9 Running Monte Carlo simulations

Monte Carlo simulations are a powerful and versatile tool used to model and analyze complex systems and processes across many fields. They are named after the Monte Carlo Casino in Monaco, reflecting the reliance on random sampling methods, which are reminiscent of the inherent randomness in gambling. This connection stems from early applications of these methods in probabilistic studies during the mid-20th century. The basic idea behind Monte Carlo simulations is to use random sampling to generate a range of possible outcomes for a given problem. These outcomes can then be analyzed to understand the probability distribution and potential variability of the results. This approach is particularly useful when analytical solutions are impractical or impossible, such as in systems with high complexity, nonlinear relationships, or numerous interacting variables. Monte Carlo simulations provide a way to approximate solutions in these challenging scenarios.

9.1 Applications and benefits of Monte Carlo simulations

9.2 Step-by-step process

9.3 Hands-on approach

9.3.1 Establishing a probability distribution (step 1)

9.3.2 Computing a cumulative probability distribution (step 2)

9.3.3 Establishing an interval of random numbers for each variable (step 3)

9.3.4 Generating random numbers (step 4)

9.3.5 Simulating a series of trials (step 5)

9.3.6 Analyzing the results (step 6)

9.4 Automating simulations on discrete data

9.4.1 Plotting and analyzing the results

9.5 Automating simulations on continuous data

9.5.1 Predicting stock prices with Monte Carlo simulations

9.5.2 Analyzing historical data (step 1)

9.5.3 Calculating log returns (step 2)

9.5.4 Computing statistical parameters (step 3)

9.5.5 Generating random daily returns (step 4)

9.5.6 Simulating prices (step 5)

9.5.7 Simulating multiple trials (step 6)

9.5.8 Analyzing the results (step 7)