Relevant bibliographies by topics / Black Scholes

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Black Scholes'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Black Scholes"

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Sugandha, Agus. "REVIEW PERSAMAAN BLACK-SCHOLES FRAKSIONAL DIMODIFIKASI." Perwira Journal of Science & Engineering 1, no. 2 (2022): 26–37. http://dx.doi.org/10.54199/pjse.v1i2.68.

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Paper ini akan dibahas solusi dari persamaan Black-Scholes fraksional yang merupakan bentuk umum dari persamaan Black-Scholes dan kebaruan penelitian tentang persamaan Black-Scholes yang dimodifikasi. Adapun metode-metode untuk mencari solusi dari persamaan Black Scholes Fraksional sudah banyak ditulis dalam banyak jurnal internasional. Solusi persamaan Black Scholes fraksional dalam hal ini ditinjau dengan pendekatan Kalkulus Fraksional. Dengan pendekatan Kalkulus Fraksional proses penyelesaian dalam mencari solusi persamaan Black Scholes Fraksional menjadi lebih efisien. Beberapa Metode yang
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Rusmaningtyas, Rahmanita Febrianti, Neva Satyahadewi, and Setyo Wira Rizki. "Perbandingan Harga Opsi Saham Tipe Eropa Menggunakan Model Black Scholes dan Black Scholes Fraksional." Jurnal EurekaMatika 9, no. 2 (2022): 177–84. http://dx.doi.org/10.17509/jem.v10i1.44454.

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One of the investment is stocks. Stocks have derivative instrument in the form of stock options. Stocks option is a contract between two parties in the form of the right to sell and buy a stocks at a certain price and time. The method used in this study is the fractional Black Scholes and Black Scholes method with time of maturity fractioned by the Hurst parameter. The purpose od this study is to compare the prices of call and put options using the Black Scholes and Fractional Back Scholes. The data using close price of Apple Inc shares within period between October 1st 2020 until September 30
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Schmitt, Markus. "Black-Scholes-Formel." Controlling 13, no. 6 (2001): 315–18. http://dx.doi.org/10.15358/0935-0381-2001-6-315.

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Sugandha, Agus, Endang Rusyaman, Sukono, and Ema Carnia. "A New Solution to the Fractional Black–Scholes Equation Using the Daftardar-Gejji Method." Mathematics 11, no. 24 (2023): 4887. http://dx.doi.org/10.3390/math11244887.

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The main objective of this study is to determine the existence and uniqueness of solutions to the fractional Black–Scholes equation. The solution to the fractional Black–Scholes equation is expressed as an infinite series of converging Mittag-Leffler functions. The method used to discover the new solution to the fractional Black–Scholes equation was the Daftardar-Geiji method. Additionally, the Picard–Lindelöf theorem was utilized for the existence and uniqueness of its solution. The fractional derivative employed was the Caputo operator. The search for a solution to the fractional Black–Schol
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Mehrdoust, Farshid, Amir Hosein Refahi Sheikhani, Mohammad Mashoof, and Sabahat Hasanzadeh. "Block-pulse operational matrix method for solving fractional Black-Scholes equation." Journal of Economic Studies 44, no. 3 (2017): 489–502. http://dx.doi.org/10.1108/jes-05-2016-0107.

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Purpose The purpose of this paper is to evaluate a European option using the fractional version of the Black-Scholes model. Design/methodology/approach In this paper, the authors employ the block-pulse operational matrix algorithm to approximate the solution of the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Findings The fractional derivative will be described in the Caputo sense in this paper. The authors show the accuracy and computational efficiency of the proposed algorithm through some numerical examples. Originality/value This is th
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Wang, Lujian, Minqing Zhang, and Zhao Liu. "The Progress of Black-Scholes Model and Black-Scholes-Merton Model." BCP Business & Management 38 (March 2, 2023): 3405–10. http://dx.doi.org/10.54691/bcpbm.v38i.4314.

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Black-Scholes (BS) model was first proposed in 1973, which has been modified by Robert Merton as the Black-Scholes-Merton (BSM) model subsequently. Contemporarily, these two models have been widely used and praised by financial scholars as well as employees. Plenty of scholars have tried to verify the accuracy of the and expressed their views on the existing defects in above models. Based on the existing literature, this article first introduces and derives the two models step by step and discusses the basic assumptions for these models. Subsequently, the applications of the two models are dem
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Janowicz, Maciej, and Andrzej Zembrzuski. "Symmetry Properties of Modified Black-Scholes Equation." Metody Ilościowe w Badaniach Ekonomicznych 22, no. 2 (2022): 77–86. http://dx.doi.org/10.22630/mibe.2021.22.2.7.

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This paper concerns the classical and conditional symmetries of the Black-Scholes equation. Modifications of the Black-Scholes equation have also been considered and their maximal algebras of invariance have been found. Examples of creation operators for the Black-Scholes eigenvalue problem have been provided.
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Muhamad Rashif Hilmi, Devi Nurtiyasari, and Angga Syahputra. "Pemanfaatan Skewness dan Kurtosis dalam Menentukan Harga Opsi Beli Asia." Quadratic: Journal of Innovation and Technology in Mathematics and Mathematics Education 2, no. 1 (2022): 7–15. http://dx.doi.org/10.14421/quadratic.2022.021-02.

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Opsi Asia adalah opsi dimana besar perhitungan keuntungannya menggunakan rata-rata harga aset selama periode kontrak. Penentuan harga Opsi Asia yang umum digunakan adalah dengan metode Black-Scholes. Metode Black-Scholes mempunyai beberapa syarat yang harus terpenuhi, salah satunya adalah logaritma dari rata-rata harga aset berdistribusi normal atau nilai skewness dan kurtosis tidak normal. Dalam aplikasinya, sangat sedikit kasus dimana syarat ini terpenuhi . Salah satu solusi dari permasalahan ini adalah memasukkan nilai skewness dan kurtosis kedalam model. Model ini menggunakan ekspansi Gram
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SABRINA, FITRI, DODI DEVIANTO, and FERRA YANUAR. "PENENTUAN HARGA OPSI TIPE EROPA DENGAN MENGGUNAKAN MODEL BLACK SCHOLES FRAKSIONAL." Jurnal Matematika UNAND 9, no. 2 (2020): 154. http://dx.doi.org/10.25077/jmu.9.2.154-161.2020.

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Harga opsi tipe Eropa dapat ditentukan dengan model Black Scholes fraksional dengan waktu jatuh tempo dapat difraksional menggunakan parameter Hurst. Gerak Brown fraksional ini dapat diformulasikan ke dalam persamaan diferensial stokastik untuk menentukan model Black Scholes fraksional. Data harga saham Microsoft Corporation (MC) dari tanggal 1 Oktober 2018 sampai 30 September 2019 dapat dibentuk ke dalam model Black Scholes fraksional. Pada saat harga pelaksanaan saham MC meningkat, harga opsi call tipe Eropa semakin menurun dan untuk harga opsi put tipe Eropa semakin meningkat. Kata Kunci: D
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Özer, H. Ünsal, and Ahmet Duran. "The source of error behavior for the solution of Black–Scholes PDE by finite difference and finite element methods." International Journal of Financial Engineering 05, no. 03 (2018): 1850028. http://dx.doi.org/10.1142/s2424786318500287.

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Black–Scholes partial differential equation (PDE) is one of the most famous equations in mathematical finance and financial industry. In this study, numerical solution analysis is done for Black–Scholes PDE using finite element method with linear approach and finite difference methods. The numerical solutions are compared with Black–Scholes formula for option pricing. The numerical errors are determined for the finite element and finite difference applications to Black–Scholes PDE. We examine the error behavior and find the source of the corresponding errors under various market situations.
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Dissertations / Theses on the topic "Black Scholes"

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Cantaloni, Francesco. "Formula di Black-Scholes comportamentale." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019.

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In questa trattazione verranno descritte alcune espressioni generali di valutazione per le opzioni che estendono i risultati classici di Black-Scholes e Merton all'ambito comportamentale. Dapprima mostreremo come estendere la nozione di agente rappresentativo al caso in cui i partecipanti al mercato siano caratterizzati da una funzione di utilità con avversione al rischio relativa costante ed eterogenea. Dopo aver presentato il teorema di esistenza dell'agente rappresentativo, deriveremo le principali implicazioni in termini di struttura a termine dei tassi di sconto e di valutazione degli str
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del, Campo Daniel, and Fredrik Söderström. "Black & Scholes vs. Marknaden." Thesis, Södertörn University College, School of Business Studies, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:sh:diva-165.

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Chávez, Fuentes Jorge Richard. "El modelo de Black-Scholes." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96422.

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Se presenta el modelo de Black-Scholes, a través del más popular de los contratos financieros, esto es, la opción de compra europea. Se establece la fórmula de valuación martingala para reclamos contingentes en general y se muestra una aplicación de ella mediante la obtención del precio del contrato call. Al final se establece también la ecuación de Black-Scholes, que es una ecuación diferencial parcial no lineal de segundo orden, y que constituye una forma alternativa para la preciación de activos derivados.
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Pavlou, Petro. "KVA in Black Scholes Pricing." Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/30880.

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The post 2007-financial crisis era has led to renewed zeal in quantifying market incompleteness when pricing contingent claims. This quantification exercise is necessary in maintaining a stable and sustainable banking operation and thus the XVAs have emerged as the metrics for market incompleteness. This dissertation focuses solely on the capital valuation adjustment (KVA) and aims to use the definition of KVA as set out by Albanese et al. (2016) in an investigation of different numerical techniques for calculating KVA. A single equity forward is considered first, followed by an equity option
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Lindström, Linnea. "Black-Scholes : En prissättningsmodell för optioner." Thesis, Umeå University, Department of Mathematics and Mathematical Statistics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-35084.

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<p>This paper aims to derive the Black-Scholes equation for readers without advanced knowledge in finance and mathematics. To succeed, this paper contains a theoretical chapter in which concepts such as options, interest rate, differential equations and stochastic variable are explained. This paper also presents the theory of stochastic processes such as the Wiener process and Ito process. In the chapter on the Black-Scholes model the Ito process is used to describe price of shares and with the help of Ito's lemma Black-Scholes equation can be derived. In the paper, assumptions are listed that
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Karlsson, Olle. "The Black-Scholes Equation and Formula." Thesis, Uppsala universitet, Analys och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-200441.

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Durrell, Fernando. "Alternatives to the Black-Scholes model." Master's thesis, University of Cape Town, 2001. http://hdl.handle.net/11427/4881.

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Bibliography: leaves 44-45.<br>In this paper, I consider alternative models to the one posited by Black and Scholes. I consider discontinuous security price movements, non-constant volatility, and models very different from the Black-Scholes model. I found that most of the model prices for the close to at-the-money options are very different from the market prices. In general, the models did poorly in producing similar prices as the market.
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Coelho, Afonso Valente Ricardo de Seabra. "American options and the Black-Scholes Model." Master's thesis, Instituto Superior de Economia e Gestão, 2020. http://hdl.handle.net/10400.5/20735.

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Mestrado em Mathematical Finance<br>Os problemas de apreçamento de opções têm sido um dos principais assuntos de em Matemática Financeira, desde a criação desse conceito nos anos 70. Mais especificamente, as opções americanas são de grande interesse nesta área do conhecimento porque são matematicamente muito mais complexas do que as opções europeias padrão e o modelo de Black-Scholes não fornece, na maioria dos casos, uma fórmula explícita para a determinação do preço deste tipo de opções. Nesta dissertação, mostramos como o estudo de opções americanas conduz à análise de problemas de frontei
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Bucic, Ida. "Heston vs Black Scholes stock price modelling." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-105614.

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In this thesis the Black Scholes and the Heston stock prices are investigated and the models are compared. The Black Scholes model assumes that the volatility is constant, while the Heston model allows stochastic volatility which is more flexible and can perform better with empirical data. Both models are analysed and simulated, and the parameters are estimated based on empirical data of S&amp;P 500. Results are based on simulations and characteristic functions which are presented with figures of probability density functions.
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Andrén, August, and Patrik Hagernäs. "Data-parallel Acceleration of PARSEC Black-Scholes Benchmark." Thesis, KTH, Skolan för informations- och kommunikationsteknik (ICT), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-128607.

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The way programmers has been relying on processor improvements to gain speedup in their applications is no longer applicable in the same fashion. Programmers usually have to parallelize their code to utilize the CPU cores in the system to gain a signicant speedup. To accelerate parallel applications furthermore there are a couple of techniques available. One technique is to vectorize some of the parallel code. Another technique is to move parts of the parallel code to the GPGPU and utilize this very good multithreading unit of the system. The main focus of this report is to accelerate the data
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Books on the topic "Black Scholes"

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Larcher, Gerhard. Die Black-Scholes-Theorie. Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-37376-4.

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Capiński, Marek. The Black-Scholes model. Cambridge University Press, 2013.

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Porak, Anatol. Die Optionspreisformel von Black und Scholes. Gabler Verlag, 1988. http://dx.doi.org/10.1007/978-3-322-89312-3.

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1951-, Levendorskiĭ Serge, ed. Non-Gaussian Merton-Black-Scholes theory. World Scientific, 2002.

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Chriss, Neil. Black-Scholes and beyond: Option pricing models. Irwin, 1997.

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Chriss, Neil. Black-Scholes and beyond: Option pricing models. McGraw-Hill, 1997.

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FINEX, ed. From Black-Scholes to black holes: New frontiers in options. Risk/FINEX, 1992.

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Corhay, Albert. The Black and Scholes theorem: An alternative proof. European Institute for Advanced Studies in Management, 1992.

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Ncube, Mthuli. The Black and Scholes option price as a random variable. Department of Applied Economics, University of Cambridge, 1992.

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Dunphy, Christina. The pricing of options by method of the Black Scholes model. Oxford Brookes University, 1999.

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Book chapters on the topic "Black Scholes"

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Franke, Jürgen, Wolfgang Härdle, and Christian Hafner. "Black-Scholes-Optionsmodell." In Einführung in die Statistik der Finanzmärkte. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-17049-2_6.

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Kythe, Prem K. "Black-Scholes Model." In Elements of Concave Analysis and Applications. Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315202259-12.

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Williams, R. "Black-Scholes model." In Graduate Studies in Mathematics. American Mathematical Society, 2006. http://dx.doi.org/10.1090/gsm/072/04.

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Ziemann, Volker. "Black-Scholes-Differentialgleichung." In Physik und Finanzen. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-36964-3_5.

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Franke, Jürgen, Wolfgang Härdle, and Christian Hafner. "Black-Scholes-Optionsmodell." In Einführung in die Statistik der Finanzmärkte. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-97127-3_6.

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Pascucci, Andrea. "Black-Scholes model." In PDE and Martingale Methods in Option Pricing. Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1781-8_7.

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Behrends, Ehrhard. "Black-Scholes-Formel." In Markovprozesse und stochastische Differentialgleichungen. Springer Fachmedien Wiesbaden, 2012. http://dx.doi.org/10.1007/978-3-658-00988-5_10.

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Maré, Eben. "Black–Scholes PDE." In A Concise Introduction to Financial Derivatives. Chapman and Hall/CRC, 2024. https://doi.org/10.1201/9781032637099-12.

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Michaelides, Panayotis G. "Black-Scholes Formula." In 21 Equations that Shaped the World Economy. Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-76140-9_20.

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Kallianpur, Gopinath, and Rajeeva L. Karandikar. "Black and Scholes Theory." In Introduction to Option Pricing Theory. Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-0511-1_10.

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Conference papers on the topic "Black Scholes"

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Li, Simo. "Empirical Analysis of Convertible Bond Pricing and Arbitrage Based on Black-Scholes Model." In International Conference on Data Science and Engineering. SCITEPRESS - Science and Technology Publications, 2024. http://dx.doi.org/10.5220/0012829300004547.

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K P, Premalatha, Vinoth Kumar V, Thilak Reddy, and Navaneetha Kumar V. "AI-Enhanced Stochastic Volatility Modelling: A Comparative Analysis with Black-Scholes and Binomial Models." In 2024 International Conference on Intelligent & Innovative Practices in Engineering & Management (IIPEM). IEEE, 2024. https://doi.org/10.1109/iipem62726.2024.10925737.

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Li, Zifan, and Zirun Chen. "A Modified Black Scholes Merton Model Based on Student’s t-distribution and GARCH model." In 2024 International Conference on Innovation, Knowledge, and Management (ICIKM). IEEE, 2024. https://doi.org/10.1109/icikm63301.2024.00013.

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Xiang, Sylvia Siyi, and Ray C. C. Cheung. "Enhanced Black-Scholes Option Pricing: Bit-Width Optimization with Automatic Differentiation and Lagrange Multipliers." In TENCON 2024 - 2024 IEEE Region 10 Conference (TENCON). IEEE, 2024. https://doi.org/10.1109/tencon61640.2024.10902678.

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Youness, Saoudi, Smaaine Ouaharahe, Hachimi Hanaa, and El Mokhi Chakib. "Pricing Basket Option in Using the Two-Dimensional Black Scholes Equation and the Monte Carlo Approach." In 2024 10th International Conference on Optimization and Applications (ICOA). IEEE, 2024. http://dx.doi.org/10.1109/icoa62581.2024.10753936.

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Shehi, Enkeleda. "Option Pricing Models: The Evolution of the Black-Scholes-Merton Model." In 10th International Scientific Conference ERAZ - Knowledge Based Sustainable Development. Association of Economists and Managers of the Balkans, Belgrade, Serbia, 2024. https://doi.org/10.31410/eraz.2024.157.

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This paper focuses on the development and impact of the Black- Scholes-Merton (Black-Scholes) model in mathematical finance. It begins with an overview of the Black-Scholes model, including its foundational assumptions, the Black-Scholes equation, and its formula for pricing European options. The paper discusses the model’s significant advantages, such as its ability to estimate market volatility and provide a self-replicating hedging strategy. It also addresses its limitations, including assumptions of constant volatility and perfect market conditions, which often do not align with real-world
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Stoynov, Pavel. "Financial models beyond the classical Black-Scholes." In RENEWABLE ENERGY SOURCES AND TECHNOLOGIES. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5127500.

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JIANG, LISHANG, and XUEMIN REN. "LIMITATIONS AND MODIFICATIONS OF BLACK-SCHOLES MODEL." In Differential Equations & Asymptotic Theory in Mathematical Physics. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702395_0007.

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Rasmussen, Maurice Lee, and Faruk Civan. "Value Assessment Using the Modified Black-Scholes Equation." In SPE Hydrocarbon Economics and Evaluation Symposium. Society of Petroleum Engineers, 2005. http://dx.doi.org/10.2118/94520-ms.

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Filiapuspa, M. H., S. F. Sari, and S. Mardiyati. "Applying Black Scholes method for crop insurance pricing." In PROCEEDINGS OF THE 4TH INTERNATIONAL SYMPOSIUM ON CURRENT PROGRESS IN MATHEMATICS AND SCIENCES (ISCPMS2018). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5132469.

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Reports on the topic "Black Scholes"

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Slavova, Angela, and Nikolay Kyurkchiev. On CNN Model of Black–Scholes Equation with Leland Correction. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2018. http://dx.doi.org/10.7546/crabs.2018.02.03.

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Slavova, Angela, and Nikolay Kyurkchiev. On CNN Model of Black–Scholes Equation with Leland Correction. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2018. http://dx.doi.org/10.7546/grabs2018.2.03.

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Tirapat, Sunti. Risk-based deposit insurance : an application to Thailand. Chulalongkorn University, 2000. https://doi.org/10.58837/chula.res.2000.19.

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This paper investigates the application of option pricing to calculate the premium of deposit insurance in Thailand during 1992-1996 period. In addition to applying the traditional Black-Scholes model, the barrier model of Boyle and Lee (1994) is examined. The barrier model takes the management (owners) action into account: the management (owners) may have strong incentive to increase the volatility of the bank’s assets since this action in crease the value of their equity. As suggested by the stylized evidence, most financial institutions in Thailand were owned by “family” and there was inade
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Baker, Dorothy. Black Content in Schools: A Model of Black Content in a School of Social Work's Curriculum. Portland State University Library, 2000. http://dx.doi.org/10.15760/etd.2098.

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Richardson, Allissa V. Trends in Mobile Journalism: Bearing Witness, Building Movements, and Crafting Counternarratives. Just Tech, Social Science Research Council, 2021. http://dx.doi.org/10.35650/jt.3010.d.2021.

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This field review examines how African American mobile journalism became a model for marginalized people’s political communication across the United States. The review explores how communication scholars’ theories about mobile journalism and media witnessing evolved since 2010 to include ethnocentric investigations of the genre. Additionally, it demonstrates how Black people’s use of the mobile device to document police brutality provided a brilliant, yet fraught, template for modern activism. Finally, it shows how Black mobile journalism created undeniable counternarratives that challenged th
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Hanushek, Eric, and Steven Rivkin. Harming the Best: How Schools Affect the Black-White Achievement Gap. National Bureau of Economic Research, 2008. http://dx.doi.org/10.3386/w14211.

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Berdan, Robert, Terrence Wiley, and Magaly Lavadenz. California Association for Bilingual Education (CABE) Position Statement on Ebonics. Center for Equity for English Learners, 1997. http://dx.doi.org/10.15365/ceel.statement.1997.1.

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In this position statement, the authors write in support of Ebonics (also known as African American Vernacular English, Black English, Black Dialect, and African American Language) as a legitimate language. The linguistic and cultural origins of Ebonics is traced, along with its legitimacy by professional organizations and the courts. CABE asserts that the role of schools and teachers is therefore to build on students’ knowledge of Ebonics rather than replace or eradicate Ebonics as they teach standard English. This position statement has implications for teacher training.
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Darling-Hammond, Sean. Fostering Belonging, Transforming Schools: The Impact of Restorative Practices. Learning Policy Institute, 2023. http://dx.doi.org/10.54300/169.703.

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Across the country, many schools have adopted restorative practices in an effort to improve school climate and student outcomes while reducing exclusionary discipline. Restorative practices are designed to proactively build community, improve relationships, and help students amend harm when conflict occurs. Using 6 years of student survey data and California administrative data, this study examines the use of restorative practices in 485 middle schools and their impact on school and student outcomes. Analyses find that exposure to restorative practices improves students’ academic achievement a
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Patton, Desmond, and Catalina Vallejo. Examining Violence and Black Grief on Social Media: An Interview with Desmond Upton Patton. Just Tech, Social Science Research Council, 2022. http://dx.doi.org/10.35650/jt.3020.d.2022.

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As part of our “What Is Just Tech?” series, we invited several social researchers—scholars, practitioners, artists, and activists—to respond to a simple yet fundamental question: “What is just technology?” This interview was conducted by Just Tech program officer Catalina Vallejo, who spoke with Desmond Upton Patton, Professor of Social Work at Columbia University and Just Tech Advisory Board member. Patton (he/him) studies how gang-involved youth conceptualize threats on social media and the extent to which social media may shape or facilitate youth and gang violence. He is the founding direc
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10

Eriksson, Katherine. Access to Schooling and the Black-White Incarceration Gap in the Early 20th Century US South: Evidence from Rosenwald Schools. National Bureau of Economic Research, 2015. http://dx.doi.org/10.3386/w21727.

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