Monte Carlo Simulation (Python) Based on Fizell (2022)

by Nikunj Bhalotia

To understand how to model risks with high variance, I developed a Python script using numpy and pandas to run a Monte Carlo simulation. Instead of relying on a single “average” prediction for future risk exposure (e.g., potential financial loss), the simulation generated 1,000 random iterations based on historical volatility.

  • Key Concept Applied: The script used norm.ppf (Percent Point Function) to generate random variables within a specified mean and standard deviation, effectively simulating “black swan” events and best/worst-case scenarios.
  • Outcome: The output provided a probability distribution rather than a single number. This allowed me to state with 95% confidence that the potential risk exposure would fall within a specific range, providing a far more defensible metric for stakeholders than a “High/Medium/Low” label.

Description: This script simulates 1,000 potential outcomes for a financial risk scenario (e.g., cost of a data breach) using historical volatility data. It calculates the 95% confidence interval (Value at Risk).

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.stats import norm
# --- CONFIGURATION ---
# Scenario: Estimating potential financial loss from a supply chain disruption
# Based on historical data, we assume a normal distribution of daily loss.
simulations = 1000          # Number of iterations
days_to_forecast = 30       # Duration of the risk event
avg_daily_loss = 5000       # Mean daily loss in GBP
std_dev_loss = 1500         # Volatility (Standard Deviation)
# --- MONTE CARLO SIMULATION ---
def run_simulation():
    results = []
    
    for i in range(simulations):
        # Generate random daily losses based on normal distribution
        # norm.ppf converts a random percentage (0-1) to a value on the distribution curve
        daily_losses = norm.ppf(np.random.rand(days_to_forecast), loc=avg_daily_loss, scale=std_dev_loss)
        
        # Cumulative sum of losses for this 30-day iteration
        total_event_cost = daily_losses.sum()
        results.append(total_event_cost)
    
    return np.array(results)
# --- EXECUTION & ANALYSIS ---
simulated_costs = run_simulation()
# Calculate Key Metrics
mean_cost = np.mean(simulated_costs)
worst_case = np.percentile(simulated_costs, 95) # 95th percentile (Value at Risk)
best_case = np.percentile(simulated_costs, 5)   # 5th percentile
print(f"--- RISK FORECAST (30 DAYS) ---")
print(f"Mean Expected Cost: £{mean_cost:,.2f}")
print(f"95% Confidence Worst Case: £{worst_case:,.2f}")
print(f"5% Confidence Best Case: £{best_case:,.2f}")
# Optional: Visualization code would go here
# plt.hist(simulated_costs, bins=50)

References:

Fizell, Z. (2022) How to Create a Monte Carlo Simulation using Python. Available at: https://towardsdatascience.com/how-to-create-a-monte-carlo-simulation-using-python-c24634a0978a/

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