Vives i Santa Eulàlia, Josep, 1963-Roch, OriolMorera Morales, Adrià2019-09-192019-09-192019-01-18https://hdl.handle.net/2445/140467Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Josep Vives i Santa Eulàlia i Oriol Roch[en] There are several paths that lead to the Black-Scholes formula. This project discusses two of them. Chapters 2 and 3 depart from the discrete Cox-Ross-Rubinstein model of prices and reveal the Black-Scholes formula for European calls and puts. Chapters 4 and 5 go one step further by considering since inception the continuous modelling of prices, in which a new concept of integral must be defined in order to formulate the Black-Scholes hypotheses from a stochastical point of view. The project ends up debating the uses of derivatives and the appropriateness of the Black-Scholes model in the real world. Moreover, the annex contains Numerical Methods that implement the models covered in this project.82 p.application/pdfengcc-by-nc-nd (c) Adrià Morera Morales, 2019http://creativecommons.org/licenses/by-nc-nd/3.0/es/Integrals estocàstiquesTreballs de fi de grauActius financers derivatsGestió de carteraMètode de MontecarloStochastic integralsBachelor's thesesDerivative securitiesPortfolio managementMonte Carlo methodinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess