quantgirluk / aleatory

📦 Python library for Stochastic Processes Simulation and Visualisation

aleatory

• Git Homepage
• Pip Repository
• Documentation

Overview

The aleatory (/ˈeɪliətəri/) Python library provides functionality for simulating and visualising stochastic processes. More precisely, it introduces objects representing a number of continuous-time stochastic processes $X = (X_t : t\geq 0)$ and provides methods to:

• generate realizations/trajectories from each process —over discrete time sets
• create visualisations to illustrate the processes properties and behaviour

Currently, aleatory supports the following processes:

• Brownian Motion
• Brownian Bridge
• Brownian Excursion
• Brownian Meander
• Geometric Brownian Motion
• Ornstein–Uhlenbeck
• Vasicek
• Cox–Ingersoll–Ross
• Constant Elasticity
• Bessel Process
• Squared Bessel Processs

Installation

Aleatory is available on pypi and can be installed as follows

pip install aleatory

Dependencies

Aleatory relies heavily on

• numpy for random number generation
• scipy and statsmodels for support for a number of one-dimensional distributions.
• matplotlib for creating visualisations

Compatibility

Aleatory is tested on Python versions 3.8, 3.9, 3.10, and 3.11

Quick-Start

Aleatory allows you to create fancy visualisations from different stochastic processes in an easy and concise way.

For example, the following code

from aleatory.processes import BrownianMotion

brownian = BrownianMotion()
brownian.draw(n=100, N=100, colormap="cool", figsize=(12,9))

generates a chart like this:

For more examples visit the Quick-Start Guide.

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aleatory's Issues

Paths fail to plot when there is only 1 histogram bin

Very nice package! I'm learning stochastic calculus and this is a really cool tool!

I found a small bug:
The paths plotted by SPExplicit.draw() are colored to match the histogram bin that their final point falls into.
If we plot N=3 or fewer paths, then we set n_bins = int(np.sqrt(N)) <= 1, and then this logic which helps set the path colors:

bin_centers = 0.5 * (bins[:-1] + bins[1:])
col = bin_centers - min(bin_centers)  # scale values to interval [0,1]
col /= max(col)

results in a divide by zero

/Users/alexrubin/code/aleatory/aleatory/utils/utils.py:76: RuntimeWarning: invalid value encountered in divide
    col /= max(col)

because col == [0.].

It seems like the 3 lines of logic above could be replaced by col = np.linspace(0, 1, n_bins, endpoint=True).

multivariate support in aleatory?

Hi there -

Very impressive package and thank you for making public!

I had an enhancement question.

Was curious if this package is planned to support multivariate processes? If I say have X commodities following various processes, with correlated random shocks.

Say two commodities, define one as GBM and the other as UO, with 70% correlation in their random draw direction. Is something like this currently feasible or something in the future plans?

My background in stochastic processes is in R, and can only point to MASS::mvrnorm as an example of the correlated draws.

Cheers!

Mistake in Vasicek definition?

Hi, I liked your package, thank you!

I believe there is a mistake in the Vasicek function

def g(x, _): return self.sigma

It should be

def g(x, _): return self.sigma * x

right?

Add fractional Brownian motion

Add simulation for fBM.
Note that there are several implementations.