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Brilliant

Math for Quantitative Finance

via Brilliant

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Overview

This course was written in collaboration with former quantitative traders from two leading firms.

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 a quantitative finance interview.

Syllabus

  • Intro to Quant Finance: See why math is the new hero of finance.
    • Financial Models: The new heroes of trading and finance are math, statistics, and computer science.
    • Probability: Probability is the cornerstone of quantitative financial modeling.
    • Value and Risk: Learn how to account for risk when making quantitative decisions.
  • Probability: Get your odds straight.
    • Probability Warm-ups: Practice the problem-solving skills required for tackling challenging probability questions.
    • Conditional Probability: In a fast-paced market, here's how to update your beliefs in light of new information.
    • Interview Preparation: Tackle two sample interview problems in probability, step-by-step.
  • Expected Value: Strategies to calculate the average outcome of random variables.
    • Expected Value: Trading is often a game of averages. Learn how to quantify them.
    • Expected Utility: When risk is involved, expected values get more complex!
    • Interview Preparation: Tackle a sample interview problem in expected value, step-by-step.
  • Variance: The real way to measure "a crazy day on Wall Street".
    • Variance: Learn essential techniques for modeling the fluctuations of assets and quantifying risk.
    • Covariance: Assets are often correlated. Get to know this tool for measuring how their relative fluctuations affect others.
    • Indicator Variables: Learn a trick for calculating variance that works even when events are dependent.
    • Interview Preparation: Tackle a sample interview problem in variance, step-by-step.
  • Statistics: Your model looks good, but are the results statistically significant?
    • Statistics: Statistics gathers information from samples to make inferences about the overall population.
    • Normal Distributions: Though it's not a perfect model, this distribution remains at the core of many pricing algorithms.
    • Log-normal Distributions: Get familiar with one of the most common distributions used to model asset prices.
  • Confidence and Estimation: Learn how to estimate and how confident you should be.
    • Hypothesis Testing: Hypothesis testing helps determine if your model is actually consistent with the real-world data.
    • Parameter Estimation: Given some 'true' model, what are the parameters for that model that fit the data?
    • Fermi Estimates: Learn how to quickly estimate values which would require extensive analysis to determine exactly.
  • Matrices: The arithmetic of linear algebra for regression, Markov chains, and more.
    • Operations: Brush up on matrix operations: addition, multiplication, transpose, and trace.
    • Inverses: Matrix inversion is an important tool to have on your belt when you're solving matrix equations.
    • Linear Systems: For large, real-world systems, this matrix approach is more effective than other ad-hoc techniques.
    • Covariance: Learn how to represent vector relationships, such as how stocks interact with each other.
  • Markov Chains: Stochastic modeling for the ever-changing markets.
    • An Overview of Markov Chains: Explore a powerful tool for representing systems that change states over time.
    • Stationary Distributions: Learn how to find the 'steady state' of an evolving system.
    • Transience and Recurrence: These advanced tools allow you to calculate the expected steps between states and much more.

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