Leveraging Monte Carlo simulations

Monte Carlo Simulations in Python

Izzy Weber

Curriculum Manager, DataCamp

Wide applicability

Monte Carlo simulations are used in fields such as...

Finance and business
Engineering
Physical sciences

Stock price prediction

A graph showing simulated stock prices over time

¹ https://marketxls.com/monte-carlo-simulation-excel

Risk management

A graph showing VaR confidence interval

¹ https://www.investopedia.com/articles/04/092904.asp https://corporatefinanceinstitute.com/course/modeling-risk-monte-carlo-simulation/

Binding site identification

protein binding site graphic

¹ https://pubs.rsc.org/en/content/articlelanding/2020/ra/d0ra01127d

Reliability analysis in engineering

a graph showing safe and failure domains

¹ www.researchgate.net/publication/228814883_Probabilistic_Transformation_Method_in_Reliability_Analysis

Benefits of Monte Carlo Simulations

Take into consideration a range of values for various inputs
Show not only what could happen, but how likely each outcome is
Make it easy to visualize the range of possible outcomes
Can examine what would have happened under different circumstances

optimize with Monte Carlo simulations

Bags of biased dice

Roll two separate dice from two bags, each containing three biased dice:

bag1 = [[1, 2, 3, 6, 6, 6], [1, 2, 3, 4, 4, 6], [1, 2, 3, 3, 3, 5]]
bag2 = [[2, 2, 3, 4, 5, 6], [3, 3, 3, 4, 4, 5], [1, 1, 2, 4, 5, 5]]

Simulation:

Pick one die from each bag randomly; roll both dice
Success if the dice outcomes add up to eight; otherwise, failure
We want to calculate the probability of success for each unique combination of dice

Biased dice simulation

def roll_biased_dice(n):
    results = {}

    for i in range(n):
        bag_index1 = random.randint(0, 2)
        die_index1 = random.randint(0, 5)
        bag_index2 = random.randint(0, 2)
        die_index2 = random.randint(0, 5)

        point1 = bag1[bag_index1][die_index1]
        point2 = bag2[bag_index2][die_index2]

        key = "%s_%s" % (point1, point2)

        if point1 + point2 == 8: 
            if key not in results:
                results[key] = 1
            else:
                results[key] += 1

Biased dice results

dice1_dice2	probability_of_success
6_2	5.54
3_5	2.67
2_6	1.45
4_4	4

Biased dice results

bag1 = [[1, 2, 3, 6, 6, 6], [1, 2, 3, 4, 4, 6], [1, 2, 3, 3, 3, 5]]
bag2 = [[2, 2, 3, 4, 5, 6], [3, 3, 3, 4, 4, 5], [1, 1, 2, 4, 5, 5]]

Simulation results of 10,000 trials: a bar chart showing probabilities of dice combination success

Biased dice results

bag1 = [[2, 2, 3, 4, 6, 6], [1, 2, 2, 4, 6, 6], [1, 2, 3, 3, 3, 3]]
bag2 = [[1, 2, 3, 4, 5, 6], [1, 3, 3, 4, 4, 6], [2, 2, 2, 3, 5, 5]]

Simulation results of 10,000 trials: a bar chart showing probabilities of dice combination success

Limitations of Monte Carlo simulations

Model output is only as good as model input
Probability of extreme events is often underestimated

Let's practice!

Monte Carlo Simulations in Python