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.

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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

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