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Maestría en Finanzas Cuantitativas

Curriculum

The program curriculum seeks to reconcile theoretical training with practical tools needed to successfully meet current challenges and requirements in the area of quantitative finance. It also seeks to foster the spirit of innovation and research in this area at the regional level.

Applicants are strongly advised to take the pre-master course Introduction to stochastic modeling, especially those who have not taken any intermediate probability and stochastic processes in their previous studies. This course aims to formally review some concepts of probability and present an introduction to the theory of stochastic processes. It has a duration of 32 hours (2 credits) and is offered as an intensive course months before the beginning of the first semester. The course will be graded as approved or not approved.

During the first semester the student acquires fundamental knowledge common to different problems of quantitative finance. Special emphasis is placed on general aspects of financial markets, financial economics and derivatives and on mathematical tools and statistics such as stochastic calculation and advanced econometrics.
 
The second semester courses are designed to allow students to acquire numerical and programming skills in the R and Python languages ​​and combine them with the tools acquired in the first semester to efficiently solve general problems of quantitative finance: construction of performance curves, optimization of portfolios, simulation, valuation of financial derivatives, modeling of time series, empirical finance, among others.
 
In the third semester, students are required to take a compulsory course of Quantitative Risk Management (2 credits - 24 hours) and must elect 4 electives (each of 2 credits) which allows them to deepen and specialize in more specific subjects, depending on their interests.

 

 

First Semester

In first semester courses the student acquires basic knowledge common to different problems of quantitative finance. Emphasis on general aspects of financial markets, financial economics and derivatives instruments in mathematical tools and statistics such as stochastic calculus and advanced Econometrics.

Code 14610001 - Credits 5

The stochastic calculus is a fundamental part of the modern theory of financial markets. Mathematical tools such as stochastic integration and stochastic differential equations allow a continuous time modeling of asset prices and other variables in financial markets. The objective of this course is to provide the student with the necessary skills to properly use this type of tools.

Contents: Brownian motion. Quadratic variation and variance of stochastic processes. Itô Integration. Itô formula. Stochastic differential equations. Principles of reflection. Distribution of maximums and minimums. Changes of measure. Martingale representation theorem. Girsanov's theorem. Kolmogorov equations. Feynman-Kac formula. Lévy processes: Infinite divisibility, definition of Lévy processes. Jumps measure, Levy measure. Lévy-Itô decomposition. Lévy–Khintchine representation.

As its main objective, this lecture seeks to have among the professionals who enroll in their postgraduate studies at the Universidad del Rosario, to ponder on the tools and basic competences of learning, which they shall put into practice in their professional life. As such, this institutional subject provides the fundamental tools for graduate students to be able to detect strengths or weaknesses and build their personal academic project from the Rosarista project. In the framework of this class, the activities will be developed and transferred to the virtual platform of institutional learning, so it will be an entirely virtual subject. In this space, students will be able to browse online for content such as multimedia products, booklets and evaluation activities, freely, without restrictions and under the guidance of a virtual tutor. The subject is divided into the following study or learning modules: Historical Tour; Academic Support Tools; History and Institutional Project.

Second Semester

Second semester courses are aimed at students to acquire skills numerical and programming in R and Python languages and combine them with the tools acquired in the first half to solve general problems of quantitative finance efficiently: construction of curves of performance, optimisation of portfolio, simulation, assessment of financial derivatives, time-series modeling, empirical finance, among others.

Code 14610006 - Credits 5

In quantitative finance, there are many problems not supporting analytical solutions and demand the application of numerical methods to approximate a solution. This course addresses the study and application of these methods for solving problems in finance. The program includes the presentation of basic tools of numerical analysis, and specific methods for solving financial problems. Throughout the course, specific applications are studied, and computational tools are developed to find solutions to valuation problems of financial instruments, estimation of yield curves, portfolio optimization, among others.

Contents: Basics of Python programming. Generation of random variables. Inverse transform, Box-Muller and the polar method of Marsaglia. Pseudo-random numbers and seeds. Halto, Faure Sequences and Sobol of quasi-random numbers. Euler-Maruyama method. Analysis of mean-variance of portfolios. Implied volatility, bootstrapping, non-analytic inverse transformation for the generation of random numbers. Roots of equations: bisection, fixed point, Newton-Raphson, secant and regula falsi. Integration methods: trapezoidal, Runge-Kutta, Simpson. Application to valuation of options. Fast Fourier and Fourier transforms. Errors, convergence and numerical stability. Monte-Carlo simulation, confidence intervals and valuation of European, American and Asian options. Extensions of Monte-Carlo methods. Antithetic variables. Control variate, moment matching, low discrepancy. Interpolation and extrapolation. Data adjustment and model calibration: Least squares, splines, Lagrange and Fourier. Discount curves. Binomial models and applications to valuation of American options. Convergence of CRR to BS. Finite Differences: Implicit and Explicit Schemes. Cholesky and LU decomposition. Iterative SOR Crank-Nicolson, PSOR, application to American and exotic options (Asian, barrier and lookback).

Third Semester

In the third semester students attend the compulsory subject quantitative risk management (2 credits - 24 hours) and should choose electives 4 (2 credits each) which allows them to deepen and specialize in more specific subjects depending on their interests.

Credits 5

Credits 8

  • Interest rate derivatives
  • Quantitative Portfolio Management
  • Credit and counterparty risk
  • Introduction to Actuarial Mathematics
  • Term structure models of interest rates
  • Behavioral Finance
  • Credit derivatives
  • Stochastic optimal control
  • Advanced models of financial markets
  • Advanced numerical methods: finite differences

Duration

This expertise can be attended with a dedication of full or parttime. The program is designed for the student to complete the programin one year and half or two years and a half, in accordance with its flexibility to attend classes and the evolutionof their degree.

Total credits per semester
 
Credits Time intensity Hours of independent work Total hours
15 12 33 45