Hands-On Machine Learning for Algorithmic Trading

How to dynamically estimate the probabilities of asset price moves

When the data consists of binary Bernoulli random variables with a certain success probability for a positive outcome, the number of successes in repeated trials follows a Binomial distribution. The conjugate prior is the Beta distribution with support over the interval [0, 1] and two shape parameters to model arbitrary prior distributions over the success probability. Hence, the posterior distribution is also a Beta distribution that we can derive by directly updating the parameters.

We will collect samples of different sizes of binarized daily S&P 500 returns, where the positive outcome is a price increase. Starting from an uninformative prior that allocates equal probability ...