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Brownian Motion for Financial Mathematics | Brownian Motion for Quants | Stochastic Calculus

In this tutorial we will investigate the stochastic process that is the building block of financial mathematics. We will consider a symmetric random walk, scaled random walk and Brownian motion. The mathematic notation and explanations are from Steven Shreve's book Stochastic Calculus for Finance II. Important properties of Brownian motion are that it is a martingale (Markov process) and that it accumulates quadratic variation at rate one per unit time. Note: Quadratic Variation is perhaps what makes Stochastic Calculus so different from Ordinary Calculus. ★ ★ Code Available on GitHub ★ ★ GitHub: https://github.com/TheQuantPy Specific Tutorial Link: https://github.com/TheQuantPy/youtube... 00:00 Intro 02:24 Symmetric Random Walk 06:55 Quadratic Variation 09:08 Scaled Symmetric Random Walk 10:20 Limit of Binomial Distribution 12:10 Brownian Motion ★ ★ 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.