{"id":"W2490025961","doi":"10.1007/978-3-319-32408-1_4","title":"Change of Time Method (CTM) and Black-Scholes Formula","year":2016,"lang":"en","type":"book-chapter","venue":"SpringerBriefs in mathematics","topic":"Stochastic processes and financial applications","field":"Economics, Econometrics and Finance","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Black–Scholes model; Martingale (probability theory); Mathematics; Mathematical proof; Cash flow; Mathematical economics; Applied mathematics; Valuation of options; Log-normal distribution; Econometrics; Economics; Finance; 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":[0.001794111,0.0008425158,0.001059745,0.001530093,0.0005670181,0.001852099,0.001590388,0.00156232,0.007733866],"category_scores_gemma":[0.005710779,0.0003747871,0.001171514,0.001671432,0.002218129,0.003462864,0.001192266,0.004275047,0.00172228],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001198974,"about_ca_system_score_gemma":0.0009085256,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001771488,"about_ca_topic_score_gemma":0.001168257,"domain_scores_codex":[0.9992268,0.0002861537,0.00003436061,0.0001294691,0.0002791267,0.00004417887],"domain_scores_gemma":[0.9988557,0.0006110029,0.0001322552,0.0001550903,0.0001731461,0.00007279355],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001037803,0.000009593935,0.00008796534,0.00005147254,0.000008726552,0.0000252449,0.00003217523,0.003505285,0.0003945434,0.9746642,0.003308211,0.01790215],"study_design_scores_gemma":[0.00001320039,0.00001711202,0.0002551443,0.00002860792,0.00001237826,0.00008743401,0.00001082026,0.07715566,0.000473634,0.9016373,0.02028783,0.00002095475],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.009458343,0.01405502,0.9359864,0.003158231,0.001735389,0.00004694009,0.0002599384,0.0002984313,0.03500128],"genre_scores_gemma":[0.3485859,0.01712693,0.5081778,0.001257853,0.004665049,0.0002880667,0.000560157,0.001625018,0.1177131],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.007733866,"threshold_uncertainty_score":0.02587229,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04646714745653256,"score_gpt":0.2504107851570359,"score_spread":0.2039436377005034,"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."}}