Math 3650 - Pricing Project – Fall 2024

1. You are an actuarial student working in the life product development area of Storrs Life Insurance Company (SLIC).  Storrs Life has been selling a 10-year Yearly Renewable Term Insurance (YRT) product for some time now and has a considerable record of company experience for this product.  You have an excel file on Husky CT which contains our current pricing assumptions and YRT premium rates for a female age 40 smoker.  On this file you will find our earned interest rates, best estimate mortality rates, the Statutory mortality rates, and the current YRT premiums that we charge a female age 40 smoker.  All other best estimate assumptions-such as face amount, are the same as those we used in class for a male age 45 non-smoker.  You should build these assumptions into your model to produce a pricing model for a female age 40 smoker for our current YRT product.  These are the premium rates and assumptions for the YRT product we currently sell, and we are not intending to change them at this time.  However, as discussed below, you will still need to perform. sensitivity tests on several key pricing assumptions in order to complete your assignment.  

2. Storrs Life major competitors have introduced Level Premium Term life products, and the popularity of this design has been cited as a cause for the declining sales numbers at SLIC.  One key competitor in particular is selling the Level Premium product at a price of $2.40 per thousand of face amount for females age 40 who are smokers.  Now you are being asked to write a report justifying your opinion as to whether or not Storrs Life should begin to sell a level premium term product, and, if so, at what premium rate per $1000 (for this assignment, just for a female smoker at issue age 40).  You will do this by comparing the risks of selling a Level Premium Term product with the risks of selling the YRT design.  You must submit a report discussing your sensitivity and scenario tests performed on the key risks incurred in selling these policies.  In particular, since the actuaries at Storrs Life are already familiar with the YRT product, but your company has never sold a level premium term design, you must discuss which risks are key risks and discuss significant differences in the key risks of these two products, as determined by your testing. Your discussion should contain an explanation of the underlying reasons that cause these differences.  You should also discuss the risks that are the same or similar between the two products and describe these risks.

3. Storrs Life’s pricing goal is a minimum Risk-Adjusted IRR of 15.0%.  The target IRR is based on distributable earnings including the allocation of Benchmark Surplus.  Your decisions should be based on this Risk-Adjusted IRR profitability measure.  Note: Storrs Life has an opportunity cost of capital of 13%.  If you choose to also discuss the net present value of your results, you should calculate the NPV using an interest rate of 13% (not 15%).

4. You must perform. sensitivity tests and at least one scenario test for both products. You may also include Break-even tests.  (If you do, Break-even tests should be based on the 13% Opportunity Cost of Capital, not the hurdle rate of 15%). You must perform. sensitivity tests on the following four key assumptions: average size face amount, earned interest rate, mortality rates and lapse rates.  For lapse rates, you should perform. two sets of sensitivity tests- one where you change only the first-year lapse rate, and a second sensitivity test for which you change only the renewal lapse rate (years 2-9 lapse rate).  Your objective is to compare the risks inherent in the level premium term design to the risks that Storrs Life is already accepting by selling the YRT product.   Therefore, it is essential that you identify any risks that are significantly different in the two designs.  (That is identify and explain assumptions that affect one policy significantly more or differently than the other).  These assumptions need special attention in your report, and you should explain these differences as best as you are able.   In fact, based on your results and analysis you may even decide to price the level premium term product using different assumptions than we use for the YRT product. If you do this, be sure to explain your reasoning.

5. For both products, you should perform. at least one scenario test- changing two related, or dependent variables on which you previously performed sensitivity tests.  Explain why you think these two assumptions are related to each other.  That is, explain why a change in one assumption would cause you to believe the other assumption would change in the direction and magnitude you tested. IMPORTANT NOTE:  It is NOT acceptable to perform. a “scenario” test in which one assumption is the first year lapse rate and the other related assumption is the year 2-9 lapse rate.  These may very well be related, but this is not a true scenario test.  It is really a different lapse rate sensitivity test.  Therefore, no credit will be given for the scenario test portion of the project if you do this.  If you want to do this test, in which first year and renewal lapse rates are affected together, then do that as part of your sensitivity tests on lapse rates!

6. On or before the due date, you must send me via email an EXCEL file with your base line pricing results for both the YRT and Level Premium Term policy and a WORD or pdf file with your report.  You will find it helpful to create two EXCEL worksheets- one for your YRT pricing and one for your Level Premium policy.  (Simply make a copy of your worksheet in the same workbook and use one copy for level premium and one for YRT). This will make it easier to compare sensitivity and scenario tests. Name your files with your last name first-something like last name model or last name report. (e.g. Williams model).  If I included any portion of your first name as the name of the EXCEL template that I had previously emailed to you, please include that portion of your first name after your last name (e.g. WilliamsRon model)

7. This project is due on Tuesday October 22, 2024, by the end of the day.  You must send me an email with your Excel files and your written report by that time.

This is a strict due date.   No projects will be accepted after the end of the day on October 22, 2024.  NO EXCEPTIONS!  As a result, you are encouraged to hand in your work prior to this date to allow for any unforeseen issues.

Your models were expected to be working by class time on Thurs. September 26, 2024. This is Day 4 of our project class work.  To help you check that your models are fully working, you should send me, by email, the results of your sensitivity tests for a female age 40 smoker.  Please send the sensitivity test results to me by the end of the day on Thursday October 3, 2024. (These tests should be based on the initial pricing assumptions provided on Husky CT and used in class).  Be sure to tell me what level premium rate you used. If you do this, I will review the sensitivity test results you performed (in the order I receive them) and let you know of any errors.  This helps to ensure that you base your reports and findings on properly working models.  No analysis is required at this time- just a simple table of some results for me to check. If I find errors, I’ll help you correct them, but only if you turn in these results by October 3.

As for working with others, you are all subject to the Code of Conduct for Candidates (SOA) and Code of Professional Ethics for Candidates (CAS). Any and all violations of these codes of conduct will be reported to the SOA and/or CAS. Violations of the UConn academic code will also be reported to the appropriate parties at UConn.

Here are the rules for what is and what is not allowed on this project:

You must build and run your own model using the unique template previously sent to you.  If you have only one or two minor issues with your model, (for example, you can’t match one of the calculations, like net investment income) then you may work with current classmates to get your models working properly. Also, if you run a sensitivity test and get what appears to be an incorrect or strange result, you may ask a current classmate if they are getting the same result for the change you are testing. However, if you encounter several issues with your model, then you may NOT ask another student to let you copy or use their model.  In that case you need to ask me for help.

You may NOT consult with former students who are not currently taking this class for any kind of help, assistance or guidance about the project or your pricing model.  And you certainly cannot use a former student’s model or template.

You must run and discuss your own sensitivity and scenario tests- not copy a model or results from somebody else.  Keep in mind that if someone asks you for help and you give them your model or let them copy your results then you are also in violation of the Actuarial Codes of Conduct, this includes providing your model to other students in the future.

You may not discuss this with other faculty members or actuaries to get advice on what to run, or for help explaining results.  This is your work, and your analysis. When in doubt, ask me for assistance. I will be glad to discuss your thinking with you, just like you would have discussions with your manager at work.  

Finally, as daunting as it may sound, have some fun with this.  It’s as close as I can come to replicating what you will really be doing on the job as a pricing actuary.  So, enjoy it!