5. Bond Default Simulations with Binomial Distribution. You hold a portfolio of 100 bonds and each has a default probability of 0.05. To understand the variability in possible default outcomes, you will simulate default in the portfolio 10 times using the Binomial distribution and plot the results as a histogram.

To simulate default counts multiple times, you can use the rbinom(n_sims, n_bonds, prob) function in R, where n_sims is the number of simulations, n_bonds is the number of bonds, and p is the default probability for a single bond.

Simulate bond default 10 times and visualize the results using a histogram.

# Define the number of bonds. n_bonds <- ___ # Define the default probability. p <- ___ # Define the number of simulations. n_sims <- ___ # Simulate default counts for the portfolio. defaults <- rbinom(n_sims, ___, ___) # Plot the histogram. hist(defaults, breaks = max(defaults) - min(defaults) + 1, main = "Histogram of Defaults", xlab = "Number of Defaults") # Define the number of bonds. n_bonds <- 100 # Define the default probability. p <- 0.05 # Define the number of simulations. n_sims <- 10 # Simulate default counts for the portfolio. defaults <- rbinom(n_sims, n_bonds, p) # Plot the histogram. hist(defaults, breaks = max(defaults) - min(defaults) + 1, main = "Histogram of Defaults", xlab = "Number of Defaults") test_error() test_object("n_bonds", incorrect_msg="Check the number of bonds.") test_object("p", incorrect_msg="Check the default probability.") test_object("n_sims", incorrect_msg="Check the number of simulations.") success_msg("Excellent work!")