The Quantitative Tools for Finance certificate provides coverage of the main applied mathematical tools required in financial markets, including areas of analysis, probability theory, stochastic processes, and statistical estimation. Thorough grounding in the theory and numerical computation is necessary for understanding and implementing financial derivative pricing, strategy development, portfolio construction, and risk management.

Who would be suited to take this program?

A person pursuing a career in financial modeling, banking, finance, insurance, or investment management. Also, this is a program for staff of larger companies with internal financial modeling, such as those within treasury departments which trade and hedge corporate exposures in the financial markets. A related job title would be a Quantitative Analyst, alongside variations of that in the areas of: portfolio management, investment strategy development, risk modeling/managing, etc. There are many positions in the named industries and others where the quantitative tools in the certificate are actively in demand. The numerical methods, simulation, regression and time series material forms a standard component of the skill set of data analysts; programming skills are at a premium across various industries.

What are the Required Courses?

Core Courses
MATH 608Partial Differential Equations for Finance3
MATH 611Numerical Methods for Computation3
MATH 666Simulation for Finance3
Electives
Select one of the following:3
Regression Analysis Methods *
Time Series Analysis
Java Programming *
Data Structures and Algorithms *

What will I learn?

• Partial Differential Equations - presents classical material on partial differential equations (PDEs), with an explicit focus on the PDEs arising in the study of stochastic processes and finance. The focus is on analytical and numerical methods for obtaining solutions in a form useful for solving problems in financial engineering. Topics include modeling with PDEs, classification of PDEs, analytical and numerical methods for PDEs and application to finance.

• Numerical Methods - presents a collection of tools used in the implementation of the models and methods of quantitative financial modeling. Numerical solution of linear systems. Interpolation and quadrature. Interative solution of nonlinear systems. Computation of eigenvalues and eigenvectors. Numerical solution of initial and boundary value problems for ODE's. Introduction to numerical solution of PDE's. Applications drawn from science, engineering, and finance.

• Simulation for Finance - presents methods of random variate generation, stochastic process simulation, variance reduction, and estimation of quantities including financial derivative prices and risk measures. Covers the use of Monte Carlo stochastic simulation for finance applications. Topics include generation of various random variables and stochastic processes (e.g., point processes, Brownian motion, diffusions), simulation methods for estimating quantities of interest (e.g., option prices, probabilities, expected values, quantiles), input modeling, and variance-reduction techniques. Students will write computer programs in C++.

• Regression Analysis Methods - regression models and the least squares criterion. Simple and multiple linear regression. Regression diagnostics. Confidence intervals and tests of parameters, regression and analysis of variance. Variable selection and model building. Dummy variables and transformations, growth models. Other regression models such as logistic regression. Using statistical software for regression analysis.

• Time Series Analysis introduces the standard models for analyzing time series in financial applications, including the ARIMA and GARCH classes. Time series models, smoothing, trend and removal of seasonality. Naive forecasting models, stationarity and ARMA models. Estimation and forecasting for ARMA models. Estimation, model selection, and forecasting of nonseasonal and seasonal ARIMA models.

• Java Programming explores object oriented programming in the Java environment, including process communication, database connectivity, multithreading, and lightweight components.

• Data Structures & Algorithms is an intensive study of the fundamentals of data structures and algorithms. The course presents the definitions, representations, and processing algorithms for data structures, and general design and analysis techniques for algorithms.

​​Why study Quantitative Tools for Finance at NJIT?

This program provides students with the theoretical knowledge as well as the practical methods and skills needed to begin or enhance careers as quantitative analysts in the financial industry.  Because of the evolving nature of financial markets and institutions, practitioners in this field must be ready to learn new ideas and methods across a broad range of disciplines including mathematics, statistics, computational science, finance, and economics. The program aims to provide the multidisciplinary foundations preparing quantitative analysts for this life-long development of skills and understanding.

Prerequisites

A minimum of a 2.8 in related coursework during a completed Bachelor's degree. Students should have a mathematical background equivalent to that of a typical undergraduate major in the engineering, physical, or mathematical sciences.

Related Degrees

The Graduate Certificate in Financial Mathematics program relates directly to the NJIT MS in Mathematical and Computational Finance.