In one of my posts I have introduced the concept of random walk forecasting, using Python for implementation. In this post I want to conduct a monte-carlo simulation in Python. More specifically, I will use monte-carlo simulation in Python to assess risks associated with stock price volatility.

## Setting up data for monte-carlo simulation in Python

For this I will use a the following fictional stock price history:

# declare list with fictional daily stock closing prices history_prices = [180,192,193,195,191,199,198,200,199,203,205,207,205,208,201,203,204,201,205,206,207] print(stockPrices)

[180, 192, 193, 195, 206, 211, 191, 204, 215, 190, 205, 207, 205, 211, 222, 215, 245, 201, 205, 206, 214]

I now proceed to importing relevant modules. Most importantly I need to use a module for visualizing the random walks and simulation. And, I need a module for generating random numbers.

## Modules for monte-carlo simulation in Python

In preparation of next steps I will now import all relevant Python modules:

# import statistics for calculating e.g. standard deviation of price history import statistics as stat # import pyplot for plotting import matplotlib.pyplot as plt # import random for random number generations import random as rnd

Assuming random stock price movement I derive standard deviation from relative changes in fictional price history such that I will be be able to model random stock price movements:

relative_prices = [] for i in range(0,len(history_prices)): if i == 0: pass else: relative_prices.append((history_prices[i]-history_prices[i-1])/(history_prices[i-1])) std_prices = stat.stdev(relative_prices) print(std_prices)

0.021375589655016836

Having modules and statistics in place I now model a random walk. I will need random walks for conducting the monte-carlo simulation in Python.

## Modeling a random walk as part of the simulation

Now I model one exemplaric random price walk for 100 days into the future, assuming random price movement based on the standard deviation of random prices. I assume a random normal distribution. The last known price in history serves as starting point:

# modeling a random price walk over 100 days # -- conduct calculation, define function def randomWalk(stdev,pastPrices): days = [i for i in range(1,101)] prices = [] price = pastPrices[-1] for i in range(1,101): price = price + price*rnd.normalvariate(0,stdev) prices.append(price) return([days,prices]) # -- conduct calculation, use function prices = randomWalk(std_prices,history_prices) # -- visualize random walk in a line plot plt.plot(prices[0],prices[1]) plt.title("random price walk") plt.xlabel("day") plt.ylabel("stock price")

Text(0, 0.5, 'stock price')

I successfully implemented and visualized a random walk. A random walk represents one possible price development trajectory. The random walk is based on historic probability, i.e. historic data. If I conduct several random walks then I can make a statement about the risk associated with the stock. Several random walks together form a monte-carlo simulation. In the next section I will implement a monte-carlo simulation in Python using above random walk model.

## Implementing the simulation model

I can repeat this process, by re-calculating additional random walks, thereby creating a monte-carlo simulation of stock price movements. In below example I repeat the random walk process for 30 separate walks:

plt.figure() for i in range(0,30): prices = randomWalk(std_prices,history_prices) plt.plot(prices[0],prices[1]) plt.title("monte-carlo simulation of stock price development") plt.xlabel("day") plt.ylabel("stock price")

Text(0, 0.5, 'stock price')

## Conclusion and relevant references

In this article I introduced the concept of a monte-carlo simulation. I used random walks of stock price developments to illustrate this. A stock price can be modeled as a random walk, and a monte-carlo simulation is a repetition of several random walks. Such as simulation can be used to evaluate risks associated with stock price volatility.

I have written several other related articles. I list them and other articles below. I recommend them to anyone interested in monte-carlo simulation.

- Link: Monte-carlo simulation in R for warehouse location risk assessment
- Link: Monte-carlo animation in R with gganimate
- Link: Simulation techniques for SCM analysts
- Link: Monte-carlo simulation definition for investors

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

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