├── src ├── .DS_Store ├── data │ ├── .DS_Store │ ├── txt │ │ └── .DS_Store │ ├── zip │ │ └── .DS_Store │ ├── drive-download-20210306T173443Z-001.zip │ └── csv │ │ ├── spxw_call_dlv_0.csv │ │ ├── spxw_call_dlv_1.csv │ │ ├── spxw_call_dlv_10.csv │ │ ├── spxw_call_dlv_11.csv │ │ ├── spxw_call_dlv_12.csv │ │ ├── spxw_call_dlv_13.csv │ │ ├── spxw_call_dlv_14.csv │ │ ├── spxw_call_dlv_15.csv │ │ ├── spxw_call_dlv_16.csv │ │ ├── spxw_call_dlv_17.csv │ │ ├── spxw_call_dlv_18.csv │ │ ├── spxw_call_dlv_19.csv │ │ ├── spxw_call_dlv_2.csv │ │ ├── spxw_call_dlv_20.csv │ │ ├── spxw_call_dlv_21.csv │ │ ├── spxw_call_dlv_22.csv │ │ ├── spxw_call_dlv_23.csv │ │ ├── spxw_call_dlv_24.csv │ │ ├── spxw_call_dlv_25.csv │ │ ├── spxw_call_dlv_26.csv │ │ ├── spxw_call_dlv_27.csv │ │ ├── spxw_call_dlv_28.csv │ │ ├── spxw_call_dlv_29.csv │ │ ├── spxw_call_dlv_3.csv │ │ ├── spxw_call_dlv_30.csv │ │ ├── spxw_call_dlv_31.csv │ │ ├── spxw_call_dlv_32.csv │ │ ├── spxw_call_dlv_33.csv │ │ ├── spxw_call_dlv_34.csv │ │ ├── spxw_call_dlv_35.csv │ │ ├── spxw_call_dlv_36.csv │ │ ├── spxw_call_dlv_37.csv │ │ ├── spxw_call_dlv_38.csv │ │ ├── spxw_call_dlv_39.csv │ │ ├── spxw_call_dlv_4.csv │ │ ├── spxw_call_dlv_40.csv │ │ ├── spxw_call_dlv_41.csv │ │ ├── spxw_call_dlv_42.csv │ │ ├── spxw_call_dlv_43.csv │ │ ├── spxw_call_dlv_44.csv │ │ ├── spxw_call_dlv_45.csv │ │ ├── spxw_call_dlv_46.csv │ │ ├── spxw_call_dlv_47.csv │ │ ├── spxw_call_dlv_48.csv │ │ ├── spxw_call_dlv_49.csv │ │ ├── spxw_call_dlv_5.csv │ │ ├── spxw_call_dlv_50.csv │ │ ├── spxw_call_dlv_51.csv │ │ ├── spxw_call_dlv_52.csv │ │ ├── spxw_call_dlv_53.csv │ │ ├── spxw_call_dlv_54.csv │ │ ├── spxw_call_dlv_55.csv │ │ ├── spxw_call_dlv_56.csv │ │ ├── spxw_call_dlv_57.csv │ │ ├── spxw_call_dlv_58.csv │ │ ├── spxw_call_dlv_59.csv │ │ ├── spxw_call_dlv_6.csv │ │ ├── spxw_call_dlv_60.csv │ │ ├── spxw_call_dlv_61.csv │ │ ├── spxw_call_dlv_62.csv │ │ ├── spxw_call_dlv_63.csv │ │ ├── spxw_call_dlv_64.csv │ │ ├── spxw_call_dlv_65.csv │ │ ├── spxw_call_dlv_66.csv │ │ ├── spxw_call_dlv_67.csv │ │ ├── spxw_call_dlv_68.csv │ │ ├── spxw_call_dlv_69.csv │ │ ├── spxw_call_dlv_7.csv │ │ ├── spxw_call_dlv_70.csv │ │ ├── spxw_call_dlv_71.csv │ │ ├── spxw_call_dlv_72.csv │ │ ├── spxw_call_dlv_73.csv │ │ ├── spxw_call_dlv_74.csv │ │ ├── spxw_call_dlv_75.csv │ │ ├── spxw_call_dlv_76.csv │ │ ├── spxw_call_dlv_77.csv │ │ ├── spxw_call_dlv_78.csv │ │ ├── spxw_call_dlv_79.csv │ │ ├── spxw_call_dlv_8.csv │ │ ├── spxw_call_dlv_80.csv │ │ ├── spxw_call_dlv_81.csv │ │ ├── spxw_call_dlv_82.csv │ │ ├── spxw_call_dlv_83.csv │ │ ├── spxw_call_dlv_84.csv │ │ ├── spxw_call_dlv_85.csv │ │ ├── spxw_call_dlv_86.csv │ │ ├── spxw_call_dlv_87.csv │ │ ├── spxw_call_dlv_88.csv │ │ ├── spxw_call_dlv_89.csv │ │ ├── spxw_call_dlv_9.csv │ │ └── spxw_call_dlv_90.csv ├── model │ └── generater.pt ├── export.py ├── unzip.py ├── result │ ├── result.csv │ ├── result1.csv │ ├── result10.csv │ ├── result11.csv │ ├── result12.csv │ ├── result13.csv │ ├── result14.csv │ ├── result15.csv │ ├── result16.csv │ ├── result17.csv │ ├── result18.csv │ ├── result19.csv │ ├── result2.csv │ ├── result20.csv │ ├── result21.csv │ ├── result22.csv │ ├── result23.csv │ ├── result24.csv │ ├── result25.csv │ ├── result26.csv │ ├── result27.csv │ ├── result28.csv │ ├── result29.csv │ ├── result3.csv │ ├── result30.csv │ ├── result31.csv │ ├── result32.csv │ ├── result33.csv │ ├── result34.csv │ ├── result35.csv │ ├── result36.csv │ ├── result37.csv │ ├── result38.csv │ ├── result39.csv │ ├── result4.csv │ ├── result40.csv │ ├── result41.csv │ ├── result42.csv │ ├── result43.csv │ ├── result44.csv │ ├── result45.csv │ ├── result46.csv │ ├── result47.csv │ ├── result48.csv │ ├── result49.csv │ ├── result5.csv │ ├── result50.csv │ ├── result51.csv │ ├── result52.csv │ ├── result53.csv │ ├── result54.csv │ ├── result55.csv │ ├── result56.csv │ ├── result57.csv │ ├── result58.csv │ ├── result59.csv │ ├── result6.csv │ ├── result60.csv │ ├── result61.csv │ ├── result62.csv │ ├── result63.csv │ ├── result64.csv │ ├── result65.csv │ ├── result66.csv │ ├── result67.csv │ ├── result68.csv │ ├── result69.csv │ ├── result7.csv │ ├── result70.csv │ ├── result71.csv │ ├── result72.csv │ ├── result73.csv │ ├── result74.csv │ ├── result75.csv │ ├── result76.csv │ ├── result77.csv │ ├── result78.csv │ ├── result79.csv │ ├── result8.csv │ ├── result80.csv │ ├── result81.csv │ ├── result82.csv │ ├── result83.csv │ ├── result84.csv │ ├── result85.csv │ ├── result86.csv │ ├── result87.csv │ ├── result88.csv │ ├── result89.csv │ ├── result9.csv │ └── result90.csv ├── metrics.py ├── dlv.py └── Project.py ├── LICENSE └── README.md /src/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Songloading/Paper-Replicate-Learning-to-Simulate-Equity-Option-Markets/HEAD/src/.DS_Store -------------------------------------------------------------------------------- /src/data/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Songloading/Paper-Replicate-Learning-to-Simulate-Equity-Option-Markets/HEAD/src/data/.DS_Store -------------------------------------------------------------------------------- /src/data/txt/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Songloading/Paper-Replicate-Learning-to-Simulate-Equity-Option-Markets/HEAD/src/data/txt/.DS_Store -------------------------------------------------------------------------------- /src/data/zip/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Songloading/Paper-Replicate-Learning-to-Simulate-Equity-Option-Markets/HEAD/src/data/zip/.DS_Store -------------------------------------------------------------------------------- /src/model/generater.pt: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Songloading/Paper-Replicate-Learning-to-Simulate-Equity-Option-Markets/HEAD/src/model/generater.pt -------------------------------------------------------------------------------- /src/data/drive-download-20210306T173443Z-001.zip: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Songloading/Paper-Replicate-Learning-to-Simulate-Equity-Option-Markets/HEAD/src/data/drive-download-20210306T173443Z-001.zip -------------------------------------------------------------------------------- /src/export.py: -------------------------------------------------------------------------------- 1 | import sys 2 | import os 3 | from google.colab import files 4 | 5 | for i in range(len(dlv)): 6 | filename = 'spxw_call_dlv_' + str(i + 26) +'.csv' 7 | with open('/data/dlv/' + filename, 'w') as f: 8 | np.savetxt(f, dlv[i], delimiter=",") 9 | -------------------------------------------------------------------------------- /src/unzip.py: -------------------------------------------------------------------------------- 1 | import sys 2 | import zipfile 3 | import os 4 | 5 | directory_zip = os.fsencode('data/zip/') 6 | 7 | for file in os.listdir(directory_zip): 8 | filename = os.fsdecode(file) 9 | with zipfile.ZipFile('data/zip/' + filename, 'r') as zip_ref: 10 | zip_ref.extractall('data/txt/') 11 | -------------------------------------------------------------------------------- /src/result/result.csv: -------------------------------------------------------------------------------- 1 | 4.688434600830078125e+00,2.177227783203125000e+01,6.580062866210937500e+00,2.363059997558593750e+00,1.674057006835937500e+00,5.000305175781250000e-01,4.117164611816406250e-01,5.092506408691406250e-01 2 | 3.059329605102539062e+01,2.172632217407226562e+01,1.053735351562500000e+01,3.927615356445312500e+01,4.234779357910156250e+00,2.262668609619140625e+00,5.859298706054687500e-01,8.948135375976562500e-02 3 | 3.892418670654296875e+01,5.671316909790039062e+01,1.107672500610351562e+01,2.183913040161132812e+01,3.478149414062500000e+00,1.111592864990234375e+01,3.742599487304687500e-02,1.578483581542968750e-01 4 | -------------------------------------------------------------------------------- /src/result/result1.csv: -------------------------------------------------------------------------------- 1 | 2.665663242340087891e+00,2.879519939422607422e+00,2.527798652648925781e+00,2.523189067840576172e+00,2.422501564025878906e+00,2.405194282531738281e+00,2.399585247039794922e+00,2.404447555541992188e+00 2 | 3.501319885253906250e+00,3.297283172607421875e+00,2.715788841247558594e+00,3.648711681365966797e+00,2.579065322875976562e+00,2.474396228790283203e+00,2.401632308959960938e+00,2.385365486145019531e+00 3 | 3.554108142852783203e+00,4.499285221099853516e+00,3.025820255279541016e+00,3.103850841522216797e+00,2.474725723266601562e+00,2.815819263458251953e+00,2.381140232086181641e+00,2.386456966400146484e+00 4 | -------------------------------------------------------------------------------- /src/result/result10.csv: -------------------------------------------------------------------------------- 1 | 2.433655738830566406e+00,2.625302314758300781e+00,2.467552661895751953e+00,2.406202316284179688e+00,2.397544384002685547e+00,2.383316516876220703e+00,2.383610725402832031e+00,2.382310390472412109e+00 2 | 2.692443370819091797e+00,2.666147232055664062e+00,2.484270572662353516e+00,2.823076725006103516e+00,2.467706680297851562e+00,2.393871784210205078e+00,2.383675575256347656e+00,2.380267620086669922e+00 3 | 2.810549259185791016e+00,3.082450389862060547e+00,2.510884761810302734e+00,2.732760906219482422e+00,2.412995338439941406e+00,2.716200351715087891e+00,2.379899501800537109e+00,2.380469799041748047e+00 4 | -------------------------------------------------------------------------------- /src/result/result11.csv: -------------------------------------------------------------------------------- 1 | 2.431619644165039062e+00,2.723820686340332031e+00,2.517529487609863281e+00,2.403826713562011719e+00,2.408900737762451172e+00,2.383785247802734375e+00,2.383998870849609375e+00,2.384355068206787109e+00 2 | 2.739214897155761719e+00,2.675744533538818359e+00,2.511961460113525391e+00,2.896946430206298828e+00,2.436751842498779297e+00,2.402267456054687500e+00,2.386057376861572266e+00,2.380447387695312500e+00 3 | 2.973463058471679688e+00,3.063858509063720703e+00,2.494256019592285156e+00,2.695477962493896484e+00,2.446338176727294922e+00,2.648441791534423828e+00,2.380074024200439453e+00,2.381074428558349609e+00 4 | -------------------------------------------------------------------------------- /src/result/result12.csv: -------------------------------------------------------------------------------- 1 | 2.590383529663085938e+00,3.006178379058837891e+00,2.445477962493896484e+00,2.453921318054199219e+00,2.407793045043945312e+00,2.405333995819091797e+00,2.391804218292236328e+00,2.410726547241210938e+00 2 | 4.134327411651611328e+00,3.241668701171875000e+00,2.679786205291748047e+00,3.677202701568603516e+00,2.485080242156982422e+00,2.495512962341308594e+00,2.397123336791992188e+00,2.383703231811523438e+00 3 | 3.593847274780273438e+00,5.378206253051757812e+00,3.095489978790283203e+00,2.931268215179443359e+00,2.441031932830810547e+00,2.448335647583007812e+00,2.380721092224121094e+00,2.385984420776367188e+00 4 | -------------------------------------------------------------------------------- /src/result/result13.csv: -------------------------------------------------------------------------------- 1 | 2.576642990112304688e+00,3.127347946166992188e+00,2.647516727447509766e+00,2.462450027465820312e+00,2.453824043273925781e+00,2.401754856109619141e+00,2.399796009063720703e+00,2.398816108703613281e+00 2 | 3.333644866943359375e+00,2.988020896911621094e+00,2.744419097900390625e+00,3.533752918243408203e+00,2.524847984313964844e+00,2.462304592132568359e+00,2.406214714050292969e+00,2.384175777435302734e+00 3 | 3.771105766296386719e+00,4.033244132995605469e+00,2.728461742401123047e+00,3.083150386810302734e+00,2.497660636901855469e+00,2.842052936553955078e+00,2.382240772247314453e+00,2.387516498565673828e+00 4 | -------------------------------------------------------------------------------- /src/result/result14.csv: -------------------------------------------------------------------------------- 1 | 2.529289245605468750e+00,2.848978042602539062e+00,2.493758678436279297e+00,2.472046375274658203e+00,2.414658069610595703e+00,2.394931793212890625e+00,2.390077590942382812e+00,2.394944190979003906e+00 2 | 3.257720470428466797e+00,2.928769588470458984e+00,2.578397750854492188e+00,3.544115543365478516e+00,2.624370098114013672e+00,2.439072608947753906e+00,2.390393257141113281e+00,2.382690429687500000e+00 3 | 3.050176143646240234e+00,4.070848941802978516e+00,2.796111583709716797e+00,2.923644542694091797e+00,2.453722476959228516e+00,2.672549247741699219e+00,2.380376338958740234e+00,2.383390426635742188e+00 4 | -------------------------------------------------------------------------------- /src/result/result15.csv: -------------------------------------------------------------------------------- 1 | 2.441498279571533203e+00,2.809292316436767578e+00,2.579538345336914062e+00,2.416059017181396484e+00,2.412536621093750000e+00,2.385437488555908203e+00,2.384778976440429688e+00,2.386723041534423828e+00 2 | 2.852980613708496094e+00,2.750498771667480469e+00,2.575049877166748047e+00,3.026648044586181641e+00,2.450002670288085938e+00,2.411629676818847656e+00,2.388175487518310547e+00,2.380902767181396484e+00 3 | 3.096560955047607422e+00,3.232636928558349609e+00,2.542033672332763672e+00,2.819792747497558594e+00,2.470194339752197266e+00,2.647603034973144531e+00,2.380187511444091797e+00,2.381734848022460938e+00 4 | -------------------------------------------------------------------------------- /src/result/result16.csv: -------------------------------------------------------------------------------- 1 | 2.555204391479492188e+00,2.974403858184814453e+00,2.494628429412841797e+00,2.468244552612304688e+00,2.411592483520507812e+00,2.403213024139404297e+00,2.392776966094970703e+00,2.404460906982421875e+00 2 | 3.659587860107421875e+00,3.230420589447021484e+00,2.743388652801513672e+00,3.634296417236328125e+00,2.464687824249267578e+00,2.488084793090820312e+00,2.400639057159423828e+00,2.383677482604980469e+00 3 | 3.717408657073974609e+00,4.820247650146484375e+00,2.889405727386474609e+00,3.059562206268310547e+00,2.452775001525878906e+00,2.513914108276367188e+00,2.380944728851318359e+00,2.386476039886474609e+00 4 | -------------------------------------------------------------------------------- /src/result/result17.csv: -------------------------------------------------------------------------------- 1 | 2.510596752166748047e+00,2.837765216827392578e+00,2.505075931549072266e+00,2.446108341217041016e+00,2.413569450378417969e+00,2.391117572784423828e+00,2.389481067657470703e+00,2.392793178558349609e+00 2 | 3.102923870086669922e+00,2.956545352935791016e+00,2.587513446807861328e+00,3.144100666046142578e+00,2.491208553314208984e+00,2.431824207305908203e+00,2.392927169799804688e+00,2.381896018981933594e+00 3 | 3.314054965972900391e+00,3.792875289916992188e+00,2.692146301269531250e+00,2.926037788391113281e+00,2.444407939910888672e+00,2.664418220520019531e+00,2.380415916442871094e+00,2.383000850677490234e+00 4 | -------------------------------------------------------------------------------- /src/result/result18.csv: -------------------------------------------------------------------------------- 1 | 2.555910110473632812e+00,3.136884689331054688e+00,2.457845211029052734e+00,2.444637298583984375e+00,2.409174442291259766e+00,2.408183574676513672e+00,2.389303684234619141e+00,2.417024612426757812e+00 2 | 4.580267906188964844e+00,3.181340217590332031e+00,2.694434165954589844e+00,3.739223480224609375e+00,2.454084396362304688e+00,2.540813446044921875e+00,2.396823883056640625e+00,2.384162425994873047e+00 3 | 3.923613548278808594e+00,5.686085700988769531e+00,3.122815132141113281e+00,2.931334972381591797e+00,2.459545612335205078e+00,2.421055793762207031e+00,2.380820751190185547e+00,2.386729240417480469e+00 4 | -------------------------------------------------------------------------------- /src/result/result19.csv: -------------------------------------------------------------------------------- 1 | 2.471363067626953125e+00,2.773385047912597656e+00,2.512822628021240234e+00,2.415201663970947266e+00,2.407011985778808594e+00,2.386575698852539062e+00,2.386707782745361328e+00,2.386884212493896484e+00 2 | 2.935040950775146484e+00,2.769612312316894531e+00,2.567058086395263672e+00,3.020231723785400391e+00,2.477991580963134766e+00,2.410799980163574219e+00,2.388799667358398438e+00,2.380978107452392578e+00 3 | 3.068753719329833984e+00,3.409122467041015625e+00,2.612145900726318359e+00,2.803980827331542969e+00,2.439169883728027344e+00,2.631452560424804688e+00,2.380198955535888672e+00,2.381688117980957031e+00 4 | -------------------------------------------------------------------------------- /src/result/result2.csv: -------------------------------------------------------------------------------- 1 | 2.530282020568847656e+00,2.848951339721679688e+00,2.493327617645263672e+00,2.447103977203369141e+00,2.414237022399902344e+00,2.393595218658447266e+00,2.391750335693359375e+00,2.391363143920898438e+00 2 | 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4.030285663315288502e+01,2.340165869021780054e+01,1.343428554438429146e+01,7.800552896739265663e+00,4.478095181461430485e+00,2.257576489884214332e+00,1.296612159159568956e+00,7.454760774559116010e-01 3 | 3.837597319768144644e+01,2.078698548207745134e+01,1.108639225710797405e+01,5.734340822642056246e+00,3.023561524665811628e+00,1.588814176974072900e+00,8.356577078222091615e-01,4.387754191467536646e-01 4 | -------------------------------------------------------------------------------- /src/data/csv/spxw_call_dlv_31.csv: -------------------------------------------------------------------------------- 1 | 1.849555684959515389e+01,1.273342232031592580e+01,8.847452931434428791e+00,5.894852478207068813e+00,3.958550676294307458e+00,2.634250152806815404e+00,1.797050159673146519e+00,1.202525579730134409e+00 2 | 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1.026819835394201164e+03,2.567049588485502909e+02,7.898614118416932683e+01,2.504438622912686085e+01,7.437848308254022989e+00,2.374176018594800208e+00,7.567921967062917199e-01,2.409629419024335306e-01 3 | 0.000000000000000000e+00,7.245598753636671745e+02,1.207599792272778672e+02,3.293453978925759884e+01,8.050665281818524477e+00,1.979671790611112536e+00,4.898984958510258503e-01,1.210221939809031644e-01 4 | -------------------------------------------------------------------------------- /src/data/csv/spxw_call_dlv_9.csv: -------------------------------------------------------------------------------- 1 | 1.107723196987845782e+01,7.542928036684561910e+00,5.172212587201603817e+00,3.581362096450567023e+00,2.440894627316497090e+00,1.655558652906740980e+00,1.142524010944139468e+00,7.875312967079671767e-01 2 | 3.423064728286451697e+01,1.898904111188704746e+01,1.006353203904826010e+01,5.565324296387695213e+00,2.950406712093724959e+00,1.594009604403227476e+00,8.803482219565480493e-01,4.687735444182796196e-01 3 | 3.475956947037939671e+01,1.796862746209550821e+01,9.583267979784270807e+00,4.747333091319954512e+00,2.503139266332339741e+00,1.275538673986759131e+00,6.708863377417796370e-01,3.522595810306441977e-01 4 | -------------------------------------------------------------------------------- /src/data/csv/spxw_call_dlv_90.csv: -------------------------------------------------------------------------------- 1 | 9.432732863564106651e+01,4.711253916054457136e+01,2.095376945493167042e+01,9.649762248981691215e+00,4.422426385393546155e+00,2.053719375553127779e+00,9.095054753482775256e-01,4.221709432418827568e-01 2 | 4.797982380192211167e+02,1.539686630660577293e+02,5.773824864977164140e+01,1.965557400843290026e+01,6.575390823231631821e+00,2.225394561056747378e+00,7.669811823830662290e-01,2.598899845945598641e-01 3 | 7.426945792822498333e+02,2.475648597607499539e+02,7.426945792822498049e+01,2.121984512234999798e+01,6.160136371260159116e+00,1.820040291508683294e+00,5.274654257141478952e-01,1.533254631455344685e-01 4 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2021 Song Luo 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /src/metrics.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import os 3 | import fnmatch 4 | import matplotlib.pyplot as plt 5 | from statsmodels.distributions.empirical_distribution import ECDF 6 | from scipy.stats import skew, kurtosis 7 | 8 | def find(pattern, path): 9 | result = [] 10 | for root, dirs, files in os.walk(path): 11 | for name in files: 12 | if fnmatch.fnmatch(name, pattern): 13 | result.append(os.path.join(root, name)) 14 | return result 15 | s = find('*.csv','data/csv/') 16 | r = find('*.csv','result/') 17 | 18 | def compare_epdf(a, b): 19 | ecdfa = ECDF(a) 20 | ecdfb = ECDF(b) 21 | return ecdfa, ecdfb 22 | 23 | def euclidean_distance(a, b): 24 | # a and b should be in same size 25 | sum = 0 26 | for i in range(a.shape[0]): 27 | for j in range(a.shape[1]): 28 | sum = sum + np.square(a[i,j] - b[i, j]) 29 | return np.sqrt(sum) 30 | # load data 31 | filelength = (len(s)) 32 | dt_arry = np.zeros((filelength, 3, 8)) 33 | i = 0 34 | for f in s: 35 | dt_arry[i,:,:] = np.loadtxt(open(f, "rb"), delimiter=",") 36 | i = i+1 37 | dt_arry = dt_arry.reshape(filelength*3*8) 38 | 39 | rs_arry = np.zeros((filelength, 3, 8)) 40 | i = 0 41 | for f in r: 42 | rs_arry[i,:,:] = np.loadtxt(open(f, "rb"), delimiter=",") 43 | i = i+1 44 | rs_arry = rs_arry.reshape(filelength*3*8) 45 | plt.hist(rs_arry, alpha=0.5, label='simulated') 46 | plt.hist(dt_arry, alpha=0.5, label='real') 47 | plt.legend(loc='upper right') 48 | plt.show() 49 | 50 | # calculate difference in cumulative epdf 51 | i = 0 52 | c = 0 53 | lim = int(filelength/5-1) 54 | for i in range(0,lim): 55 | suba = rs_arry[i*24:(i+1)*24] 56 | subb = dt_arry[i*24:(i+1)*24] 57 | max = np.max(subb) 58 | ecdfa, ecdfb = compare_epdf(suba, subb) 59 | c = c + abs(ecdfa(max) - ecdfb(max)) 60 | print('cumulative ecdf: ' + str(c)) 61 | 62 | skewR = skew(dt_arry) 63 | skewF = skew(rs_arry) 64 | print('skew diff: ' + str(abs(skewR-skewF)/90)) 65 | 66 | kurR = kurtosis(dt_arry) 67 | kurF = kurtosis(rs_arry) 68 | print('kurtosis diff: ' + str(abs(kurR-kurF)/filelength)) 69 | 70 | # rs_arry = rs_arry.reshape((filelength,3,8)) 71 | # dt_arry = dt_arry.reshape((filelength, 3, 8)) 72 | 73 | # min_eu = 100 74 | # for i in range(filelength): 75 | # no = euclidean_distance(rs_arry[i,:,:], dt_arry[i,:,:]) 76 | # if no< min_eu: 77 | # min_eu = no 78 | # print('min corrrelation: ' + str(min_eu)) 79 | -------------------------------------------------------------------------------- /src/dlv.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import pandas as pd 3 | # %matplotlib inline 4 | from matplotlib import pyplot as plt 5 | import os 6 | import sys 7 | 8 | def closest(target, lst): 9 | diff = sys.maxsize 10 | sol = 0; 11 | for i in lst: 12 | temp = abs(i - target) 13 | if (temp < diff): 14 | diff = temp; 15 | sol = i; 16 | return sol; 17 | 18 | def kij_func(t, s, spxw_call_clean): 19 | kij = [] 20 | for j in t: 21 | # k_j represent the strikes at jth maturity 22 | kj = [] 23 | # finding the closest maturity/strike if no particular data 24 | t_temp = spxw_call_clean['okey_maturity'].unique() 25 | j_temp = closest(j, t_temp); 26 | iv = spxw_call_clean[(spxw_call_clean['okey_maturity'] == j_temp)]['prtIv'].mean() 27 | n = len(s) 28 | # k_j^i represent the ith strike at jth maturity 29 | for i in range(n): 30 | kj.append(np.round(np.exp((3 * ((2 *(i + 1) - (n - 1)) / (n + 1)) * iv * np.sqrt(j)) - 0.5 * iv *iv * j), 2)) 31 | kij.append(kj) 32 | return np.asarray(kij) 33 | 34 | def thetaij_func(t, s, spxw_call_clean): 35 | thetaij = [] 36 | # theta_j represent the theta at jth maturity 37 | for j in t: 38 | thetaj = [] 39 | # finding the closest maturity if no particular data 40 | t_temp = spxw_call_clean['okey_maturity'].unique() 41 | j_temp = closest(j, t_temp); 42 | # theta_j^i represent the ith theta at jth maturity 43 | for i in s: 44 | # finding the closest strike if no particular data 45 | s_temp = np.asarray(spxw_call_clean[(spxw_call_clean['okey_maturity'] == j_temp)]['okey_xx']) 46 | i_temp = closest(i, s_temp) 47 | 48 | thetaj.append(-1 * np.asarray(spxw_call_clean[(spxw_call_clean['okey_maturity'] == j_temp) & (spxw_call_clean['okey_xx'] == i_temp)]['prtTh'])[0]) 49 | thetaij.append(thetaj) 50 | return np.asarray(thetaij) 51 | 52 | def gammaij_func(t, s, spxw_call_clean): 53 | gammaij = [] 54 | # gamma_j represent the gamma at jth maturity 55 | for j in t: 56 | gammaj = [] 57 | # finding the closest maturity if no particular data 58 | t_temp = spxw_call_clean['okey_maturity'].unique() 59 | j_temp = closest(j, t_temp) 60 | # gamma_j^i represent the ith theta at jth maturity 61 | for i in s: 62 | # finding the closest strike if no particular data 63 | s_temp = np.asarray(spxw_call_clean[(spxw_call_clean['okey_maturity'] == j_temp)]['okey_xx']) 64 | i_temp = closest(i, s_temp) 65 | 66 | gammaj.append(np.asarray(spxw_call_clean[(spxw_call_clean['okey_maturity'] == j_temp) & (spxw_call_clean['okey_xx'] == i_temp)]['prtGa'])[0]) 67 | 68 | gammaij.append(gammaj) 69 | return np.asarray(gammaij) 70 | 71 | def tj_func(t): 72 | tj = [] 73 | # calculating the time difference 74 | for i in range(len(t) - 1): 75 | tj.append(t[i + 1] - t[i]) 76 | return np.asarray(tj) 77 | 78 | def dlv_func(thetaij, gammaij, kij, tj, t, s, spxw_call_clean): 79 | dlvij = [] 80 | for j in range(len(tj)): 81 | dtj = tj[j] 82 | dlvj = [] 83 | for i in range(len(s)): 84 | if gammaij[j][i] != 0 and kij[j][i] != 0: 85 | dlvj.append( 86 | np.sqrt(2 * thetaij[j][i] / (gammaij[j][i] * kij[j][i] * kij[j][i] * dtj)) 87 | ) 88 | else: 89 | dlvj.append(0) 90 | dlvij.append(dlvj) 91 | return np.asarray(dlvij) 92 | 93 | directory_txt = os.fsencode('/data/txt/') 94 | DF_list = list() 95 | spxw_call_data = 0; 96 | 97 | for file in os.listdir(directory_txt): 98 | filename = os.fsdecode(file) 99 | if filename.endswith(".txt"): 100 | date = filename[-14:-4] 101 | print(date) 102 | data = pd.read_csv('/data/txt/' + filename, sep="\t") 103 | EQT = pd.DataFrame(data) 104 | # Import and Create Fields 105 | df = EQT[['okey_tk', 106 | 'okey_yr', 'okey_mn', 'okey_dy', 107 | 'okey_xx', 108 | 'okey_cp', 109 | 'prtSize', 'prtPrice', 110 | 'prtIv', 111 | 'prtGa', 'prtTh', 'surfOpx']] 112 | df['okey_ymd'] = pd.to_datetime(df['okey_yr'].astype(str) + '/' + df['okey_mn'].astype(str) + '/' + df['okey_dy'].astype(str)) 113 | df['okey_maturity'] = df['okey_ymd'] - np.datetime64(date) 114 | df['okey_maturity'] = df['okey_maturity'].dt.days 115 | df = df.drop_duplicates().sort_values(by=['okey_maturity']) 116 | 117 | # SPX Weekly Call 118 | spxw_call = df.loc[(df['okey_tk'] == 'SPXW') & (df['okey_cp'] == 'Call')] 119 | spxw_call = spxw_call[['okey_xx', 120 | 'okey_maturity', 121 | 'prtSize', 'prtPrice', 122 | 'prtIv', 123 | 'prtGa', 'prtTh', 'surfOpx']] 124 | grouped_df = spxw_call.groupby(['okey_maturity', 'okey_xx']) 125 | spxw_call_clean = grouped_df.mean().reset_index() 126 | spxw_call_data += spxw_call_clean.shape[0] 127 | plt.scatter(spxw_call_clean['okey_xx'], spxw_call_clean['okey_maturity']) 128 | plt.xlabel('option price') 129 | plt.ylabel('date') 130 | DF_list.append(spxw_call_clean) 131 | 132 | # time = np.sort(spxw_call_clean['okey_maturity'].unique()/365) 133 | # strike = spxw_call_clean.groupby(['okey_xx']).size().reset_index(name='count') 134 | # s = np.sort(np.asarray(strike.loc[strike['count'] > 20]['okey_xx'])) 135 | # print('maturity', time * 365) 136 | # print('strike', s) 137 | plt.show() 138 | 139 | t = [20, 50, 71, 106] 140 | s = [3230, 3240, 3250, 3260, 3270, 3280, 3290, 3300] 141 | 142 | dlv = [] 143 | for i in range(0, len(DF_list)): 144 | spxw_call_clean = DF_list[i] 145 | kij = kij_func(t, s, spxw_call_clean) 146 | thetaij = thetaij_func(t, s, spxw_call_clean) 147 | gammaij = gammaij_func(t, s, spxw_call_clean) 148 | tj = tj_func(t) 149 | dlv_ind = dlv_func(thetaij, gammaij, kij, tj, t, s, spxw_call_clean) 150 | print(dlv_ind) 151 | dlv.append(dlv_ind) 152 | -------------------------------------------------------------------------------- /src/Project.py: -------------------------------------------------------------------------------- 1 | import torch 2 | import torch.nn as nn 3 | import torch.optim as optim 4 | import torchvision 5 | import torchvision.datasets as datasets 6 | from torch.utils.data import DataLoader,TensorDataset 7 | import numpy as np 8 | from torch.autograd import Variable 9 | import os 10 | import fnmatch 11 | from datetime import datetime 12 | import argparse 13 | 14 | 15 | 16 | 17 | def NormalizeData(data): 18 | return 2*(data - np.min(data)) / (np.max(data) - np.min(data))-1 19 | 20 | def Z_Score_NormalizeData(data): 21 | mean = np.mean(data) 22 | std = np.std(data) 23 | return (data - mean)/std 24 | 25 | def find(pattern, path): 26 | result = [] 27 | for root, dirs, files in os.walk(path): 28 | for name in files: 29 | if fnmatch.fnmatch(name, pattern): 30 | result.append(os.path.join(root, name)) 31 | return result 32 | 33 | 34 | class Discriminator(nn.Module): 35 | def __init__(self, input_size): 36 | super(Discriminator, self).__init__() 37 | 38 | self.model = nn.Sequential( 39 | nn.Linear(int(np.prod(input_size)), 512), 40 | nn.LeakyReLU(0.2, inplace=True), 41 | nn.Linear(512, 256), 42 | nn.LeakyReLU(0.2, inplace=True), 43 | nn.Linear(256, 1), 44 | nn.Sigmoid(), 45 | ) 46 | 47 | def forward(self, data): 48 | data_flat = data.view(data.size(0), -1) 49 | validity = self.model(data_flat) 50 | 51 | return validity 52 | 53 | 54 | class Generator(nn.Module): 55 | def __init__(self, input_size): 56 | super().__init__() 57 | def block(in_feat, out_feat, normalize=True): 58 | layers = [nn.Linear(in_feat, out_feat)] 59 | if normalize: 60 | normlayer = nn.BatchNorm1d(out_feat, 0.8) 61 | layers.append(normlayer) 62 | layers.append(nn.LeakyReLU(0.2, inplace=True)) 63 | return layers 64 | self.model = nn.Sequential( 65 | *block(input_size, 128, normalize=False), 66 | *block(128, 256), 67 | *block(256, 512), 68 | *block(512, 1024), 69 | nn.Linear(1024, int(np.prod(input_size))), 70 | nn.Tanh() 71 | ) 72 | 73 | def forward(self, x): 74 | return self.model(x) 75 | 76 | 77 | # Parameters 78 | device = "cuda" if torch.cuda.is_available() else "cpu" 79 | parser = argparse.ArgumentParser() 80 | parser.add_argument("--num_epochs", type=int, default=10, help="number of epochs of training") 81 | parser.add_argument("--batch_size", type=int, default=3, help="batch size (cannot be 1 for training)") 82 | parser.add_argument("--learning_rate", type=float, default=3e-4, help="learning rate") 83 | parser.add_argument("--save_model", type=bool, default=False, help="Save model?") 84 | parser.add_argument("--mode", default='Tran', help="Train or Test") 85 | parser.add_argument("--dlv_path", default='data/spxw_call_dlv_0.csv', help="Load Path for Testing DLV") 86 | parser.add_argument("--recursive", type=bool, default=True, help="Recursively Testing DLV?") 87 | parser.add_argument("--recursive_length", type=int, default=2, help="Length of Recursively Testing DLV") 88 | opt = parser.parse_args() 89 | 90 | input_size = 3 * 8 * 1 # 24 91 | min = -0.3406041746517267 92 | max = 7.910383934523679 93 | mean = 59.93618814995941 94 | std = 175.9702100282392 95 | if opt.mode == 'Train': 96 | # initialize networks 97 | disc = Discriminator(input_size).to(device) 98 | gen = Generator(input_size).to(device) 99 | print(disc) 100 | print(gen) 101 | optimizerD = optim.Adam(disc.parameters(), lr=opt.learning_rate) 102 | optimizerG = optim.Adam(gen.parameters(), lr=opt.learning_rate) 103 | adversarial_loss = nn.BCELoss() 104 | 105 | 106 | # Find all file names 107 | s = find('*.csv', 'data/csv/') 108 | 109 | # load & normalize data 110 | dt_arry = np.zeros((len(s), 3, 8)) 111 | i = 0 112 | for f in s: 113 | dt_arry[i,:,:] = np.loadtxt(open(f, "rb"), delimiter=",") 114 | i = i+1 115 | dt_arry = Z_Score_NormalizeData(dt_arry) 116 | dt_arry = NormalizeData(dt_arry) 117 | dt_tensor = torch.Tensor(dt_arry) 118 | my_dataset = TensorDataset(dt_tensor) 119 | dataloader = torch.utils.data.DataLoader( 120 | my_dataset, 121 | batch_size= opt.batch_size, 122 | shuffle=False, 123 | drop_last=True 124 | ) 125 | 126 | # # load data (for dummy data) 127 | # result1 = np.loadtxt(open("E:/Northwestern/COMP_SCI 496 Adv Deep Learning/spxw_call_dlv.csv", "rb"), delimiter=",") 128 | # result2 = np.loadtxt(open("E:/Northwestern/COMP_SCI 496 Adv Deep Learning/2.csv", "rb"), delimiter=",") 129 | # result3 = np.loadtxt(open("E:/Northwestern/COMP_SCI 496 Adv Deep Learning/3.csv", "rb"), delimiter=",") 130 | # result4 = np.loadtxt(open("E:/Northwestern/COMP_SCI 496 Adv Deep Learning/4.csv", "rb"), delimiter=",") 131 | # result5 = np.loadtxt(open("E:/Northwestern/COMP_SCI 496 Adv Deep Learning/5.csv", "rb"), delimiter=",") 132 | # result6 = np.loadtxt(open("E:/Northwestern/COMP_SCI 496 Adv Deep Learning/6.csv", "rb"), delimiter=",") 133 | # result7 = np.loadtxt(open("E:/Northwestern/COMP_SCI 496 Adv Deep Learning/7.csv", "rb"), delimiter=",") 134 | # result8 = np.loadtxt(open("E:/Northwestern/COMP_SCI 496 Adv Deep Learning/8.csv", "rb"), delimiter=",") 135 | # result9 = np.loadtxt(open("E:/Northwestern/COMP_SCI 496 Adv Deep Learning/9.csv", "rb"), delimiter=",") 136 | # result = np.stack((result1, result2, result3, result4, result5, result6, result7, result8, result9)) 137 | # tensor_x = torch.Tensor(result) 138 | # my_dataset = TensorDataset(tensor_x) 139 | # dataloader = torch.utils.data.DataLoader( 140 | # my_dataset, 141 | # batch_size= batch_size, 142 | # shuffle=True, 143 | # ) 144 | 145 | # initialize and normalize sigma_t for testing 146 | fixed_noise = dt_arry[0,:,:].reshape(1,24) 147 | fixed_noise = torch.Tensor(fixed_noise) 148 | cuda = True if torch.cuda.is_available() else False 149 | Tensor = torch.cuda.FloatTensor if cuda else torch.FloatTensor 150 | 151 | for epoch in range(opt.num_epochs): 152 | for batch_idx, data in enumerate(dataloader): 153 | # Adversarial ground truths 154 | valid = Variable(Tensor(data[0].size(0), 1).fill_(1.0), requires_grad=False) 155 | fake = Variable(Tensor(data[0].size(0), 1).fill_(0.0), requires_grad=False) 156 | 157 | # Configure input 158 | real_imgs = Variable(data[0].type(Tensor)) 159 | 160 | # ----------------- 161 | # Train Generator 162 | # ----------------- 163 | 164 | optimizerG.zero_grad() 165 | 166 | # Sample noise as generator input 167 | z = Variable(Tensor(np.random.normal(0, 1, (data[0].shape[0], 24)))) 168 | 169 | # Generate a batch of images 170 | gen_dlvs = gen(z) 171 | 172 | # Loss measures generator's ability to fool the discriminator 173 | g_loss = adversarial_loss(disc(gen_dlvs), valid) 174 | 175 | g_loss.backward() 176 | optimizerG.step() 177 | 178 | # --------------------- 179 | # Train Discriminator 180 | # --------------------- 181 | 182 | optimizerD.zero_grad() 183 | 184 | # Measure discriminator's ability to classify real from generated samples 185 | real_loss = adversarial_loss(disc(real_imgs), valid) 186 | fake_loss = adversarial_loss(disc(gen_dlvs.detach()), fake) 187 | d_loss = (real_loss + fake_loss) / 2 188 | 189 | d_loss.backward() 190 | optimizerD.step() 191 | 192 | 193 | if batch_idx == 0: 194 | print( 195 | f"Epoch [{epoch}/{opt.num_epochs}] Batch {batch_idx}/{len(dataloader)} \ 196 | Loss D: {d_loss:.4f}, loss G: {g_loss:.4f}" 197 | ) 198 | ## temp test after training 199 | with torch.no_grad(): 200 | gen.eval() #need to be eval mode since feeding one single sample to batchnorm layer 201 | fake = gen(fixed_noise).reshape(3, 8) 202 | fake = (fake+1)/2*(max-min)+min 203 | fake_in_right_scale = (fake * std) + mean 204 | np.savetxt("result/result.csv", fake_in_right_scale, delimiter=",") 205 | 206 | if opt.save_model: 207 | print('model saving to: model/generater.pt') 208 | torch.save(gen.state_dict(), 'model/generater.pt') 209 | else: 210 | with torch.no_grad(): 211 | # load model and DLV with start time-series 212 | generator = Generator(input_size).to(device) 213 | generator.load_state_dict(torch.load('model/generater.pt')) 214 | generator.eval() 215 | test_dlv = np.loadtxt(open(opt.dlv_path, "rb"), delimiter=",") 216 | test_dlv= Z_Score_NormalizeData(test_dlv) 217 | test_dlv = NormalizeData(test_dlv) 218 | print('start with testing dlv:' +opt.dlv_path) 219 | if opt.recursive: 220 | print('start recursively testing') 221 | result = test_dlv 222 | for i in range(opt.recursive_length): 223 | gaussian_noise = np.random.normal(0, 0.3, 24).reshape(1,24) #add gaussian noise 224 | if torch.is_tensor(result): 225 | result = result.numpy() 226 | result = result.reshape(1,24) + gaussian_noise 227 | result = result.astype(float) 228 | tensor_x = torch.Tensor(result) 229 | result = generator(tensor_x).reshape(3, 8) 230 | fake = (result+1)/2*(max-min)+min 231 | fake_in_right_scale = (fake+1)/2*(max-min)+min 232 | filename = 'result/result' + str(i+1) + '.csv' # 1 indexing 233 | print('result save to:'+filename) 234 | np.savetxt(filename, fake_in_right_scale, delimiter=",") 235 | else: 236 | print('start testing single dlv') 237 | tensor_x = torch.Tensor(test_dlv) 238 | result = generator(tensor_x).reshape(3, 8) 239 | fake = (result+1)/2*(max-min)+min 240 | fake_in_right_scale = (fake+1)/2*(max-min)+min 241 | print('result save to: result/result.csv') 242 | np.savetxt("result/result.csv", fake_in_right_scale, delimiter=",") 243 | 244 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Deep Hedging: Learning to Simulate Equity Option Markets 2 | 3 | Welcome to our paper replicate project- [Deep Hedging: Learning to Simulate Equity Option Markets](https://arxiv.org/pdf/1911.01700.pdf) by Song Luo and Yunshu Zhang. 4 | ### **Note:** If you have trouble reading any image below, please refresh the page and use GitHub Default Light as appearance. 5 | This paper is divided into seven parts; they are: 6 | 7 | - Description fo the Problem 8 | - Shortcoming of the Eisting Methods 9 | - Exploratory Data Analysis 10 | - GAN 11 | - Train and Test Model 12 | - Evaluation 13 | - Existing Problem 14 | 15 | ### **Description of the Problem** 16 | 17 | There is growing interest in applying reinforcement learning techniques to the problem of managing a portfolio of derivatives. This involves not only the underlying assets but also the available exchange-traded options. Hence, in order to train an options trading model, we need more time-series data that includes option prices. The reason why the simulator is a hot topic today. 18 | 19 | - The amount of useful real-life data available is limited. This motivates the need for a realistic simulator. 20 | - This paper constructs realistic equity option market simulators based on generative adversarial networks. 21 | - This is the first time that GANs can be applied to the task of generating multivariate financial time series. 22 | 23 | ### **Shortcoming of the Existing Methods** 24 | 25 | Lack of option data is already a long-term issue. But none of the models have been used in this area. 26 | 27 | - **Classical derivative pricing model** also require generators like GANs, but these are **not realistic**. They typically limited to a small number of driving factors. 28 | - **PCA** focus on only **implied volatility data**. 29 | - **Risk-neutral market model** focus on ensuring the martingale property **rather than realistic**. 30 | - **GANs** have been used to create/generate realistic synthetic time series for **asset prices**. 31 | 32 | As we notices, none of them focusing on the realistic. Although GANs could generate realistic synthetic, only apply on asset prices. Neural networks has not been applied to option market generation yet. 33 | 34 | ### **Exploratory Data Analysis** 35 | 36 | We are using the option data from SpiderRock. And we are generating option data of SPX weekly calls from January, February, March, June, and July 2020. 37 | 38 | Note: The data is not provided here, if needed, please contact (@Songloading and @jyszhang2020). After put the data into the data/zip folder, then using the below to unpack the zip files into txt file. 39 | 40 | ```shellscript 41 | #!./src 42 | python ./unzip.py 43 | ``` 44 | 45 | ##### Data 46 | 47 | According to the dummy data, it contains 88 fields , including every option print along with quote, surface, and so on at print time. Below is the head of the dataset. 48 | 49 | | okey_ts | okey_tk | okey_yr | okey_mn | okey_dy | okey_xx | okey_cp | prtNumber | ticker_ts | ticker_tk | prtExch | prtSize | prtPrice | prtType | prtOrders | prtClusterNum | prtClusterSize | prtVolume | cxlVolume | bidCount | askCount | bidVolume | askVolume | ebid | eask | ebsz | easz | eage | prtSide | prtTimestamp | netTimestamp | timestamp | oBid | oAsk | oBidSz | oAskSz | oBidEx | oAskEx | oBidExSz | oAskExSz | oBidCnt | oAskCnt | uPrc | yrs | rate | sdiv | ddiv | oBid2 | oAsk2 | oBidSz2 | oAskSz2 | uBid | uAsk | xDe | xAxis | prtIv | prtDe | prtGa | prtTh | prtVe | prtRo | calcErr | surfVol | surfOpx | surfAtm | prtProbability | oBidM1 | oAskM1 | uBidM1 | uAskM1 | uPrcM1 | sVolM1 | sOpxM1 | sDivM1 | sErrM1 | pnlM1 | pnlM1Err | oBidM10 | oAskM10 | uBidM10 | uAskM10 | uPrcM10 | sVolM10 | sOpxM10 | sDivM10 | sErrM10 | pnlM10 | pnlM10Err | 50 | | ------- | ------- | ------- | ------- | ------- | ------- | ------- | ---------- | --------- | --------- | ------- | ------- | -------- | ------- | --------- | ------------- | -------------- | --------- | --------- | -------- | -------- | --------- | --------- | ---- | ---- | ---- | ---- | ---- | ------- | ------------ | ------------ | --------- | ---- | ---- | ------ | ------ | ------ | ------ | -------- | -------- | ------- | ------- | ---------- | ------ | ------ | ------ | ---- | ----- | ----- | ------- | ------- | ---------- | ---------- | ------ | ------ | ------ | ----- | ------ | ------- | ------ | ------ | ------- | ------- | ------- | ------- | -------------- | ------ | ------ | ---------- | ---------- | ---------- | ------ | ------ | ------ | ------ | ------ | -------- | ------- | ------- | ---------- | ---------- | ---------- | ------- | ------- | ------- | ------- | ------ | --------- | 51 | | NMS | SPXW | 2020 | 2 | 10 | 3355 | Call | 1.1014E+18 | CBOE | SPX | CBOE | 25 | 6.2 | 73 | 0 | 1 | 25 | 25 | 0 | 0 | 0 | 0 | 0 | 6 | 6.4 | 39 | 4 | -1 | Mid | 1.5811E+18 | 1.5811E+18 | 00:03.4 | 6 | 6.4 | 39 | 4 | CBOE | CBOE | 39 | 4 | 1 | 1 | 3344.61304 | 0.0086 | 0.0182 | 0.0477 | 0 | 0 | 0 | 0 | 0 | 3344.48804 | 3344.73804 | 0.1534 | 0.3308 | 0.0882 | 0.342 | 0.0134 | -2.4852 | 1.1365 | 0.0975 | None | 0.0893 | 6.3188 | 0.0957 | 0 | 5.7 | 6.1 | 3343.23804 | 3343.48804 | 3343.24304 | 0.0894 | 5.8712 | 0.0483 | None | 0.1398 | No | 5.8 | 6.2 | 3343.48804 | 3343.73804 | 3343.73304 | 0.0893 | 6.0421 | 0.0458 | None | 0.143 | No | 52 | 53 | We find that these 10 fields are extremely useful for us: 54 | 55 | - okey_tk: Option symbol 56 | - okey_yr: Option expiration year 57 | - okey_mn: Option expiration month 58 | - okey_dy: Option expiration day 59 | - okey_xx: Option strike 60 | - okey_cp: Option call 61 | - prtlv: Print implied vol 62 | - prtGa: Print gamma 63 | - prtTh: Print theta 64 | - surfOpx: SR surface price 65 | 66 | ```python 67 | EQT = pd.DataFrame(data) 68 | df = EQT[['okey_tk', 69 | 'okey_yr', 'okey_mn', 'okey_dy', 70 | 'okey_xx', 71 | 'okey_cp', 72 | 'prtSize', 'prtPrice', 73 | 'prtIv', 74 | 'prtGa', 'prtTh', 'surfOpx']] 75 | ``` 76 | 77 | Then based on the expiration date, we calculating the maturity. 78 | 79 | ```python 80 | df['okey_ymd'] = pd.to_datetime(df['okey_yr'].astype(str) + '/' 81 | + df['okey_mn'].astype(str) 82 | + '/' + df['okey_dy'].astype(str)) 83 | df['okey_maturity'] = df['okey_ymd'] - np.datetime64(date) 84 | df['okey_maturity'] = df['okey_maturity'].dt.days 85 | ``` 86 | 87 | ##### Choosing Strike and Maturity 88 | 89 | Since not all the strikes and maturity are evenly distributed, and we want to avoid all the 0 entry for our matrix. 90 | 91 | ![img](https://lh4.googleusercontent.com/a7T_IXfjw4pNunlvus34cB8lolUQZHcwUsjdLVXpaiDdGsbPDnCx-sM5a10SMqThK7qm1e-LbYHYMrDef9Uxr8UeVpRdsA38gWi34hZN7v-QgvmYTPaeQxxUZvKwkd2dlplrFLHX-iM) 92 | 93 | Aftering plotting strike vs maturity, we decided use this set of K and M. 94 | 95 | **K = [3230, 3240, 3250, 3260, 3270, 3280, 3290, 3300]** 96 | 97 | **M = [20, 50, 71, 106]** 98 | 99 | We denote Nk as strike K's dimension; Nm as maturity M's dimentsion. 100 | 101 | ##### Discrete Local Volatility (DLV) 102 | 103 | ###### What is DLV 104 | 105 | Discrete Local Volatility (DLV) also stand for discrete “Backward Local Volatility” which is a discrete version of [Dupire’s Local Volatility](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.320.5063&rep=rep1&type=pdf). . DLV converges to the proper Dupire models as the strike and maturity grid increases in density, and therefore retains its intuitive features. 106 | 107 | ###### Why DLV 108 | 109 | Option prices are subject to strict ordering constraints because of no-arbitrage consideration. For example, since the call option payoff is a non-increasing function of strike, the option price must also be non-increasing. The violation of this rule would constitute an arbitrage opportunity. Because of this, it is necessary to convert plain data into DLV $N_k * N_m$ dimension. 110 | 111 | ###### How to Compute DLV 112 | 113 | Regarding how to compute DLV, here is the formular. 114 | 115 | ![img](https://lh4.googleusercontent.com/LzdZwHFXIdidXV8XM8bYY6aXMKCm5fWADE3REX0a_yIXQBtRk20AzWMRtSfWkRz5r1NzLWFm3PYuPRn-JL8hoMcXvSaT8t_EZyf2-QQBjWRkI_BJcLhnHODV0-KhBSLw1Rtll6ZBtDo) 116 | 117 | Since not all of the date has contains the specific strike set and maturity set, we decide to choose the closest strike price or maturity. 118 | 119 | ```python 120 | import sys 121 | def closest(target, lst): 122 | diff = sys.maxsize 123 | sol = 0; 124 | for i in lst: 125 | temp = abs(i - target) 126 | if (temp < diff): 127 | diff = temp; 128 | sol = i; 129 | return sol; 130 | ``` 131 | 132 | **Maturities** (![img](https://latex.codecogs.com/png.latex?%5Cinline%20d_%7Bt%7D)): 133 | 134 | We define 135 | 136 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20d_%7Bt+j%7D%5E+%20%3A%3D%20t_%7Bj+1%7D-t_%7Bj%7D) 137 | 138 | and 139 | 140 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20d_%7Bt+j%7D%5E-%20%3A%3D%20t_%7Bj%7D-t_%7Bj-1%7D) 141 | 142 | ```python 143 | def tj_func(t): 144 | tj = [] 145 | # calculating the time difference 146 | for i in range(len(t) - 1): 147 | tj.append(t[i + 1] - t[i]) 148 | return np.asarray(tj) 149 | ``` 150 | 151 | **Strikes** (![img](https://latex.codecogs.com/png.latex?%5Cinline%20k_%7Bj%7D%5E%7Bi%7D)): 152 | 153 | We refer to the nj strikes of the jth maturity as (![img](https://latex.codecogs.com/png.latex?%5Cinline%20k_%7Bj%7D%3D%28k_%7Bj%7D%5E%7B-1%7D%2Ck_%7B0%7D%5E%7Bj%7D%2C...%2Ck_%7Bj%7D%5E%7Bn_%7Bj%7D%7D%29). 154 | 155 | Because of requiring of increasing strikes, an practical remedy is “Jordinson scaling”, which to scale the process by its growth rate,or, equivalently, by providing a widening grid for the process. We denote this as ![img](https://latex.codecogs.com/png.latex?%5Cinline%20k_%7Bj%7D%5E%7Bi%7D). 156 | 157 | ```python 158 | def kij_func(t, s, spxw_call_clean): 159 | kij = [] 160 | # k_j represent the strikes at jth maturity 161 | for j in t: 162 | # kj represent the strikes at jth time 163 | kj = [] 164 | # finding the closest maturity/strike if no particular data 165 | t_temp = spxw_call_clean['okey_maturity'].unique() 166 | j_temp = closest(j, t_temp); 167 | iv = spxw_call_clean[(spxw_call_clean['okey_maturity'] == j_temp)]['prtIv'].mean() 168 | n = len(s) 169 | # k_j^i represent the ith strike at jth maturity 170 | for i in range(n): 171 | kj.append(np.round(np.exp((3 * ((2 *(i + 1) - (n - 1)) / (n + 1)) * iv * np.sqrt(j)) - 0.5 * iv *iv * j), 2)) 172 | kij.append(kj) 173 | return np.asarray(kij) 174 | ``` 175 | 176 | Both ![img](https://latex.codecogs.com/png.latex?%5Cinline%20%5CGamma_%7Bj%7D%5E%7Bi%7D) and ![img](https://latex.codecogs.com/png.latex?%5Cinline%20b%5CTheta%20_%7Bj%7D%5E%7Bi%7D) are define in the dataset. Although no need to calculate them, we have to put them together. 177 | 178 | ```python 179 | def thetaij_func(t, s, spxw_call_clean): 180 | thetaij = [] 181 | # theta_j represent the theta at jth maturity 182 | for j in t: 183 | thetaj = [] 184 | # finding the closest maturity if no particular data 185 | t_temp = spxw_call_clean['okey_maturity'].unique() 186 | j_temp = closest(j, t_temp); 187 | # theta_j^i represent the ith theta at jth maturity 188 | for i in s: 189 | # finding the closest strike if no particular data 190 | s_temp = np.asarray(spxw_call_clean[(spxw_call_clean['okey_maturity'] == j_temp)]['okey_xx']) 191 | i_temp = closest(i, s_temp) 192 | 193 | thetaj.append(-1 * np.asarray(spxw_call_clean[(spxw_call_clean['okey_maturity'] == j_temp) & (spxw_call_clean['okey_xx'] == i_temp)]['prtTh'])[0]) 194 | thetaij.append(thetaj) 195 | 196 | return np.asarray(thetaij) 197 | ``` 198 | 199 | ```python 200 | def gammaij_func(t, s, spxw_call_clean): 201 | gammaij = [] 202 | # gamma_j represent the gamma at jth maturity 203 | for j in t: 204 | gammaj = [] 205 | # finding the closest maturity if no particular data 206 | t_temp = spxw_call_clean['okey_maturity'].unique() 207 | j_temp = closest(j, t_temp); 208 | # gamma_j^i represent the ith theta at jth maturity 209 | for i in s: 210 | # finding the closest strike if no particular data 211 | s_temp = np.asarray(spxw_call_clean[(spxw_call_clean['okey_maturity'] == j_temp)]['okey_xx']) 212 | i_temp = closest(i, s_temp) 213 | 214 | gammaj.append(np.asarray(spxw_call_clean[(spxw_call_clean['okey_maturity'] == j_temp) & (spxw_call_clean['okey_xx'] == i_temp)]['prtGa'])[0]) 215 | gammaij.append(gammaj) 216 | 217 | return np.asarray(gammaij) 218 | ``` 219 | 220 | Last but not the least, puting all together. 221 | 222 | ```python 223 | def dlv_func(thetaij, gammaij, kij, tj, t, s, spxw_call_clean): 224 | dlvij = [] 225 | for j in range(len(tj)): 226 | dtj = tj[j] 227 | dlvj = [] 228 | for i in range(len(s)): 229 | if gammaij[j][i] != 0 and kij[j][i] != 0: 230 | dlvj.append( 231 | np.sqrt(2 * thetaij[j][i] / (gammaij[j][i] * kij[j][i] * kij[j][i] * dtj)) 232 | ) 233 | else: 234 | dlvj.append(0) 235 | dlvij.append(dlvj) 236 | return np.asarray(dlvij) 237 | ``` 238 | 239 | And here is a head of our example DLV. 240 | 241 | ![img](/Users/joycefeifei/Library/Application Support/typora-user-images/image-20210309011145177.png) 242 | 243 | In order to dive more into this how does the DLV come from, please read through [Discrete Local Volatility for Large Time Steps (Short Version)](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2783409), [Arbitrage-free market models for option prices](http://www.nccr-finrisk.uzh.ch/media/pdf/wp/WP428_D1.pdf). 244 | 245 | All of the above loading data, preprocessing data and computing DLV could be done by running the below script: 246 | 247 | ```shellscript 248 | #!./src 249 | python ./dlv.py 250 | ``` 251 | 252 | And finally export all the DLV csv file. 253 | 254 | ```shellscript 255 | #!./src 256 | python ./export.py 257 | ``` 258 | 259 | ### **GANs Model** 260 | 261 | ##### Problem Formulation 262 | 263 | ###### Compute DLV 264 | 265 | As we illustrate above, compute DLV based on K and M, and denote it as ![img](https://latex.codecogs.com/png.latex?%5Cinline%20%5Csigma_%7Bt%7D). 266 | 267 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20%5Csigma%3D%20%5B%5Csigma_%7Bt%7D%28K%2CM%29%5D_%7B%28K%2CM%29%5Cin%20K%20%5Ctimes%20M%7D%29%5D%2C%20t%20%5Cin%20%5Cmathbb%7BN%7D_%7B0%7D) 268 | 269 | 270 | 271 | ###### Regular Time Series 272 | 273 | Base on the previous sigma function. We could easily generate the plain time-series formula. This formula involved mapping function g, noise Z, and state S. We assume that the historical process will evolves through a conditional model in the time series problem. The mapping function g relates noise and state to the next time step, in such form 274 | 275 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20%5Csigma_%7Bt+1%7D%3Dg%28Z_%7Bt+1%7D%2CS_t%29%2Ct%20%5Cin%20%5Cmathbb%7BN%7D_%7B0%7D) 276 | 277 | where 278 | 279 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20g%3AL%5E%7B2%7D%28%5Cmathbb%7BR%7D%5E%7BN_%7BZ%7D%7D%29%5Ctimes%20L%5E%7B2%7D%28%5Cmathbb%7BR%7D%5E%7BN_%7BS%7D%7D%29%5Crightarrow%20L%5E%7B2%7D%28%5Cmathbb%7BR%7D%5E%7BN_%7BK%7D%5Ctimes%20N_%7BM%7D%7D%29) 280 | 281 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20Z_%7Bt+1%7D%5Csim%20N%280%2CI%29) 282 | 283 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20S_%7Bt%2C%5Ctheta%7D%3Df%28%5Csigma_%7Bt%2C%5Ctheta%7D%2C...%2C%5Csigma_%7B0%2C%5Ctheta%7D%29) 284 | 285 | 286 | 287 | It is easy to understand noise Z and state S. But how could we determine what mapping function g. 288 | 289 | ###### Deep Neural Network 290 | 291 | The objective is to approximate the mapping ![img](https://latex.codecogs.com/png.latex?%5Cinline%20Z_%7Bt+1%7D) and ![img](https://latex.codecogs.com/png.latex?%5Cinline%20S_%7Bt%7D) to ![img](https://latex.codecogs.com/png.latex?%5Cinline%20%5Csigma_%7Bt+1%7D) which ideally allows us to generate more data from a given state ![img](https://latex.codecogs.com/png.latex?%5Cinline%20S_%7Bt%7D).Then we could represent this mapping through a deep neural network. 292 | 293 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20%5Ctilde%7B%5Csigma%7D_%7Bt+1%2C%5Ctheta%7D%3Dg_%7B%5Ctheta%7D%28Z_%7Bt+1%7D%2C%5Ctilde%7BS%7D_%7Bt%2C%5Ctheta%7D%29) 294 | 295 | where 296 | 297 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20g%3AL%5E%7B2%7D%28%5Cmathbb%7BR%7D%5E%7BN_%7BZ%7D%7D%29%5Ctimes%20L%5E%7B2%7D%28%5Cmathbb%7BR%7D%5E%7BN_%7BS%7D%7D%29%5Ctimes%20%5CTheta%20%5Crightarrow%20L%5E%7B2%7D%28%5Cmathbb%7BR%7D%5E%7BN_%7BK%7D%5Ctimes%20N_%7BM%7D%7D%29) 298 | 299 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20Z_%7Bt+1%7D%5Csim%20N%280%2CI%29) 300 | 301 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20%5Ctilde%7BS%7D_%7Bt%2C%5Ctheta%7D%3Df%28%5Ctilde%7B%5Csigma%7D_%7Bt%2C%5Ctheta%7D%2C...%2C%5Ctilde%7B%5Csigma%7D_%7B0%2C%5Ctheta%7D%29) 302 | 303 | It is adding ![img](https://latex.codecogs.com/png.latex?%5Cinline%20g_%7B%5Ctheta%7D) as a mapping that relates noise and state to the next time step. ![img](https://latex.codecogs.com/png.latex?%5Cinline%20%5Ctheta) is a nn parameters. 304 | 305 | The optimal outcome is to approximate a parameter vector ![img](https://latex.codecogs.com/png.latex?%5Cinline%20%5Ctheta%20_%7BML%7D) inherit the same dynamics in terms of distributional and dependence properties. 306 | 307 | 308 | 309 | ##### Overview of GAN 310 | 311 | GAN refers to Generative Adversarial Networks, which has two sets of networks: the generator and the discriminator. The idea is that the generator tries to generate result that seems to be from real domain while the discriminator recieves both the generator-generated result and real data and gives a probability that the given input is from the real domain. The goal probability for discriminator is 0.5: the discriminator cannot tell the input is real or fake. To understand this better, let's take a look at GAN's loss function: 312 | 313 | ![img](https://latex.codecogs.com/gif.latex?min_%7BG%7Dmax_%7BD%7DV%28D%2CG%29%20%3D%20%5Cmathbb%7BE%7D_%7B_%7Bx%7D%7D%5Blog%28D%28x%29%29%5D%20+%20%5Cmathbb%7BE%7D_%7B_%7Bz%7D%7D%5Blog%281%20-%20D%28G%28z%29%29%29%5D) 314 | 315 | where: 316 | - ![img](https://latex.codecogs.com/gif.latex?D%28x%29) is the discriminator's estimate of the probability that real data instance x is from real domain, 317 | - ![img](https://latex.codecogs.com/gif.latex?E_%7Bx%7D) is the expected value over all real data instances, 318 | - ![img](https://latex.codecogs.com/gif.latex?G%28z%29) is the generator-generated result, 319 | - ![img](https://latex.codecogs.com/gif.latex?D%28G%28z%29%29) is the discriminator's estimate of the probability that a fake instance is real, and 320 | - ![img](https://latex.codecogs.com/gif.latex?E_%7Bz%7D) is the expected value over all random inputs to the generator. 321 | 322 | The loss functions for both networks are the same except that we want to minimize it for generater and vice versa for discriminator. This is where the term "advsersarial" comes from. GAN has been proven to be effective at generating fake images and image style transfering. In our case, we are going to use GAN to generate simulated DLVs based on the real DLVs, i.e 323 | ![img](https://latex.codecogs.com/png.latex?%5Cinline%20%5Csigma_%7Bt+1%7D%3Dg%28Z_%7Bt+1%7D%2CS_t%29%2Ct%20%5Cin%20%5Cmathbb%7BN%7D_%7B0%7D) 324 | 325 | ##### Define the architecture 326 | The architecture of GAN we used is very similar to the one from https://github.com/eriklindernoren/PyTorch-GAN. Both the generator and the discriminator recieve the input DLV with size of 3*8 = 24. The last layer of the generator is a tanh activation layer, which we will talk about in the next section while the one for the discriminator is sigmoid, which maps the values from linear layer to the range from 0 to 1. 327 | 328 | ```python 329 | Generator( 330 | (model): Sequential( 331 | (0): Linear(in_features=24, out_features=128, bias=True) 332 | (1): LeakyReLU(negative_slope=0.2, inplace=True) 333 | (2): Linear(in_features=128, out_features=256, bias=True) 334 | (3): BatchNorm1d(256, eps=0.8, momentum=0.1, affine=True, track_running_stats=True) 335 | (4): LeakyReLU(negative_slope=0.2, inplace=True) 336 | (5): Linear(in_features=256, out_features=512, bias=True) 337 | (6): BatchNorm1d(512, eps=0.8, momentum=0.1, affine=True, track_running_stats=True) 338 | (7): LeakyReLU(negative_slope=0.2, inplace=True) 339 | (8): Linear(in_features=512, out_features=1024, bias=True) 340 | (9): BatchNorm1d(1024, eps=0.8, momentum=0.1, affine=True, track_running_stats=True) 341 | (10): LeakyReLU(negative_slope=0.2, inplace=True) 342 | (11): Linear(in_features=1024, out_features=24, bias=True) 343 | (12): Tanh() 344 | ) 345 | ) 346 | 347 | Discriminator( 348 | (model): Sequential( 349 | (0): Linear(in_features=24, out_features=512, bias=True) 350 | (1): LeakyReLU(negative_slope=0.2, inplace=True) 351 | (2): Linear(in_features=512, out_features=256, bias=True) 352 | (3): LeakyReLU(negative_slope=0.2, inplace=True) 353 | (4): Linear(in_features=256, out_features=1, bias=True) 354 | (5): Sigmoid() 355 | ) 356 | ) 357 | ``` 358 | 359 | ##### Normalize the Data 360 | As for training purpose, we want to normalize the data before fitting to the model. Specific reason can be found here: https://stackoverflow.com/questions/4674623/why-do-we-have-to-normalize-the-input-for-an-artificial-neural-network. However, our data is not normaly distributed, which can be seen from the histogram below, and thus we use Z-score normalization. 361 | ![img](https://drive.google.com/uc?export=view&id=1N6l-pm-nzNhLXNue5T_GqE3sn2TkcHq9) 362 | 363 | As mentioned in the previous section, we use tanh as our last layer for the generator. This is because as we normalize the input from -1 to 1, we will also want the output from the model in this range. The max&min normalization is used for this purpose. The normalization functions we used are: 364 | ```python 365 | def NormalizeData(data): 366 | return 2*(data - np.min(data)) / (np.max(data) - np.min(data))-1 367 | 368 | def Z_Score_NormalizeData(data): 369 | mean = np.mean(data) 370 | std = np.std(data) 371 | return (data - mean)/std 372 | ``` 373 | 374 | ### Train and Test the model 375 | - Train a model: 376 | ```shellscript 377 | #!./src 378 | python ./Project.py --mode=Train --num_epochs=np --batch_size=bs --learning_rate=lr --save_model=sm 379 | ``` 380 | where you should replace np, bs, lr, and sm by your choice. e.g: 381 | ```shellscript 382 | #!./src 383 | python ./Project.py --mode=Train --num_epochs=100 --batch_size=3 --learning_rate=3e-4 --save_model=True 384 | ``` 385 | If the save_model argument is true, the parameters of your generator should be saved to the model folder. We strongly recommend to set the batch size less than 5 because of the limit of data. 386 | 387 | - Test a model: 388 | ```shellscript 389 | #!./src 390 | python ./Project.py --mode=Test --dlv_path=dp --recursive=r --recursive_length=rl 391 | ``` 392 | where dp, r, and rl are the path to the starting DLV, if you want to test the model recursively (other wise it only generate one single result), and how many steps you want to test the model. e.g: 393 | ```shellscript 394 | #!./src 395 | python ./Project.py --mode=Test --dlv_path='data/spxw_call_dlv_0.csv' --recursive=True --recursive_length=10 396 | ``` 397 | This will test the model starting with DLV of Jan 1st, 2020 and you should expect there are 10 results generated, which represent the simulated DLVs from Jan 2nd, 2020 to Jan 11th, 2020. 398 | 399 | 400 | ### **Evaluation** 401 | The performance of the model is evaluated by three metrics: CEPDF (Cumulative Empirical Probability Density Function), Skew, and Kurtosis. 402 | - CEPDF: 403 | Since we want our simulated results to match the real data, the Empirical Probability Density Function can be used for examing the distributional properties. Due to the random extreme values in the real dataset, we bining the time series data such that each bin contains only 5 DLVs. Then calculate the EPDF for both simulated and real bins. The result is calculated by suming the differences between each bin. 404 | Let ![img](https://latex.codecogs.com/gif.latex?%5Cbeta%20_%7Bh%7D%20%3D%20%5B%7B%5Cbeta%20_%7B1%7D%2C...%5Cbeta%20_%7BK%7D%7D%5D) be the bins 405 | Thus we can find the empirical probability density function for each bin: 406 | ![img](https://latex.codecogs.com/gif.latex?%5Ctilde%7Bf_%7Bh%7D%7D%3A%5Cbeta%20_%7Bh%7D%20%5Crightarrow%20%5Cmathbb%7BR%7D_%7B%5Cgeq%200%7D) 407 | 408 | ![img](https://latex.codecogs.com/gif.latex?%5Ctilde%7Bf_%7Bg%7D%7D%3A%5Cbeta%20_%7Bh%7D%20%5Crightarrow%20%5Cmathbb%7BR%7D_%7B%5Cgeq%200%7D) 409 | 410 | where ![img](https://latex.codecogs.com/gif.latex?%5Ctilde%7Bf_%7Bh%7D%7D) and ![img](https://latex.codecogs.com/gif.latex?%5Ctilde%7Bf_%7Bg%7D%7D) refer to the epdf for real and simulated bins 411 | 412 | Then we can calculate the cumulative difference: 413 | ![img](https://latex.codecogs.com/gif.latex?%5Csum_%7BB%5Cin%5Cbeta%20_%7Bh%7D%7D%5Cleft%20%7C%20%5Ctilde%7Bf%7D_%7Bh%7D%20-%20%5Ctilde%7Bf%7D_%7Bg%7D%20%5Cright%20%7C) 414 | 415 | - Skew & Kurtosis: 416 | Skew and Kurtosis are measurements of the asymmetry and the flatness of the probability distribution. In financial applications higher order moments such as the skewness and kurtosis are of interest as they determine the propensity to generate extremal values. 417 | For calculation, we simply find the Skew and Kurtosis for both the simulated and the real distributions, and subtract them: 418 | 419 | ![img](https://latex.codecogs.com/gif.latex?%5Cfrac%7B1%7D%7BN%7D%5Csum%20%5Cleft%20%5C%7C%20Skew%28a_%7Bh%7D%29%20-%20Skew%28a_%7Bg%7D%29%20%5Cright%20%5C%7C) 420 | 421 | and similarly: 422 | 423 | ![img](https://latex.codecogs.com/gif.latex?%5Cfrac%7B1%7D%7BN%7D%5Csum%20%5Cleft%20%5C%7C%20Kurtosis%28a_%7Bh%7D%29%20-%20Kurtosis%28a_%7Bg%7D%29%20%5Cright%20%5C%7C) 424 | 425 | where: 426 | ![img](https://latex.codecogs.com/gif.latex?a_%7Bh%7D) and ![img](https://latex.codecogs.com/gif.latex?a_%7Bg%7D) are the real and simulated DLVs. 427 | 428 | - Evaluate: 429 | ```shellscript 430 | #!./src 431 | python ./metrics.py 432 | ``` 433 | Note: Please ensure that the number of files in **result** folder is greater than 10 and also please include only the csv files you want to test in the **result** folder. 434 | ### Existing Problem 435 | 436 | - Hardware issue 437 | 438 | Since all of the option data file are pretty large it is hard to loading them or mauniplate them at the same time. It is better to have a virtual machine to handle it or Google Colab. 439 | 440 | - Lack of data 441 | 442 | Right now we are using the data from five months from 2020, which is definitely not enough to run a deep learning model, compare to the original paper that using nine years' data. 443 | 444 | We find that we could acquire more data from the [Wikitter](https://www.wikitter.com/). Hence lacking of data should not be a huge deal in the furture study. 445 | 446 | - 2020 stock market crash 447 | 448 | 2020 is not a good year in terms of the stock market. As we all know, the global stock market crash began on 20 February 2020 and ended on 7 April. And we are using February and March data for training which will cause bias. 449 | 450 | We think that maybe GANs is not robust enough to handle such case. There will be a lot of room for us to develop a more powerful model. 451 | 452 | - Computing DLV issue 453 | 454 | As we showed above, computing DLV requires a lot of work and financial mathematical knowledge. If it is possible, we should get in touch with JP Morgan computer scientist in order to ensure we are calculating it in the correct way. 455 | 456 | --------------------------------------------------------------------------------