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Trading stock volatility with the Ornstein-Uhlenbeck process

Understanding and modelling volatility accurately is of utmost importance in financial mathematics. The emergence of volatility clustering in financial markets can make estimating volatility very difficult. Here we explain how to use a stochastic model called Ornstein-Uhlenbeck process to model volatility. We explain the mathematics of using a method called Maximum Likelihood Estimation (MLE) to estimate the parameters of the Ornstein-Uhlenbeck process based on S&P500 historical/realised volatility. We also explain how to derive the dynamics of the stochastic process using Ito Calculus, this is required for deriving the Probability Density Function (PDF) of the Ornstein-Uhlenbeck process used in the MLE method. Finally, we simulate the volatility using the continuous-time stochastic process at a particular time step with no approximations, and also create sample paths using Euler method to discretize the stochastic differential equation (SDE). ★ ★ Code Available on GitHub ★ ★ GitHub: https://github.com/TheQuantPy Specific Tutorial Link: https://github.com/TheQuantPy/youtube... 00:00 Intro 01:43 Volatility Clustering 04:20 Using MLE for estimating model parameters 11:00 Determining distribution of Ornstein-Uhlenbeck process 14:51 Using MLE for Ornstein-Uhlenbeck Volatility Model 18:36 Simulating Volatility Model in Python ★ ★ QuantPy GitHub ★ ★ Collection of resources used on QuantPy YouTube channel. https://github.com/thequantpy ★ ★ Discord Community ★ ★ Join a small niche community of like-minded quants on discord.   / discord   ★ ★ Support our Patreon Community ★ ★ Get access to Jupyter Notebooks that can run in the browser without downloading python.   / quantpy   ★ ★ ThetaData API ★ ★ ThetaData's API provides both realtime and historical options data for end-of-day, and intraday trades and quotes. Use coupon 'QPY1' to receive 20% off on your first month. https://www.thetadata.net/ ★ ★ Online Quant Tutorials ★ ★ WEBSITE: https://quantpy.com.au ★ ★ Contact Us ★ ★ EMAIL: [email protected] Disclaimer: All ideas, opinions, recommendations and/or forecasts, expressed or implied in this content, are for informational and educational purposes only and should not be construed as financial product advice or an inducement or instruction to invest, trade, and/or speculate in the markets. Any action or refraining from action; investments, trades, and/or speculations made in light of the ideas, opinions, and/or forecasts, expressed or implied in this content, are committed at your own risk an consequence, financial or otherwise. As an affiliate of ThetaData, QuantPy Pty Ltd is compensated for any purchases made through the link provided in this description.