Miniatura

Fitxers

memoria.pdf (516.98 KB)

Tipus de document

Treball de fi de grau

Data de publicació

2014-07-15

Llicència de publicació

cc-by-nc-nd (c) Maite Marquès Llorens, 2014
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/62406

Models estocàstics del tipus d'interès

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Resum

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]).

Descripció

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

Matèries

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

Matèries (anglès)

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

Citació

Col·leccions

Treballs Finals de Grau (TFG) - Matemàtiques

Citació

MARQUÈS LLORENS, Maite. Models estocàstics del tipus d'interès. [consulta: 21 de gener de 2026]. [Disponible a: https://hdl.handle.net/2445/62406]

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