Mathematical Methods for Quantitative Finance
link Source: www.edx.org
date_range Starts on June 28, 2023
event_note Ends on September 18, 2023
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assignment Level : Advanced
chat_bubble_outline Language : English
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Key Information

credit_card Free access
verified_user Fee-based Certificate
timer 120 hours in total

About the content

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.

  • 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


How to Prepare

There are a number of prerequisites for this course: Calculus (multivariable), probability and statistics, linear algebra, and basic programming skills. Learners are urged to thoroughly review the 15.455x Prerequisites and Resources site* which details these prerequisites and provides a robust suite of resources to prepare you for this advanced math course, including a readiness assessment to help you confirm that you have a solid understanding of the 15.455x prerequisite material, and to indicate directions of study in case you need to build on your current foundations prior to starting the course.

*Please note that you will need to enroll in order to access the Prerequisite and Resources site. To do so, click the link above, then click "Enroll."

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Prerequisite

  • Calculus
  • Probability and statistics
  • Linear algebra
  • Basic programming skills.

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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

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Instructors

Paul F. Mende
Senior Lecturer, Sloan School of Management
Massachusetts Institute of Technology

Egor Matveyev
Executive Director of MicroMasters Program in Finance
Massachusetts Institute of Technology

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Platform

Edx

Harvard University, the Massachusetts Institute of Technology, and the University of California, Berkeley, are just some of the schools that you have at your fingertips with EdX. Through massive open online courses (MOOCs) from the world's best universities, you can develop your knowledge in literature, math, history, food and nutrition, and more. These online classes are taught by highly-regarded experts in the field. If you take a class on computer science through Harvard, you may be taught by David J. Malan, a senior lecturer on computer science at Harvard University for the School of Engineering and Applied Sciences. But there's not just one professor - you have access to the entire teaching staff, allowing you to receive feedback on assignments straight from the experts. Pursue a Verified Certificate to document your achievements and use your coursework for job and school applications, promotions, and more. EdX also works with top universities to conduct research, allowing them to learn more about learning. Using their findings, edX is able to provide students with the best and most effective courses, constantly enhancing the student experience.

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Excelente!

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Published on August 30, 2021
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