In today’s post I will provide another example that shows how numba can speed up a numerical simulation. I apply the module to a monte-carlo simulation of stock price random walks. This is a popular monte-carlo simulation example and I also provided and example of this in a blog post several years ago.

Monte-carlo simulation with numba in Python

In below code segment I import relevant modules and parts of modules. As I pointed out in an earlier post numba works very well with numpy, for example, but not that well with pandas. I implement two versions of a price random walk monte-carlo simulation. Both simulations repeat n random walks that have a duration of 365 days. Each day the price movement is randomly distributed in accordance with a random normal distribution with specified mean daily return and specified standard deviation of daily returns.

import numpy as np
from matplotlib import pyplot as plt
import random
import time
from numba import njit

def random_walker(n: int, length: int) -> np.ndarray:

    arr = np.zeros((n, length), dtype = float)

    for i in range(n):

        idx = 100

        for j in range(length):
            
            idx += idx*random.gauss(0.00015, 0.02)

            arr[i, j] = idx
    
    return arr

@njit
def nb_random_walker(n: int, length: int) -> np.ndarray:

    arr = np.zeros((n, length), dtype = float)

    for i in range(n):

        idx = 100

        for j in range(length):
            
            idx += idx*random.gauss(0.00015, 0.02)

            arr[i, j] = idx
    
    return arr

I now execute the random simulation runs. First, I run the simulation without numba. I do so two times. For each run I register the duration of simulation execution and print it into the terminal. After that I execute the numba-optimized simulation for a total of three times. For each time I print simulation runtime into the terminal for the purpose of being able to compare simulation runtimes.

You can see the code below:

# --- monte carlo run without numba ------------------
starttime = time.time()
arr = random_walker(10000, 365)
endtime = time.time()

print("monte carlo random walk without NUMBA; 1st time: ")
print(endtime-starttime)

starttime = time.time()
arr = random_walker(10000, 365)
endtime = time.time()

print("monte carlo random walk without NUMBA; 2nd time: ")
print(endtime-starttime)

# --- monte carlo run with numba --------------------
starttime = time.time()
arr = nb_random_walker(10000, 365)
endtime = time.time()

print("monte carlo random walk with NUMBA; 1st time: ")
print(endtime-starttime)

starttime = time.time()
arr = nb_random_walker(10000, 365)
endtime = time.time()

print("monte carlo random walk with NUMBA; 2nd time: ")
print(endtime-starttime)

starttime = time.time()
arr = nb_random_walker(10000, 365)
endtime = time.time()

print("monte carlo random walk with NUMBA; 3rd time: ")
print(endtime-starttime)

The output is as follows:

monte carlo random walk without NUMBA; 1st time: 
1.9413235187530518
monte carlo random walk without NUMBA; 2nd time: 
1.8833050727844238
monte carlo random walk with NUMBA; 1st time: 
0.6361069679260254
monte carlo random walk with NUMBA; 2nd time: 
0.07375526428222656
monte carlo random walk with NUMBA; 3nd time: 
0.07474732398986816

In this case numba improved monte-carlo simulation runtime by almost factor 3 in the first run. For the second run and for every run after that the optimized monte-carlo simulation is more than 25 times faster! The first time the numba-optimized function is called it has to be “compiled”. For every call after that the function executes even faster – as you can see from above test results!

And by the way, this is what the random walks look like:

Final remarks and related content

In this article I demonstrated how numba, a module in Python, makes monte-carlo simulations significantly faster. However, you must be aware of the constraints that come along with this module. As I pointed out you will be able to get the most out of numba if you have a numerical framework. Furthermore, be aware of the modules and packages that work well with numba – and the ones that don’t. For example, numpy works well with numba while pandas does not.

You can read more here:

• Link: https://github.com/LinnartSF?tab=repositories

You can also see another example in Pyhton here:

• Link: Faster Python simulations

Linnart Felkl

Data scientist focusing on simulation, optimization and modeling in R, SQL, VBA and Python