to construct a Monte Carlo simulation that will estimate an aggregate loss distribution. The exercise has two
Question:
to construct a Monte Carlo simulation that will estimate an aggregate loss distribution. The exercise has two parts: the first is a relatively simple problem for which you can develop the answer analytically (Questions A-C); the second part requires you estimate the aggregate loss distribution once you are confident in your simulating abilities (Questions D-F). In addition to the Excel spreadsheet commands we have used already, the following new commands will be used to complete this question: IF(), COUNTIF(), RAND(), and VLOOKUP().
Use the following data to answer the following questions.
Frequency | Severity | ||
# Claims | Prob | Loss | Prob |
0 | .5 | 500 | 1/3 |
1 | .2 | 3000 | 1/3 |
2 | .3 | 5000 | 1/3 |
A. Determine the mean and standard deviation statistics for the frequency and severity distributions respectively.Show your calculation.
B. Calculate the mean and standard deviation of the aggregate loss distribution fromyour answers to question A.1 Show your calculation.
C. Determine the aggregate loss distribution by calculating the probability of each outcome analytically.Show your calculation.
D. Calculate the mean and standard deviation of simulated aggregate losses using your probability distribution from part D. Discuss how well you were able to replicate the actual distribution and compare your simulation results based on 100 trial and 1000 trials.
E. Plot in a chart the actual probability distribution based on part C and the two loss distributions based upon the N=100 and N=1000 trials. (That is, you should draw three graphs for this question.)
Corporate Finance Core Principles and Applications
ISBN: 978-1259289903
5th edition
Authors: Stephen Ross, Randolph Westerfield, Jeffrey Jaffe, Bradford Jordan