Relevant bibliographies by topics / Black-Scholes PDE

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

Academic literature on the topic 'Black-Scholes PDE'

Author: Grafiati
Published: 4 June 2021
Last updated: 26 April 2022

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Journal articles on the topic "Black-Scholes PDE"

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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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RIGATOS, GERASIMOS G. "BOUNDARY CONTROL OF THE BLACK–SCHOLES PDE FOR OPTION DYNAMICS STABILIZATION." Annals of Financial Economics 11, no. 02 (2016): 1650009. http://dx.doi.org/10.1142/s2010495216500093.

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The objective of the paper is to develop a boundary control method for the Black–Scholes PDE which describes option dynamics. It is shown that the procedure for numerical solution of Black–Scholes PDE results into a set of nonlinear ordinary differential equations (ODEs) and an associated state equations model. For the local subsystems, into which a Black–Scholes PDE is decomposed, it becomes possible to apply boundary-based feedback control. The controller design proceeds by showing that the state-space model of the Black–Scholes PDE stands for a differentially flat system. Next, for each sub
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Rigatos, G., and P. Siano. "Feedback control of the multi-asset Black–Scholes PDE using differential flatness theory." International Journal of Financial Engineering 03, no. 02 (2016): 1650008. http://dx.doi.org/10.1142/s2424786316500080.

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A method for feedback control of the multi-asset Black–Scholes PDE is developed. By applying semi-discretization and a finite differences scheme the multi-asset Black–Scholes PDE is transformed into a state-space model consisting of ordinary nonlinear differential equations. For this set of differential equations it is shown that differential flatness properties hold. This enables to solve the associated control problem and to succeed stabilization of the options’ dynamics. It is shown that the previous procedure results into a set of nonlinear ordinary differential equations (ODEs) and to an
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Hu, Jinhao, and Siqing Gan. "High order method for Black–Scholes PDE." Computers & Mathematics with Applications 75, no. 7 (2018): 2259–70. http://dx.doi.org/10.1016/j.camwa.2017.12.002.

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El-Khatib, Youssef. "A Homotopy Analysis Method for the Option Pricing PDE in Post-Crash Markets." Mathematical Economics Letters 2, no. 3-4 (2014): 45–50. http://dx.doi.org/10.1515/mel-2013-0014.

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AbstractWe investigate a solution for the option pricing partial differential equation (PDE) in a market suffering from a financial crisis. The post-crash model assumes that the volatility is stochastic. It is an extension of the famous Black and Scholes model. Therefore, the option pricing PDE for the crisis model is a generalization of the Black and Scholes PDE. However, to the best knowledge, it does not have a closed form solution for the general case. In this paper, we provide a solution for the pricing PDE of a European option during financial crisis using the homotopy analysis method.
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Ogunyebi, SN, SE Fadugba, TO Ogunlade, et al. "Direct Solution of the Black-Scholes PDE Models with Non-Integer Order." Journal of Physics: Conference Series 2199, no. 1 (2022): 012003. http://dx.doi.org/10.1088/1742-6596/2199/1/012003.

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Abstract This paper presents a direct solution of Black-Scholes PDE models with non-integer order via the non-integer iterative method. The Black-Scholes PDE models of non-integer order became popular and accepted globally by option traders for the valuation of financial derivatives over the period of time and the study of its numerical approaches has a wide range of applications in the real world.. The performance of the method has been confirmed and measured.
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Wilmott, Paul. "The two best ways to derive the Black–Scholes PDE." China Finance Review International 10, no. 2 (2019): 168–74. http://dx.doi.org/10.1108/cfri-12-2018-0153.

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Purpose The purpose of this paper is to explain the Black–Scholes model with minimal technical requirements and to illustrate its impact from a business perspective. Design/methodology/approach The paper employs simple accounting concepts and an argument part based on business need. Findings The Black–Scholes partial differential equation can be derived in many ways, some easy to understand, some hard, some useful and others not. The two methods in this paper are extremely insightful. Originality/value The paper takes a big-picture view of derivatives valuation. As such, it is a simple accompa
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Han, Yuecai, and Chunyang Liu. "Asian Option Pricing under an Uncertain Volatility Model." Mathematical Problems in Engineering 2020 (April 21, 2020): 1–10. http://dx.doi.org/10.1155/2020/4758052.

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In this paper, we study the asymptotic behavior of Asian option prices in the worst-case scenario under an uncertain volatility model. We derive a procedure to approximate Asian option prices with a small volatility interval. By imposing additional conditions on the boundary condition and splitting the obtained Black–Scholes–Barenblatt equation into two Black–Scholes-like equations, we obtain an approximation method to solve a fully nonlinear PDE.
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Hossan, Md Shorif, Md Shafiqul Islam, and Md Kamrujjaman. "Efficient Numerical Schemes for Computations of European Options with Transaction Costs." European Journal of Mathematical Analysis 2 (February 17, 2022): 9. http://dx.doi.org/10.28924/ada/ma.2.9.

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This paper aims to find numerical solutions of the non-linear Black-Scholes partial differential equation (PDE), which often appears in financial markets, for European option pricing in the appearance of the transaction costs. Here we exploit the transformations for the computational purpose of a non-linear Black-Scholes PDE to modify as a non-linear parabolic type PDE with reliable initial and boundary conditions for call and put options. Several schemes are derived rigorously using the finite volume method (FVM) and finite difference method (FDM), which is the novelty of this paper. Stabilit
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Prabakaran, Sellamuthu. "CONSTRUCTION OF THE BLACK-SCHOLES PDE WITH JUMP-DIFFUSION MODEL." Far East Journal of Mathematical Sciences (FJMS) 110, no. 1 (2019): 131–63. http://dx.doi.org/10.17654/ms110010131.

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Dissertations / Theses on the topic "Black-Scholes PDE"

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Yang, Yuankai. "Pricing American and European options under the binomial tree model and its Black-Scholes limit model." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-68264.

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We consider the N step binomial tree model of stocks. Call options and put options of European and American type are computed explicitly. With appropriate scaling in time and jumps,  convergence of the stock prices and the option prices are obtained as N-> infinite. The obtained convergence is the Black-Scholes model and, for the particular case of European call option, the Black-Scholes formula is obtained. Furthermore, the Black-Scholes partial differential equation is obtained as a limit from the N step binomial tree model. Pricing of American put option under the Black-Scholes model is
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Pagliarani, Stefano. "Metodi perturbativi per E.D.P e applicazioni in finanza matematica." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amslaurea.unibo.it/1392/.

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In questa tesi si discute di alcuni modelli di pricing per opzioni di tipo europeo e di opportuni metodi perturbativi che permettono di trovare approssimazioni soddisfacenti dei prezzi e delle volatilità implicite relative a questi modelli.
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Constantin, Robert, and Denis Gerzic. "An Evaluation of Swedish Municipal Borrowing via Nikkei-linked Loans." Thesis, Linköpings universitet, Produktionsekonomi, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-153259.

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In this master thesis, we compare three different types of funding alternatives from a Swedish municipality's point of view, with the main focus on analysing a Nikkei-linked loan. We do this by analysing the resulting interest rate and the expected exposures, taking collateral into consideration. We conclude, with certainty, that there are many alternatives for funding and that they each need to be analysed and compared on many levels to be able to make a correct decision as to which ones to choose. An important part of this is to consider the implications of the newest regulations and risk ex
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Fischbach, Pascal. "Derivate für FX-Absicherungen." St. Gallen, 2008. http://www.biblio.unisg.ch/org/biblio/edoc.nsf/wwwDisplayIdentifier/05608120001/$FILE/05608120001.pdf.

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Wilkens, Sascha. "Optionsbewertung und Risikomanagement unter gemischten Verteilungen : theoretische Analyse und empirische Evaluation am europäischen Terminmarkt /." Wiesbaden : Dt. Univ.-Verl, 2003. http://www.gbv.de/dms/zbw/372731589.pdf.

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Zufferey, Yannick. "Contrôle combiné stochastique et stratégies d'entreprise /." [S.l.] : [s.n.], 2002. http://www.gbv.de/dms/zbw/361237359.pdf.

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Furrer, Marc. "Numerical Accuracy of Least Squares Monte Carlo." St. Gallen, 2008. http://www.biblio.unisg.ch/org/biblio/edoc.nsf/wwwDisplayIdentifier/01650217002/$FILE/01650217002.pdf.

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Duan, Fangjing. "Option pricing models and volatility surfaces." St. Gallen, 2005. http://www.biblio.unisg.ch/org/biblio/edoc.nsf/wwwDisplayIdentifier/03607991001/$FILE/03607991001.pdf.

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Jönsson, Ola. "Option pricing and Bayesian learning /." Lund: Univ., Dep. of Economics, 2007. http://www.gbv.de/dms/zbw/541563130.pdf.

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Gruber, Alfred. "A taxonomy of risk-neutral distribution methods : theory and implementation /." [S.l. : s.n.], 2003. http://www.gbv.de/dms/zbw/362419094.pdf.

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Books on the topic "Black-Scholes PDE"

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Back, Kerry E. Option Pricing. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0016.

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Options, option portfolios, put‐call parity, and option bounds are explained. Changes of numeraire (measure) are discussed, and the Black‐Scholes formula is derived. The fundamental PDE for an option value is explained. The option greeks are defined, and delta hedging is explained. The smooth pasting condition for valuing an American option is explained.
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Book chapters on the topic "Black-Scholes PDE"

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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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Patel, Kuldip Singh, and Mani Mehra. "High-Order Compact Finite Difference Method for Black–Scholes PDE." In Mathematical Analysis and its Applications. Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2485-3_32.

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Rigatos, Gerasimos G. "Stabilization of the Multi-asset Black–Scholes PDE Using Differential Flatness Theory." In State-Space Approaches for Modelling and Control in Financial Engineering. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52866-3_13.

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Koh, W. S., R. R. Ahmad, S. H. Jaaman, and J. Sulaiman. "Pricing Asian Option by Solving Black–Scholes PDE Using Gauss–Seidel Method." In Proceedings of the Third International Conference on Computing, Mathematics and Statistics (iCMS2017). Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-7279-7_18.

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Rigatos, Gerasimos G. "Stabilization of Financial Systems Dynamics Through Feedback Control of the Black-Scholes PDE." In State-Space Approaches for Modelling and Control in Financial Engineering. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52866-3_12.

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Rigatos, Gerasimos G. "Kalman Filtering Approach for Detection of Option Mispricing in the Black–Scholes PDE." In State-Space Approaches for Modelling and Control in Financial Engineering. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52866-3_6.

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"The Black–Scholes PDE." In Stochastic Finance. Chapman and Hall/CRC, 2013. http://dx.doi.org/10.1201/b16359-9.

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"Black–Scholes PDE and formulas." In An Introduction to Financial Option Valuation. Cambridge University Press, 2004. http://dx.doi.org/10.1017/cbo9780511800948.009.

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"◾ Solving the Black Scholes PDE." In Quantitative Finance. Chapman and Hall/CRC, 2014. http://dx.doi.org/10.1201/b16039-26.

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"Finite Differences and the Black-Scholes PDE." In A Workout in Computational Finance. John Wiley & Sons, Ltd, 2013. http://dx.doi.org/10.1002/9781119973515.ch3.

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Conference papers on the topic "Black-Scholes PDE"

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Laszlo, Endre, Zoltan Nagy, Michael B. Giles, Istvan Reguly, Jeremy Appleyard, and Peter Szolgay. "Analysis of parallel processor architectures for the solution of the Black-Scholes PDE." In 2015 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2015. http://dx.doi.org/10.1109/iscas.2015.7169062.

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Benk, Janos, and Dirk Pfluger. "Hybrid parallel solutions of the Black-Scholes PDE with the truncated combination technique." In 2012 International Conference on High Performance Computing & Simulation (HPCS). IEEE, 2012. http://dx.doi.org/10.1109/hpcsim.2012.6266992.

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Rigatos, Gerasimos. "A Kalman filtering approach for detection of option mispricing in the Black-Scholes PDE model." In 2014 IEEE Conference on Computational Intelligence for Financial Engineering & Economics (CIFEr). IEEE, 2014. http://dx.doi.org/10.1109/cifer.2014.6924098.

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Volders, K. "Stability of central finite difference schemes on non-uniform grids for the Black–Scholes PDE with Neumann boundary condition." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756624.

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