Stochastic Differential Equations for Quant Finance

🚀 Master Quantitative Skills with Quant Guild https://quantguild.com 📈 Interactive Brokers for Algorithmic Trading https://www.interactivebrokers.com/mk... 👾 Join the Quant Guild Discord server here   / discord   ___________________________________________ 🪐 Jupyter Notebook https://github.com/romanmichaelpaoluc... *Roman's Overview of ODE/PDE/SDEs* *ODEs*: representing a function as its derivative which can be solved via analytical or numerical techniques to recover said function *PDEs*: can be constructed using a variety of arguments and used to solve for option prices analytically or numerically (finite-differences) *SDEs*: solutions can be constructed analytically or numerically to produce option prices via the Law of Large Numbers (LLN, Monte Carlo Simulation) *Black-Scholes Model*: The analytical price is given by the solution to the Black-Scholes equation which can be solved analytically or numerically. The argument assumes a geometric Brownian motion, which can ALSO produce prices via Monte Carlo simulation - I have many videos discussing this idea! I hope you enjoyed, this was a long one! Roman ___________________________________________ 📖 Chapters: 00:00 - Introduction 02:57 - Understanding Differential Equations (ODEs) 07:15 - How to Think About Differential Equations 09:59 - Understanding Partial Differential Equations (PDEs) 11:31 - Black-Scholes Equation as a PDE 16:49 - ODEs, PDEs, SDEs in Quant Finance 18:17 - Understanding Stochastic Differential Equations (SDEs) 22:30 - Linear and Multiplicative SDEs 23:34 - Solving Geometric Brownian Motion 37:43 - Analytical Solution to Geometric Brownian Motion 40:22 - Analytical Solutions to SDEs and Statistics 43:21 - Numerical Solutions to SDEs and Statistics 47:29 - Tactics for Finding Option Prices 49:46 - Closing Thoughts and Future Topics ___________________________________________ ▶️ Related Videos Ito's Lemma Clearly and Visually Explained    • Ito's Lemma Clearly and Visually Explained   Ito Integration Clearly and Visually Explained    • Ito Integration Clearly and Visually Expla...   Monte Carlo Simulation and Black-Scholes for Pricing Options    • Monte Carlo Simulation and Black-Scholes f...   Why Monte Carlo Simulation Works    • Why Monte Carlo Simulation Works   Expected Stock Returns Don't Exist    • Expected Stock Returns Don't Exist   How to Trade    • How to Trade   How to Trade with an Edge    • How to Trade with an Edge   ___________________________________________ 🗂️ Resources 📚 Quant Guild Library: https://github.com/romanmichaelpaoluc... 🌎 GitHub: https://github.com/RomanMichaelPaolucci https://github.com/Quant-Guild 📝 Medium (Blog):   / quantguild     / quant   ___________________________________________ 🛠️ Projects The Gaussian Cookbook: https://gaussiancookbook.com Recipes for simulating stochastic processes: https://papers.ssrn.com/sol3/papers.c... ___________________________________________ 💬 Socials TikTok:   / quantguild   Instagram:   / quantguild   X/Twitter: https://x.com/quantguild/ LinkedIn (personal):   / rmp99   LinkedIn (company):   / quant-guild   ___________________________________________