A few weeks ago, on 2023-10-02, I announced esgtoolkit v1.0.0 for Python.

Well, v1.0.0 for Python is more like a proof of concept as of today, as there isn’t an exact mapping with the R API so far. Next week, most likely in a v1.1.0 for both, the Python version will be aligned with the R version – as much as possible.

For those who aren’t familiar with esgtoolkit yet, I’ve been developing and maintaining it (with a lot of roller coasters, still not sure why) for R since 2014. e.s.g here, stands for Economic Scenarios Generators, but the name has become less relevant since diffusion models are widely used in Physics and – more recently – in Generative AI (for images).

You can read this document (focusing on quantitative finance) for an introductory review: https://www.researchgate.net/publication/338549100_ESGtoolkit_a_tool_for_stochastic_simulation_v020.

Examples of use of esgtoolkit in Python

1 - Install and import packages

!pip install matplotlib numpy pandas esgtoolkit

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from esgtoolkit import simdiff

2 - Code examples

2 - 1 Ornstein-Uhlenbeck process

kappa = 1.5
V0 = theta = 0.04
sigma_v = 0.2
theta1 = kappa * theta
theta2 = kappa
theta3 = sigma_v

sims_OU = simdiff(
    n=7,
    horizon=5,
    frequency="quarterly",
    model="OU",
    x0=V0,
    theta1=theta1,
    theta2=theta2,
    theta3=theta3,
)

print(sims_OU)

      Series 1  Series 2  Series 3  Series 4  Series 5  Series 6  Series 7
0.00  0.040000  0.040000  0.040000  0.040000  0.040000  0.040000  0.040000
0.25 -0.007010 -0.049564 -0.018269  0.071842  0.040483 -0.019586  0.049868
0.50 -0.011616 -0.039839 -0.017487  0.019752  0.072648  0.020594 -0.032688
0.75  0.135263 -0.100929 -0.105646 -0.001864  0.031349  0.005971 -0.051103
1.00  0.111387 -0.117995  0.121822 -0.074206  0.088102 -0.012538 -0.044094
1.25  0.099907 -0.121014  0.197554 -0.128390  0.054566 -0.075927  0.136858
1.50  0.225026 -0.212136  0.054084 -0.050274  0.077840 -0.043452  0.051887
1.75  0.205826 -0.063020  0.015887  0.015550  0.158005 -0.083190  0.067913
2.00  0.047863 -0.017940 -0.015713  0.027641  0.157605 -0.184567  0.065723
2.25 -0.012206 -0.095284  0.067129  0.108862  0.093491 -0.146234 -0.022997
2.50 -0.033261  0.052185  0.051653  0.259280  0.173120 -0.010915 -0.009278
2.75  0.092319  0.084145  0.069256  0.149523  0.214823 -0.043251  0.127294
3.00  0.106138  0.045591  0.057713 -0.078409  0.206151  0.033776  0.137867
3.25  0.119071  0.118922  0.048578  0.042976  0.174218 -0.099979  0.110721
3.50  0.103628  0.167896  0.160688 -0.017439  0.079580 -0.060866  0.053169
3.75  0.037109  0.196812  0.104011 -0.057185  0.181329  0.014241 -0.123167
4.00  0.187892  0.205535  0.211189  0.059226  0.086787  0.047556  0.022749
4.25  0.183402  0.200231  0.027754  0.029329  0.255620  0.054057 -0.094369
4.50 -0.026393  0.144932  0.080618 -0.069723  0.316742 -0.004079  0.009713
4.75  0.053196  0.086456  0.078305 -0.020204  0.210432 -0.061564  0.179312
5.00  0.009414  0.040016  0.084439 -0.013027  0.071045 -0.115703  0.014640

2 - 2 Geometric Brownian motion

sims_GBM = simdiff(
    n=10,
    horizon=5,
    frequency="semi-annual",
    model="GBM",
    x0=V0,
    theta1=theta1,
    theta2=theta2,
    theta3=theta3,
)

print(sims_GBM)

     Series 1  Series 2      Series 3  Series 4  Series 5  Series 6  Series 7  \
0.0  0.040000  0.040000  4.000000e-02  0.040000  0.040000  0.040000  0.040000   
0.5  0.012960  0.086032  7.566884e-03  0.036919  0.011241  0.030725  0.035130   
1.0  0.005961  0.073984  3.525718e-03  0.015851  0.005294  0.017501  0.012107   
1.5  0.018284  0.066449  6.972174e-04  0.024051  0.000812  0.009819  0.004992   
2.0  0.011569  0.043875  1.889517e-04  0.035840  0.004758  0.024617  0.000995   
2.5  0.007791  0.014286  5.717045e-05  0.050299  0.010060  0.011376  0.000187   
3.0  0.028206  0.055817  5.609877e-06  0.061307  0.001795  0.033362  0.000152   
3.5  0.027002  0.055569  8.009562e-06  0.064775  0.000687  0.003789  0.000143   
4.0  0.004144  0.004052  5.533457e-06  0.035614  0.000246  0.004136  0.000089   
4.5  0.001174  0.005006  9.715489e-07  0.015116  0.000330  0.002770  0.000139   
5.0  0.000430  0.001780  2.156546e-06  0.005928  0.000178  0.002045  0.000718   

     Series 8  Series 9  Series 10  
0.0  0.040000  0.040000   0.040000  
0.5  0.013951  0.023629   0.067367  
1.0  0.000707  0.020877   0.070761  
1.5  0.001207  0.008273   0.053518  
2.0  0.000334  0.009621   0.016144  
2.5  0.000095  0.004471   0.040134  
3.0  0.000165  0.003732   0.012467  
3.5  0.000071  0.007014   0.074483  
4.0  0.000011  0.006534   0.222215  
4.5  0.000008  0.002715   0.101611  
5.0  0.000004  0.005391   0.020085

3 - Spaghetti plot

#plt.style.use('seaborn-darkgrid')
 
palette = plt.get_cmap('Set1')
 
for num, column in enumerate(sims_GBM):
    
    plt.plot(sims_GBM.index, sims_GBM[column], marker='', color=palette(num), linewidth=1, alpha=0.9, label=column)

# Add legend
plt.legend(loc=1, ncol=2)
 
# Add titles
plt.title("esgtoolkit.simdiff's result for Geometric Brownian Motion", loc='left', fontsize=12, fontweight=0, color='orange')
plt.xlabel("Time")
plt.ylabel("Series")

# Show the graph
plt.show()

Geometric Brownian motion simulations

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