　fitness　of　five　SDEs　to　forecast　the　spot　price.　To　reduce　the　degree　of　smog,　we　develop　a　new　trading　scheme　in　which　firms　have　to　hand　many　more　allowances　to　the　government　when　they　emit　one　unit　of　air　pollution　on　heavy　pollution　days,　versus　one　allowance　on　clean　days.　Thus,　we　set　up　the　SDE　MRSRP　model　with　Markovian　switching　to　analyse　the　evolution　of　the　spot　price　in　such　a　scheme.　The　analysis　shows　that　the　allowances　spot　price　will　not　jump　too　much　in　the　new　scheme.　The　findings　of　this　study　could　contribute　to　developing　a　new　type　of　emissions　trading.　©　2017　by　the　author.