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Paul F. Mende
and
Egor Matveyev
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.
Read more
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.
Read more
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.
Register for this course and see more details by visiting:
OpenCourser.com/course/qxe3du/mathematical
What's inside
Learning objectives
- 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
- * 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."
- 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
- * 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."
Syllabus
Learning modules:
Probability: review of laws probability; common distributions of financial mathematics; CLT, LLN, characteristic functions, asymptotics.
Read more
Syllabus
Learning modules:
Probability: review of laws probability; common distributions of financial mathematics; CLT, LLN, characteristic functions, asymptotics.
Read more
Statistics: statistical inference and hypothesis tests; time series tests and econometric analysis; regression methods
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.
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.
Linear algebra: review of axioms and operations on linear spaces; covariance and correlation matrices; applications to asset pricing.
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.|
Numerical methods: Monte Carlo techniques; quadratic programming
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Develops skills for quants, traders, investment managers, and analysts who make decisions in uncertain environments
Taught by Paul F. Mende and Egor Matveyev, experts with decades of experience in the field
Covers a wide range of topics relevant to financial decision-making, including time-series models, optimization, and linear algebra of asset pricing
Emphasizes applied computational techniques, equipping learners with practical skills for real-world applications
Follows the curriculum of the MicroMasters® Program in Finance, ensuring alignment with industry standards
Relies on extensive mathematical prerequisites, including calculus, probability, and linear algebra, requiring learners to have a strong foundational understanding
Save this course
Save Mathematical Methods for Quantitative Finance to your list so you can find it easily later:
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Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Mathematical Methods for Quantitative Finance with these
activities:
Exploration of stochastic processes and simulation techniques
Show steps
Expand your problem-solving prowess with expert guidance on simulating and predicting change over time.
Show steps
Probability and statistics exercises
Show steps
Beef up your problem-solving prowess by wading through numerous probability and statistics questions.
Show steps
Calculus review
Show steps
Realize enhanced confidence by practicing with essential mathematical tools.
Show steps
Five other activities
Expand to see all activities and additional details
Show all eight activities
Study group on advanced topics
Show steps
Engage in lively discussions with peers to clarify complex concepts and reinforce understanding.
Show steps
Quantitative Finance (2nd edition) by Keith R. Ward
Show steps
Stay a beat ahead by delving into this comprehensive guide that bridges the gap between theoretical knowledge and industry applications in quantitative finance.
View
Investment Analysis & Portfolio Management
on Amazon
Show steps
Tutoring fellow students
Show steps
Solidify your knowledge by explaining concepts to others and guiding their learning journey.
Show steps
Design a portfolio optimization tool
Show steps
Put your learning to the test by building a tool that addresses portfolio optimization challenges.
Show steps
-
Identify investor risk tolerance and financial goals.
-
Research and select appropriate asset classes.
-
Develop an optimization algorithm to allocate assets.
-
Test and validate the tool's performance.
-
Create a user-friendly interface for the tool.
Kaggle competition on financial modeling
Show steps
Sharpen your skills and gain recognition in the field by tackling real-world financial modeling challenges in a competitive setting.
Show steps
Exploration of stochastic processes and simulation techniques
Show steps
Expand your problem-solving prowess with expert guidance on simulating and predicting change over time.
Show steps
Show steps
Show steps
Probability and statistics exercises
Show steps
Beef up your problem-solving prowess by wading through numerous probability and statistics questions.
Show steps
Show steps
Show steps
Calculus review
Show steps
Realize enhanced confidence by practicing with essential mathematical tools.
Show steps
Show steps
Show steps
Five other activities
Expand to see all activities and additional details
Show all eight activities
Study group on advanced topics
Show steps
Engage in lively discussions with peers to clarify complex concepts and reinforce understanding.
Show steps
Show steps
Show steps
Quantitative Finance (2nd edition) by Keith R. Ward
Show steps
Stay a beat ahead by delving into this comprehensive guide that bridges the gap between theoretical knowledge and industry applications in quantitative finance.
View
Investment Analysis & Portfolio Management
on Amazon
Show steps
Show steps
Show steps
Tutoring fellow students
Show steps
Solidify your knowledge by explaining concepts to others and guiding their learning journey.
Show steps
Show steps
Show steps
Design a portfolio optimization tool
Show steps
Put your learning to the test by building a tool that addresses portfolio optimization challenges.
Show steps
Show steps
Show steps
- Identify investor risk tolerance and financial goals.
- Research and select appropriate asset classes.
- Develop an optimization algorithm to allocate assets.
- Test and validate the tool's performance.
- Create a user-friendly interface for the tool.
Kaggle competition on financial modeling
Show steps
Sharpen your skills and gain recognition in the field by tackling real-world financial modeling challenges in a competitive setting.
Show steps
Show steps
Show steps
Career center
Learners who complete Mathematical Methods for Quantitative Finance will develop knowledge and skills
that may be useful to these careers:
Quantitative Analyst
Quantitative Analyst
A Quantitative Analyst uses mathematics and financial theory to research, analyze, value, and manage various types of financial instruments and assets. The course will allow you to develop the tools needed to make predictions in the face of uncertainty, a skill that is crucial to this role. Additionally, the course will help build a foundation in probability distributions in finance, continuous-time stochastic processes, optimization, and statistical and econometric analysis. Each of these topics is important to the success of a quant, as each is needed to explore and subsequently profit from market inefficiencies.
Investment Manager
Investment Manager
An Investment Manager provides investment advisory services to individuals and organizations. The course will allow you to develop the tools needed to make predictions in the face of uncertainty, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions in finance, continuous-time stochastic processes, optimization, and statistical and econometric analysis. Each of these topics is essential to building a successful investment portfolio for either personal or client accounts.
Portfolio Manager
Portfolio Manager
A Portfolio Manager develops and executes investment strategies for clients. The course will allow you to develop the tools needed to make predictions in the face of uncertainty, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions in finance, continuous-time stochastic processes, optimization, and statistical and econometric analysis. Each of these topics is essential to building a successful investment portfolio for either personal or client accounts.
Financial Analyst
Financial Analyst
A financial analyst gathers financial data and prepares financial reports to help individuals and organizations make informed decisions. The course will allow you to develop the tools needed to make predictions in the face of uncertainty, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions in finance, continuous-time stochastic processes, optimization, and statistical and econometric analysis. Each of these topics is needed to build strong financial models that can accurately forecast future outcomes.
Quant Developer
Quant Developer
A Quant Developer uses computer programming to develop and implement quantitative financial models. The course will allow you to develop the tools needed to make predictions in the face of uncertainty, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions in finance, continuous-time stochastic processes, optimization, and statistical and econometric analysis. Knowing how to apply each of these topics to computer code will make you a strong candidate for this role.
Risk Manager
Risk Manager
A Risk Manager identifies, assesses, and mitigates financial risks for an organization. The course will allow you to develop the tools needed to make predictions in the face of uncertainty, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions in finance, continuous-time stochastic processes, optimization, and statistical and econometric analysis. Each of these topics is essential to identifying and addressing the different types of risk that an organization may face.
Financial Engineer
Financial Engineer
A Financial Engineer uses financial theory to develop and implement financial instruments and strategies. The course will allow you to develop the tools needed to make predictions in the face of uncertainty, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions in finance, continuous-time stochastic processes, optimization, and statistical and econometric analysis. Each of these topics is essential to the success of a financial engineer.
Market Risk Analyst
Market Risk Analyst
A Market Risk Analyst assesses the risks associated with financial markets. The course will allow you to develop the tools needed to make predictions in the face of uncertainty, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions in finance, continuous-time stochastic processes, optimization, and statistical and econometric analysis. Each of these topics is essential to accurately evaluating the risk associated with the various financial markets.
Credit Risk Analyst
Credit Risk Analyst
A Credit Risk Analyst assesses the risks associated with lending money. The course will allow you to develop the tools needed to make predictions in the face of uncertainty, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions in finance, continuous-time stochastic processes, optimization, and statistical and econometric analysis. Each of these topics is essential to making informed lending decisions.
Insurance Analyst
Insurance Analyst
An insurance analyst assesses the risks and costs associated with insurance policies. The course will allow you to develop the tools needed to make predictions in the face of uncertainty, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions in finance, continuous-time stochastic processes, optimization, and statistical and econometric analysis. Each of these topics is essential to accurately evaluating the risk associated with various insurance policies.
Actuary
Actuary
An actuary analyzes the financial risks associated with insurance policies. The course will allow you to develop the tools needed to make predictions in the face of uncertainty, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions in finance, continuous-time stochastic processes, optimization, and statistical and econometric analysis. Each of these topics is essential to appropriately pricing and setting insurance policy rates.
Data Scientist
Data Scientist
A Data Scientist uses data analysis to extract insights from data. The course will introduce the basic tools needed to gather, analyze, and interpret data, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions, statistical and econometric analysis, and Monte Carlo simulation. Each of these topics is essential to success in this field.
Statistician
Statistician
A Statistician collects, analyzes, and interprets data. The course will introduce the basic tools needed to gather, analyze, and interpret data, a skill that is essential to this role. Additionally, the course will help build a foundation in probability distributions, statistical and econometric analysis, and Monte Carlo simulation. Each of these topics is essential to success in this field.
Economist
Economist
An Economist studies the production, distribution, and consumption of goods and services. The course may help build a foundational understanding of the mathematics behind economic theory, but only takes you so far on the path to becoming an economist. Nevertheless, a strong foundational understanding is helpful and is an essential part of the role.
Software Engineer
Software Engineer
A software engineer designs, develops, and maintains software systems. The course may help build a foundational understanding of the mathematics behind modern software, but only takes you so far on the path to becoming a software engineer. Nevertheless, a strong foundational understanding is helpful and is an essential part of this role.
For more career information including salaries, visit:
OpenCourser.com/course/qxe3du/mathematical
Reading list
We've selected 14 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Mathematical Methods for Quantitative Finance.
Comprehensive textbook on the mathematical and statistical methods used in financial markets. It covers a wide range of topics, including probability theory, stochastic processes, financial derivatives, and numerical methods, with a focus on applications to pricing and risk management.
Provides a comprehensive overview of the mathematical and statistical tools used to analyze financial markets, and good companion to 15.455x. It covers material on probability theory, stochastic processes, optimization, and numerical methods, with a focus on applications to risk management and portfolio optimization.
Classic textbook on the mathematics of financial markets. It covers a wide range of topics, including probability theory, stochastic processes, financial derivatives, and numerical methods, with a focus on applications to pricing and risk management.
Comprehensive guide to the models and techniques used in financial risk management. It covers a wide range of topics, including probability theory, stochastic processes, financial derivatives, and numerical methods, with a focus on applications to risk management.
Comprehensive introduction to continuous-time stochastic calculus, with a focus on applications to financial markets. It covers a wide range of topics, including Brownian motion, stochastic differential equations, and stochastic integrals, with a focus on applications to pricing and risk management.
Is an accessible introduction to the mathematics of financial derivatives, with a focus on applications to pricing and risk management. It covers a wide range of topics, including probability theory, stochastic processes, financial derivatives, and numerical methods.
Is an introduction to econometrics, with a focus on applications to financial markets. It covers a wide range of topics, including time series analysis, regression analysis, and forecasting, with a focus on applications to portfolio management and risk management.
Save
Is an introduction to data science, with a focus on applications to finance. It covers a wide range of topics, including data collection, data cleaning, and data analysis, with a focus on applications to portfolio management and risk management.
Is an introduction to Python programming, with a focus on applications to finance. It covers a wide range of topics, including data analysis, visualization, and machine learning, with a focus on applications to portfolio management and risk management.
Comprehensive introduction to time series analysis, with a focus on applications to financial data. It covers a wide range of topics, including time series models, forecasting, and statistical inference, with a focus on applications to financial data.
Is an introduction to numerical methods, with a focus on applications to financial modeling. It covers a wide range of topics, including random number generation, Monte Carlo simulation, and finite difference methods, with a focus on applications to pricing and risk management.
Is an introduction to machine learning, with a focus on applications to asset management. It covers a wide range of topics, including supervised learning, unsupervised learning, and reinforcement learning, with a focus on applications to portfolio management and risk management.
Is an introduction to deep learning, with a focus on applications to finance. It covers a wide range of topics, including deep neural networks, convolutional neural networks, and recurrent neural networks, with a focus on applications to pricing and risk management.
Is an introduction to econometrics, with a focus on applications to financial data. It covers a wide range of topics, including time series analysis, regression analysis, and forecasting, with a focus on applications to portfolio management and risk management.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/qxe3du/mathematical
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Effort
10 to 14 hours per week for 12 weeks
Level
Advanced
Via
edX
Institution
Massachusetts Institute of Technology
Instructors
Paul F. Mende
Egor Matveyev
Session
June 26, 2024
- September 16, 2024
Language
English
Transcript
English
This course belongs to a
collection
called
Finance. It's comprised of four courses:
- Foundations of Modern Finance I
- Foundations of Modern Finance II
- Mathematical Methods for Quantitative Finance (viewing)
- Derivatives Markets: Advanced Modeling and Strategies
Good to know
Develops skills for quants, traders, investment managers, and analysts who make decisions in uncertain environments
Taught by Paul F. Mende and Egor Matveyev, experts with decades of experience in the field
Covers a wide range of topics relevant to financial decision-making, including time-series models, optimization, and linear algebra of asset pricing
Emphasizes applied computational techniques, equipping learners with practical skills for real-world applications
Follows the curriculum of the MicroMasters® Program in Finance, ensuring alignment with industry standards
Relies on extensive mathematical prerequisites, including calculus, probability, and linear algebra, requiring learners to have a strong foundational understanding
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