The Stochastic Ledger

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Stochastic Ledger

Some properties of stochastic processes

In a past note we built up an intuitive idea of stochastic processes. Here we discuss a number of important properties. First, let's recall the definition of a stochastic process. Definition (Stochastic process): Let \( T \) be an index set. A stochastic process with state space \( (E,\mathcal E)

Price consolidation and an application of the Jaccard Index

Yesterday, while working on one of my projects to do with quantifying areas of concentrated liquidity, I arrived at a possibly interesting application of, and use for, the Jaccard Index. The problem was to construct some sort of normalised measure for the overlap of price bars. I basically defined a

Stochastic processes

We will talk frequently about stochastic processes on this blog. They are fundamental to quantitative finance, and a basic understanding of stochastic calculus will be an important prerequisite for many of the topics considered later. We start with a basic introduction to discrete time stochastic processes, in which the time

The mathematics of Black–Scholes, and why it is not predictive

There is a certain elegance to the Black–Scholes equation. From a particular vantage, it looks like physics. It has a diffusion term, a drift term, a boundary condition, and a solution that appears to give randomness structure. For anyone with a physics background and familiarity with stochastic processes, statistical

Digital markets and their structure

While drafting the inaugural entry on price action and the theory of market structure, I found myself thinking about how to organise a series of posts that introduce the technical and quantitative details. In the process, I realised there is a still a question of motivation. To satisfy this question,

Price action and the microstructure theory of markets

I find financial markets fascinating, not only as a venue for trading but also as a source of rich statistical structure. Whilst price action may at first seem random, with explanation as to the behaviour of price charts appearing subjective, price action is not “random” in a coin-flip sense.