SMART Trading Strategies

Tag: Brownian Motion

  • Algorithmic Trading by EP Chan (Notes Part 1)

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    This post summarizes some notes that I took from the book “Algorithmic Trading” by Ernest Chan. I’m already familiar with some concepts, so these notes only cover the new concepts I learned. I strongly recommend that you buy the book (it’s a good book) for more details and information. Chapter 1: Backtesting and Automated Execution…

  • Brownian Motion 2

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    This is just another post that discusses the Brownian Motion (based on the MIT OpenCourseWare lecture embedded below).

  • Probability Density Functions for Random Walk

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    If Xt is a random walk that starts from 0 at t=0, Xt​~N(μt,σ2t). Its probability density is given by For a pure Brownian motion (which is a continuous RW), μ = 0 and σ = 1. This PDF satisfies the diffusion equation. For a random walk that starts elsewhere, its probability density is given by…

  • Itô Processes and Itô’s Lemma

    Itô Processes and Itô’s Lemma

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    Itô process is like a generalized random walk and Itô’s lemma gives us a formula for doing calculus with Itô processes. Itô Process An Itô process is defined as a stochastic process of the form where X and B are both time dependent and B is a Guassian Brownian random variable. adt is a deterministic…

  • Brownian Motion

    Brownian Motion

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    In this post, we are going to scale the random walk to change it from a discrete time model to a continuous time model. This is going to give us a Brownian motion. Let us first declare Ba,b as a Brownian motion with a time step of “a” and a total duration of “b”. We…