Barrier Option Pricing by Branching Processes Georgi K. Mitov ∗ Svetlozar T. Rachev † Young Shin Kim Frank J. Fabozzi Georgi K. Mitov Institute of Mathematics and Informatics, Bulgarian Academy of Science ”Acad. G. Bonchev” Str., Bl. 8, 1113, Sofia, Bulgaria and Senior Quant, FinAnalytica Inc. E-mail: georgi.mitov@finanalytica.com Svetlozar T. Rachev Chair-Professor, Chair of Statistics, Econometrics and Mathematical Finance, School of Economics and Business Engineering, University of Karlsruhe and KIT, Kollegium am Schloss, Bau II, 20.12, R210, Postfach 6980, D-76128, Karlsruhe, Germany and Department of Statistics and Applied Probability, University of California, Santa Barbara, and Chief-Scientist, FinAnalytica Inc. E-mail: rachev@statistik.uni-karlsruhe.de Young Shin Kim Department of Statistics, Econometrics and Mathematical Finance, School of Economics and Business Engineering, University of Karlsruhe and KIT Kollegium am Schloss, Bau II, 20.12, R210, Postfach 6980, D-76128, Karlsruhe, Germany E-mail: aaron.kim@statistik.uni-karlsruhe.de Frank J. Fabozzi Professor in the Practice of Finance, Yale School of Management, 135 Prospect Street, Box 208200, New Haven, CT 06520-8200, USA E-mail: frank.fabozzi@yale.edu * Georgi Mitov is supported by the German Academic Exchange Service (DAAD) and in part by NSF- Bulgaria (grant VU-MI-105/20-05). † Svetlozar Rachev gratefully acknowledges research support by grants from Division of Mathematical, Life and Physical Sciences, College of Letters and Science, University of California, Santa Barbara, the Deutschen Forschungsgemeinschaft, and the Deutscher Akademischer Austausch Dienst. 1