Maximum likelihood estimation of GARCH parameters (FRM T2-26)

[My xls is here https://trtl.bz/2NlLn7d] GARCH(1,1) is the popular approach to estimating volatility, but its disadvantage (compared to STDDEV or EWMA) is that you need to fit three parameters. Maximum likelihood estimation, MLE, is an immensely useful statistical approach that can be used to find "best fit" parameters. In this video, I replicate John Hull's example (the data is S&P 500 index values) to find the best fit alpha (α), beta (β), and omega (ω). Keep in mind that the long-run variance = ω/(1 - α - β), such that indirectly this is solving for a long-run (aka, unconditional) variance. Discuss this video here in our forum: https://trtl.bz/2QhZY6u Subscribe here https://www.youtube.com/c/bionicturtl... to be notified of future tutorials on expert finance and data science, including the Financial Risk Manager (FRM), the Chartered Financial Analyst (CFA), and R Programming! If you have questions or want to discuss this video further, please visit our support forum (which has over 50,000 members) located at http://bionicturtle.com/forum You can also register as a member of our site (for free!) at https://www.bionicturtle.com/register/ Our email contact is [email protected] (I can also be personally reached at [email protected]) For other videos in our Financial Risk Manager (FRM) series, visit these playlists: Texas Instruments BA II+ Calculator    • Texas Instruments BA II+ Calculator   Risk Foundations (FRM Topic 1)    • Risk Foundations (FRM Topic 1)   Quantitative Analysis (FRM Topic 2)    • Quantitative Analysis (FRM Topic 2)   Financial Markets and Products: Intro to Derivatives (FRM Topic 3, Hull Ch 1-7)    • Financial Markets and Products: Intro to D...   Financial Markets and Products: Option Trading Strategies (FRM Topic 3, Hull Ch 10-12)    • Financial Markets and Products: Option Tra...   FM&P: Intro to Derivatives: Exotic options (FRM Topic 3)    • FM&P: Intro to Derivatives: Exotic options...   Valuation and Risk Models (FRM Topic 4)    • Valuation and RIsk Models (FRM Topic 4)   Coming Soon .... Market Risk (FRM Topic 5) Credit Risk (FRM Topic 6) Operational Risk (FRM Topic 7) Investment Risk (FRM Topic 8) Current Issues (FRM Topic 9) For videos in our Chartered Financial Analyst (CFA) series, visit these playlists: Chartered Financial Analyst (CFA) Level 1 Volume 1    • Level 1 Chartered Financial Analyst (CFA ®...   #bionicturtle #risk #financialriskmanager #FRM #finance #expertfinance Our videos carefully comply with U.S. copyright law which we take seriously. Any third-party images used in this video honor their specific license agreements. We occasionally purchase images with our account under a royalty-free license at 123rf.com (see https://www.123rf.com/license.php); we also use free and purchased images from our account at canva.com (see https://about.canva.com/license-agree.... In particular, the new thumbnails are generated in canva.com. Please contact [email protected] or [email protected] if you have any questions, issues or concerns.