BA in International Economcis & Finance

[EconomicsStudent]

I'm currently studying International Economics & Finance but I am looking to pursue graduate studies in Quantitative Finance. I'm from Toronto and there's a very good MMF program at University of Toronto here, which I am thinking of applying to after graduation.

I'm in my first semester. I will post the relevant "quantitative courses" and if anyone can tell me if they are appropriate prerequisites for a quantitative finance program or if I need additional math courses, I would really appreciate it.

Introduction to Mathematics for Economics - This course is an introduction to fundamental mathematical techniques which are used frequently in Economics. The first part of the course covers some basic concepts such as sets, relations and functions, exponential and logarithmic functions, and linear and nonlinear equations. The second part of the course deals with single variable differential calculus: limits, continuity, differentiation, sequences, power series, optimization as well as definite and indefinite integrals.

Linear Algebra - This course applies Matrix Algebra to the modelling of Linear Business Systems. Topics include Matrices and Linear Transformations, Determinants and Subspaces.

Mathematics for Economics - This course introduces the students to mathematical topics beyond the high school calculus. It reviews differential calculus, then introduces topics such as basic matrix algebra, constrained optimization, comparative statistics for general function modes, and their application in economics.

Statistics for Economics I - This course is an introduction to descriptive and inferential statistics. Descriptive statistics consists of characterizing data sets by both frequency distributions and measures of central tendency and dispersion. Inferential statistics consists of techniques to make predictions or probabilistic statements about a whole population by studying the properties of a sample drawn from the population. Because inferential statistics depends on the probability theory, some probability laws will be studied, including the Binomial, Normal and t-distributions.

Statistics for Economics II - This course is a continuation of the topics covered in ECN 129, Statistics for Economics I. It includes such topics as goodness of fit tests, Type 1 and Type II errors, analysis of variance, the assumptions underlying the classical linear regression model, simple regression and multiple regression.

Econometrics I - This course examines what happens when economic data do not satisfy the assumptions of the Classical Linear Regression Model. It explains why ordinary least squares methods are not appropriate in the presence of, for example, autocorrelation or heteroscedasticity, and how estimation techniques have to be modified to take these problems into account. Extensive use will be made of software packages like T.S.P.

Econometrics II - Extends the econometric principles developed in ECN 627. Major topics include: qualitative variables, distributed lag models, single equation forecasting, simultaneous equation systems and two and three stage least squares estimation. Assignments are processed using TSP software.

Investment Analysis II - This course is entirely dedicated to studying derivative securities-forward and futures contracts and how they modify the risk characteristics of a portfolio, how the exchange, clearing house and marketing to market systems work, arbitrage pricing, relationships, interest rate and currency swaps and the use of various types of options contracts and their use for hedging risk.

Financial Risk Management - This course looks at the question of how a financial institution controls and hedges itself against all of the various risks that it faces. The course looks at liquidity management, deposit insurance, capital adequacy, credit risk management, loan securitization, interest rate forwards, futures, swaps, caps, floors and collars and how banks use these derivative products to manipulate its exposure to various types of risk. (looking over the course outline for this course, it's basically an introduction to risk management and financial engineering. it uses Hull's "Risk Management and Financial Institutions" and "Fundamentals of Futures and Options Markets")

Additionally I have experience with Excel/VBA and to a lesser extent, MATLab.

 

[EconomicsStudent]

To rephrase the question, I know I need more math courses, but which ones would best complement the courses I posted in my OP?

 

[Sanket Patel]

Take math courses from the math department. The "math" course you'd take as an Econ major are generally watered down - I speak from experience.

At a minimum you'll need:

3 Semester of Calculus
Ordinary Differential Equations
Partial Differential Equations
Linear Algebra - something beyond simple row reductions and determinants
Probability Theory - preferably calculus based
Real Analysis
Some type of Stochastic Processes course- if you're able to fit it in
Game Theory - as an Econ student, this is a must

Also, you'll need some programming courses - an object oriented language such at C++ would be ideal.

You can find the minimum requirement for the Baruch MFE here; keep in mind that the list constitutes a bare minimum.

 

[EconomicsStudent]

Thanks.

I'm going to check with my department to see if it's possible to take the math courses from the math department directly.

I gather you were also an econ major? Was it possible for you to take courses from the math department in place of the econ math courses?

 

[Sanket Patel]

As an undergrad, I double majored in Finance and Economics and I minored in Mathematics. You should able to take whatever course you want from the math department provided that you satify the pre-reqs. You should also be able to substitute the Mathematics for Economics with Calculus classes from the math department.

You might also want to check if whether you're able to substitute either one of both of the statistics courses with a Mathematical Statistics (like this, for example) course instead. Mathematical statistics along with Econometrics is a very good combination.

 

[EconomicsStudent]

Ok, searching through the math courses I found a few that I might be able to substitute for the Econ Math courses:

Linear Algebra - Systems of linear equations, determinants, vectors, geometry, linear transformations, matrices and graphs, number fields, applications.

Calculus and Computational Methods I - Calculus of functions of one variable and related numerical topics. Derivatives of algebraic, trigonometric and exponential functions, techniques of integration, numerical integration.

Calculus and Computational Methods II - Integration techniques, improper integrals, sequences, infinite series, power series, partial derivatives, maxima and minima.

Calculus III - Multiple Integrals, curves and surfaces in 3-space. Div, grad and curl operators, line and surface integrals, theorems of Green, Gauss, and Stokes, numerical methods, integral transforms.

Probability and Statistics I - Probability and Statistics I: Descriptive statistics. Probability (Laws of probability. Conditional probability. Discrete probability distributions (binomial, hypergeometric, Poisson). Continuous probability distributions, Normal, t-exponential, x². Applications of discrete and continuous distributions. Sampling distributions (sample mean, sample proportion, difference between two samples, difference between two sample proportions). Sampling distribution concerning mean variance and proportion for one or two populations. Estimation for large and small samples. Hypothesis testing concerning mean, variance and proportion for one or two populations, (large samples and small samples) including paired data testing.

Probability and Statistics II - A continuation of the introductory topics covered in MTH 304. Contingency Tables. Goodness of fit tests. Type I and Type II errors. Correlation. Regression. ANOVA One and two-way. A statistics computer package may be used in this course.

Differential Equations - First-order differential equations with applications. Linear higher-order differential equations with applications. Laplace transform methods. Simultaneous Differential Equations. Use of Maple to solve differential equations.

Differential Equations II - Series solutions of differential equations. Bessel's equation and Bessel functions. Legendre's differential equation. Derivation of some partial differential equations (P.D.E.). Solution of P.D.E.'s using separation of variables.

Introduction to Stochastic Processes - Probability of a function of several variables, martingales, conditional expectations, maximum likelihood estimators, random walks, stochastic processes (stationary and ergodic). Applications of statistical processes in science.

 

[Sanket Patel]

That's a good list. Just add a C++ course and you'll be in good shape. The only thing left now is to actually take those courses and get an A in each one. If you're feeling particularly adventerous, you can always find reading material from the Master Reading List thread. I'd recommend starting with Hull then Neftci.

 

[EconomicsStudent]

Would a C++ course be a must? I already have some experience with VBA & MATLAB.

I've been reading a multitude of quantitative finance related material in the last 1-1.5 years as my interest in the field has developed. But I will definitely check out that thread. Thanks.

Has anyone heard anything about the MMF program at University of Toronto? How reputable is it? The only other graduate quant program in Ontario I know of is the Master of Quantitative Finance at Waterloo.

 

[EconomicsStudent]

I'm considering taking additional math courses on top of the ones already mentioned. If I had to choose 2-3 from the following, which would be better suited for quantitative finance?

Numerical Analysis I - Errors and floating point arithmetic. Solutions of non-linear equations including fixed point iteration. Matrix computations and solutions of systems of linear equations. Interpolation. Finite difference methods. Least squares fit. Cubic spline interpolation. Numerical integration. Numerical solution of ordinary differential equations. Taylor series method. Euler method.

Numerical Analysis II - Numerical solutions for initial value and boundary value problems for ordinary differential equations. Runge-Kutta, Multi-step, Hybrid methods. Convergence criteria. Error analysis aspects. Shooting, finite- difference, Rayleigh-Ritz methods. Matrix eigenvalue problem. Jacobi, Givens, Householder, Power methods. Numerical double interpolation and multiple integration. Non-linear systems of equations. Numerical solutions to partial differential equations. This course will include laboratory classes using electronic calculators and computer terminals.

Operations Research I - Linear Programming and the Simplex Algorithm. Sensitivity analysis, duality, and the dual simplex algorithm. Transportation and Assignment Problems, Network models. Integer programming.

Operations Research II - Nonlinear programming, decision making, inventory models, Markov chains, queuing theory, dynamic programming, Simulation.

Fourier Analysis - An advanced course in Fourier Methods dealing with the application of Fourier series, Fourier transforms, convolution, correlation, discrete and fast Fourier transforms.

Complex Analysis - DeMoivre's theorem. Roots and Powers of complex numbers. Functions of a complex variable. Limits and continuity. Cauchy-Riemann equations. Exponential, trigonometric, hyperbolic and logarithmic functions. Conformal transformations. Integration in the complex plane. Residue theorem and some of its applications. Laplace and Fourier transforms.

 

[Stefan Zota]

I'm considering taking additional math courses on top of the ones already mentioned. If I had to choose 2-3 from the following, which would be better suited for quantitative finance?

Numerical Analysis I - Errors and floating point arithmetic. Solutions of non-linear equations including fixed point iteration. Matrix computations and solutions of systems of linear equations. Interpolation. Finite difference methods. Least squares fit. Cubic spline interpolation. Numerical integration. Numerical solution of ordinary differential equations. Taylor series method. Euler method.

Numerical Analysis II - Numerical solutions for initial value and boundary value problems for ordinary differential equations. Runge-Kutta, Multi-step, Hybrid methods. Convergence criteria. Error analysis aspects. Shooting, finite- difference, Rayleigh-Ritz methods. Matrix eigenvalue problem. Jacobi, Givens, Householder, Power methods. Numerical double interpolation and multiple integration. Non-linear systems of equations. Numerical solutions to partial differential equations. This course will include laboratory classes using electronic calculators and computer terminals.

Operations Research I - Linear Programming and the Simplex Algorithm. Sensitivity analysis, duality, and the dual simplex algorithm. Transportation and Assignment Problems, Network models. Integer programming.

Operations Research II - Nonlinear programming, decision making, inventory models, Markov chains, queuing theory, dynamic programming, Simulation.

Fourier Analysis - An advanced course in Fourier Methods dealing with the application of Fourier series, Fourier transforms, convolution, correlation, discrete and fast Fourier transforms.

Complex Analysis - DeMoivre's theorem. Roots and Powers of complex numbers. Functions of a complex variable. Limits and continuity. Cauchy-Riemann equations. Exponential, trigonometric, hyperbolic and logarithmic functions. Conformal transformations. Integration in the complex plane. Residue theorem and some of its applications. Laplace and Fourier transforms.

The syllabus for all courses that you provided is interesting. As a preparation, I would choose Numerical Analysis I/II and Operations Research I

 

[bigbadwolf]

Complex Analysis - DeMoivre's theorem. Roots and Powers of complex numbers. Functions of a complex variable. Limits and continuity. Cauchy-Riemann equations. Exponential, trigonometric, hyperbolic and logarithmic functions. Conformal transformations. Integration in the complex plane. Residue theorem and some of its applications. Laplace and Fourier transforms.

From a finance point of view, this is probably dispensable. Looks like they'll be using the book by Churchill and Brown for this course (Churchill has been the text for courses like this for the last 40 or 50 years).