Markov Chains for Quant Finance

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*🚀 Master Quantitative Skills with Quant Guild* https://quantguild.com *📅 Meet with me 1:1* https://calendly.com/quantguild-support *📈 Interactive Brokers for Algorithmic Trading* https://www.interactivebrokers.com/mkt/?src=quantguildY&url=%2Fen%2Fwhyib%2Foverview.php *👾 Join the Quant Guild Discord server here* https://discord.com/invite/MJ4FU2c6c3 ___________________________________________ *🪐 Jupyter Notebook* https://github.com/romanmichaelpaolucci/Quant-Guild-Library/blob/main/2025%20Video%20Lectures/49.%20Markov%20Chains%20for%20Quant%20Finance/markov_chains.ipynb TL;DW Executive Summary: - When modeling something as a random variable *independence* is way too strong of an assumption that can lead to extremely inaccurate models - A major correction can be applied by considering the simplifying assumption of local conditional dependence rather than full independence - Markov chains effectively model these dynamics and enable us to estimate probabilities and expectations from an initial state given a local dependency structure - The transition matrices and corresponding probabilities can be easily estimated from data using the result from MLE - Though Markov chains aid in the modeling process offering more *accurate* or *reasonable* estimates there are many assumptions that are still violated in practice - Typically, Markov chains are a first step in the modeling process (regime switching or HMM models, for example) - understanding them is the first step toward more comprehensive applications I hope you enjoyed! - Roman ___________________________________________ *📖 Chapters:* 00:00 - Markov Chains 03:59 - Random Variables 07:11 - Modeling Uncertain Events 11:27 - Stochastic Processes 13:22 - Independence 14:28 - Real World Example 20:15 - Markov Chains 25:04 - State Transition Probabilities 27:40 - Multi-Step Transition Probabilities 29:53 - Example: Multi-Step State Transition Probability 31:12 - Example: State Distribution Vector 36:48 - Key Properties of Markov Chains 37:26 - Applying Markov Chains in the Real World 38:55 - Maximum Likelihood Estimation (MLE) 41:38 - Real World Quant Model 43:49 - Key Properties and Assumptions of the MLE 46:02 - TL;DW Executive Summary ___________________________________________ *🗣️ Shout Outs* A special thank you to my members on YouTube for supporting my channel and enabling me to continue to create videos just like this one! *⭐ Quant Guild Directors* Dr. Jason Pirozzolo ___________________________________________ *▶️ Related Videos* *Quant Builds 🔨* How to Build an Options Volatility Trading Tool in Python with Interactive Brokers https://youtu.be/_hFw36wfmds How to Build a Volatility Trading Dashboard in Python with Interactive Brokers https://youtu.be/19-rFVgJVkg *Statistics and Trading Profitability Over Time (Edge) 📈* Expected Stock Returns Don't Exist https://youtu.be/iXNSBn5xqrA How to Trade https://youtu.be/NqOj__PaMec How to Trade Option Implied Volatility https://youtu.be/kQPCTXxdptQ How to Trade with an Edge https://youtu.be/NlqpDB2BhxE How to Trade with the Kelly Criterion https://youtu.be/7tvW3NvRnPk Quant Trader on Retail vs Institutional Trading https://youtu.be/j1XAcdEHzbU Quant on Trading and Investing https://youtu.be/CKXp_sMwPuY ___________________________________________ *🗂️ Resources* *📚 Quant Guild Library:* https://github.com/romanmichaelpaolucci/Quant-Guild-Library *🌎 GitHub:* https://github.com/RomanMichaelPaolucci https://github.com/Quant-Guild *📝 Medium (Blog):* https://quantguild.medium.com/ https://medium.com/quant-guild ___________________________________________ *🛠️ Projects* *The Gaussian Cookbook:* https://gaussiancookbook.com *Recipes for simulating stochastic processes:* https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5332011 ___________________________________________ *💬 Socials* *TikTok:* https://www.tiktok.com/@quantguild *Instagram:* https://www.instagram.com/quantguild/ *X/Twitter:* https://x.com/quantguild/ *LinkedIn (personal):* https://www.linkedin.com/in/rmp99/ *LinkedIn (company):* https://www.linkedin.com/company/quant-guild ___________________________________________