Markov Chains (and HMM) for Quantitative Finance Modeling

This episode provides a detailed explanation of Markov chains and their application in quantitative finance, specifically demonstrating how they can model the transitions within a portfolio of loans to avoid the pitfalls of assuming naive independence. The source begins by introducing random variables and stochastic processes, then uses a real-world example of loan delinquency states (e.g., current, 30-59 days late) to illustrate why the Markov property—which assumes the future state depends only on the current state—is superior to assuming that each transition is entirely independent. The video then explains key concepts like the state transition diagram, the transition matrix, and how the Chapman-Kolmogorov equation allows for calculating multi-step transition probabilities. Finally, the source discusses how to estimate these probabilities using maximum likelihood estimation (MLE) and briefly mentions advanced topics like hidden Markov models and regime switching models as future areas of study