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Math for Quantitative Finance

Tour the mathematics used to model the chaos of the financial markets.

In this course, we'll dive into statistical modeling, matrices, and Markov chains, and guide you through the powerful mathematics and statistics used to model the chaos of the financial markets.

By the end of this course, you’ll have the skills needed to ace any quantitative finance interview.

Interactive
quizzes

26

Concepts and
exercises

230+
  1. 1

    Intro to Quant Finance

    See why math is the new hero of finance.

    1. Financial Models

      The new heroes of trading and finance are math, statistics, and computer science.

    2. Probability

      Probability is the cornerstone of quantitative financial modeling.

    3. Value and Risk

      Learn how to account for risk when making quantitative decisions.

  2. 2

    Probability

    Get your odds straight.

    1. Included with
      Brilliant Premium

      Probability Warm-ups

      Practice the problem-solving skills required for tackling challenging probability questions.

    2. Included with
      Brilliant Premium

      Conditional Probability

      In a fast-paced market, here's how to update your beliefs in light of new information.

    3. Included with
      Brilliant Premium

      Interview Preparation

      Tackle two sample interview problems in probability, step-by-step.

  3. 3

    Expected Value

    Strategies to calculate the average outcome of random variables.

    1. Included with
      Brilliant Premium

      Expected Value

      Trading is often a game of averages. Learn how to quantify them.

    2. Included with
      Brilliant Premium

      Expected Utility

      When risk is involved, expected values get more complex!

    3. Included with
      Brilliant Premium

      Interview Preparation

      Tackle a sample interview problem in expected value, step-by-step.

  4. 4

    Variance

    The real way to measure "a crazy day on Wall Street".

    1. Included with
      Brilliant Premium

      Variance

      Learn essential techniques for modeling the fluctuations of assets and quantifying risk.

    2. Included with
      Brilliant Premium

      Covariance

      Assets are often correlated. Get to know this tool for measuring how their relative fluctuations.

    3. Included with
      Brilliant Premium

      Indicator Variables

      Learn a trick for calculating variance that works even when events are dependent.

    4. Included with
      Brilliant Premium

      Interview Preparation

      Tackle a sample interview problem in variance, step-by-step.

  5. 5

    Statistics

    Your model looks good, but are the results statistically significant?

    1. Included with
      Brilliant Premium

      Statistics

      Statistics gathers information from samples to make inferences about the overall population.

    2. Included with
      Brilliant Premium

      Normal Distributions

      Though it's not a perfect model, this distribution remains at the core of many pricing algorithms.

    3. Included with
      Brilliant Premium

      Log-normal Distributions

      Get familiar with one of the most common distributions used to model asset prices.

  6. 6

    Confidence and Estimation

    Learn how to estimate and how confident you should be.

    1. Included with
      Brilliant Premium

      Hypothesis Testing

      Hypothesis testing helps determine if your model is actually consistent with the real-world data.

    2. Included with
      Brilliant Premium

      Parameter Estimation

      Given some 'true' model, what are the parameters for that model that fit the data?

    3. Included with
      Brilliant Premium

      Fermi Estimates

      Learn how to quickly estimate values which would require extensive analysis to determine exactly.

  7. 7

    Matrices

    The arithmetic of linear algebra for regression, Markov chains, and more.

    1. Included with
      Brilliant Premium

      Operations

      Brush up on matrix operations: addition, multiplication, transpose, and trace.

    2. Included with
      Brilliant Premium

      Inverses

      Matrix inversion is an important tool to have on your belt when you're solving matrix equations.

    3. Included with
      Brilliant Premium

      Linear Systems

      For large, real-world systems, this matrix approach is more effective than other ad-hoc techniques.

    4. Included with
      Brilliant Premium

      Covariance

      Learn how to represent vector relationships, such as how stocks interact with each other.

  8. 8

    Markov Chains

    Stochastic modeling for the ever-changing markets.

    1. Included with
      Brilliant Premium

      An Overview of Markov Chains

      Explore a powerful tool for representing systems that change states over time.

    2. Included with
      Brilliant Premium

      Stationary Distributions

      Learn how to find the 'steady state' of an evolving system.

    3. Included with
      Brilliant Premium

      Transience and Recurrence

      These advanced tools allow you to calculate the expected steps between states and much more.