{"id":"W2580676852","doi":"","title":"Polynomial chaos solution to the Black Scholes equation with a random volatility","year":2012,"lang":"en","type":"article","venue":"ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH","topic":"Probabilistic and Robust Engineering Design","field":"Decision Sciences","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Applied mathematics; Volatility (finance); Black–Scholes model; Orthonormal basis; Polynomial chaos; SABR volatility model; Polynomial; Implied volatility; Mathematical analysis; Econometrics; Monte Carlo method; Physics; Statistics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006021162,0.0003561458,0.0005841311,0.0003680498,0.0003719529,0.0008353593,0.0004335286,0.0008413975,0.000977308],"category_scores_gemma":[0.003124961,0.0002000005,0.0006145858,0.0004830426,0.0008089134,0.001408681,0.0007078922,0.0009534291,0.0001226345],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004327336,"about_ca_system_score_gemma":0.0008466209,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002335067,"about_ca_topic_score_gemma":0.0009073137,"domain_scores_codex":[0.9996625,0.0001027242,0.0000149274,0.00004809271,0.0001257409,0.00004606907],"domain_scores_gemma":[0.9993908,0.0003230241,0.000114886,0.00003869934,0.0000934854,0.00003909488],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00007535415,0.0000226421,0.001067597,0.00007110233,0.00003171126,0.0002366313,0.00009723274,0.5440424,0.007462576,0.4387548,0.0004161055,0.007721921],"study_design_scores_gemma":[0.000009227684,0.00001578655,0.0001285248,0.000002361065,0.000004329067,0.00002913838,0.000007141211,0.9762058,0.0005824753,0.02277895,0.0002286922,0.000007579028],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1525939,0.0005346651,0.841435,0.0005642697,0.00008316366,0.00002665294,0.00005690317,0.00009000467,0.004615387],"genre_scores_gemma":[0.9569833,0.0005161875,0.03771846,0.00005449829,0.00005505238,0.00003622754,0.00005800953,0.00002854021,0.004549816],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002335067,"threshold_uncertainty_score":0.004642963,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2196513406010074,"score_gpt":0.4089540125590754,"score_spread":0.189302671958068,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}