• Length:
12 Weeks
• Effort:
10–14 hours per week
• Price:

FREE
Add a Verified Certificate for \$450 USD

• Institution
• Subject:
• Level:
• Language:
English
• Video Transcript:
English
• Course Type:
Instructor-led on a course schedule

## Prerequisites

• Calculus
• Probability and statistics
• Linear algebra

Modern finance is the science of decision making in an uncertain world, and its language is mathematics. As part of the MicroMasters® Program in Finance, this course develops the tools needed to describe financial markets, make predictions in the face of uncertainty, and find optimal solutions to business and investment decisions.

This course will help anyone seeking to confidently model risky or uncertain outcomes. Its topics are essential knowledge for applying the theory of modern finance to real-world settings. Quants, traders, risk managers, investment managers, investment advisors, developers, and engineers will all be able to apply these tools and techniques.

The course is excellent preparation for anyone planning to take the CFA exams.

### What you'll learn

Skip What you'll learn
• Probability distributions in finance
• Time-series models: random walks, ARMA, and GARCH
• Continuous-time stochastic processes
• Optimization
• Linear algebra of asset pricing
• Statistical and econometric analysis
• Monte Carlo simulation
• Applied computational techniques

### Syllabus

Skip Syllabus

Learning modules:

1. Probability: review of laws probability; common distributions of financial mathematics; CLT, LLN, characteristic functions, asymptotics.

2. Statistics: statistical inference and hypothesis tests; time series tests and econometric analysis; regression methods

3. Time-series models: random walks and Bernoulli trials; recursive calculations for Markov processes; basic properties of linear time series models (AR(p), MA(q), GARCH(1,1)); first-passage properties; applications to forecasting and trading strategies.

4. Continuous time stochastic processes: continuous time limits of discrete processes; properties of Brownian motion; introduction to Itô calculus; solving differential equations of finance; applications to derivative pricing and risk management.

5. Linear algebra: review of axioms and operations on linear spaces; covariance and correlation matrices; applications to asset pricing.

6. Optimization: Lagrange multipliers and multivariate optimization; inequality constraints and quadratic programming; Markov decision processes and dynamic programming; variational methods; applications to portfolio construction, algorithmic trading, and best execution.|

7. Numerical methods: Monte Carlo techniques; quadratic programming

## Meet your instructors

Paul F. Mende
Senior Lecturer, Sloan School of Management
Massachusetts Institute of Technology
Egor Matveyev
Senior Lecturer and Research Scientist in Finance, Sloan School of Management
Massachusetts Institute of Technology

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### Who can take this course?

Unfortunately, learners from one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. EdX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.