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Bachelor thesis

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2014-07-15

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cc-by-nc-nd (c) Maite Marquès Llorens, 2014
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/62406

Models estocàstics del tipus d'interès

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The aim of this final project is to study the pricing of zero-coupon bonds of different interest rate models in a continuous-time market in the absence of arbitrage opportunities, specifically, the Vasicek model and the Cox-Ingersoll-Ross model. First, this study needs to analyze the basis of the stochastic modeling of continuous-time market which includes to study some notions about the stochastic calculus. So, first the chapters 1 and 2 have some useful concepts and results of stochastic calculus like the Brownian motions, the stochastic integrals, the Itô calculus, the stochastic differential equations... Then, in the chapter 3 some economic concepts, the model of continuous-time market and the concept of portfolio self-financing, are defined; and also, this Black-Scholes pricing are studied. Later, in the chapter 4, some common models short term interest rate models are introduced. Last, in the chapter 5, the pricing of zero-coupon bonds are studied following the two named models in the former chapter, the Vasicek model and Cox-Ingersoll-Ross model, using pricing from chapter 3. During all the project, we suppose all the affirmations about finite random variables and stochastic processes are true P almost surely. To sum up, we have used different resources but overall, we have based on the books Introduction to stochastic calculus applied to finance ([Lam]) and An elementary introduction to stochastic interest rate modeling ([Pri]).

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2014, Director: Josep Vives i Santa Eulàlia

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Processos estocàstics, Treballs de fi de grau, Moviment brownià, Equacions diferencials estocàstiques, Variables aleatòries, Mercat financer, Bons, Models matemàtics

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Stochastic processes, Bachelor's theses, Brownian movements, Stochastic differential equations, Random variables, Financial market, Bonds, Mathematical models

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Treballs Finals de Grau (TFG) - Matemàtiques

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MARQUÈS LLORENS, Maite. Models estocàstics del tipus d'interès. [consulted: 16 of October of 2026]. Available at: https://hdl.handle.net/2445/62406

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