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Business Task Risk Management Of Equity–‐Linked Life Insurance Policies Background

You are an actuarial analyst working for a boutique life insurance company operating in Australia. Your company has historically focused on traditional insurance products (e.g. Term life, endowment policies). After a recent strategic review of the company’s operations, the CEO has asked your team (comprising of actuaries, actuarial analysts, and headed by the chief actuary) to investigate the possibility of introducing an equity linked life insurance product. Such products explicitly combine features of equity investments and life insurance, and have been gaining increasing interest in the market place.

The chief actuary has tasked you to model the risks and costs of such a product. In particular, a main task is to develop a (partial) hedging strategy (as discussed in the next section) for such a product, and illustrate and analyse its outcomes.

You are to produce a professional report for the chief actuary (and the team). The report should include (at least) two major sections

1. Main body of the professional business report – this will address the main business aspects for the task and be primarily focused on the outputs.However, sufficient summary information on your modelling (e.g. assumptions, key ideas behind the model, observations and insights) must also
be provided.

2. Appendix – all technical details must be provided. This includes a clear presentation of your model including any mathematical equations used. While your spreadsheet (or similar – you can use any software you prefer as long as
all calculations are clear) is not required to be submitted at this stage,sufficient information must be provided in a way such that another member of your team can implement and build the model, if necessary.

Note that the structure of the main body and technically appendix may very well be different as their purposes are different. However, where relevant it is recommended that a clear relationship / cross reference be included for clarity.

Task Specifics
The equity linked policy pays the following per unit of investment (for the sake of presentation you may wish to consider $100 dollar of investment) at the end of the year

– If the policyholder is alive: initial investment* Max(1+ average stock index return over the year, 0.98)
– If policyholder is dead: initial investment* 0.98

The stock index to be considered is the market accumulation index (i.e. with dividends re-invested). The “average stock index return” is defined to be the ((average of the stock index in 3 months, 6 months, 9 months, and 1 year), minus the starting index), and divided by the initial stock index.

As an example, if the index at time 0, 3month, 6month, 9month, 1year was 1, 0.9,1.1,

1.2, and 1.3, respectively, then the payoff is (for $100 investment) $112.50.
Assume that the interest rate is 3% p.a. (continuous compounding)As the payout from the policy involves elements of both financial risk and mortality risk, it is not possible to completely hedge the risk by trading in the financial market.

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A number of techniques have been suggested in the literature, but the chief actuary has asked you to investigate the method of ‘risk minimization’ as presented in the paper by Moller (2001).

In terms of technical details, your report must address the following

Parameter estimation – binomial tree
• Estimate the parameters for your binomial tree model (with time steps at times 0, 3 months, 6 months, 9 months, and 1 year) for the stock • index. Historical data for the index is attached. You should consider in
particular the discussion and method outlined in the section on the

• Binomial Lattice model in the text by Luenberger.
• The resulting parameters must be clearly provided in your report.
• You should briefly describe how you have estimated the parameters,
including any approximations used (if any).

(2) Derivation of the replicating portfolio and strategy (and associated costs over time) for a purely financial option with the same payoff as the equity linked contract, but without the mortality component.

(3) Derivation of the hedging portfolio and cost of a risk minimizing strategy for the equity-linked insurance contract.

• Find the portfolio and cost of the portfolio at each node of the binomialtree, for someone who is alive at that point.

• Find the portfolio and cost of the portfolio at each node of the binomial tree, for someone who is dead at that point.

(4 )llustration of the cost (in particular the additional cost incurred) and portfolio for a group of equity-linked insurance contracts under the ‘risk minimization’ approach. For this illustration, you should assume that there
were originally 20 policies, but in the first period (i.e. 3 months) the stock price went to the lower branch, and 2 people died. Illustrate the resulting cost.

(5) For a portfolio starting with 20 policies, use simulation techniques to find the distribution of costs at each time point, and also summarize the present value of these costs. Present the first three moments of the (present
value of) costs, and also a histogram of the (present value of) costs.

• Note that you will need to consider the number of simulations required.
• A clear description of your algorithm in you simulation must also be

Note that each life underlying the equity-linked contracts can be assumed to be independent and will have a force of mortality equal to 0.2 per annum.

Important – for all tasks, it is important that sufficient information must be provided for the reader to review your approach, techniques and results (the majority of the fine detail should be included in the appendix).

Written Communication

Written communication of results (10 marks) – Communication of quantitative results in a concise and easy-to-read manner is a skill that is vital in practice. As such, up to 10 marks will be given for the presentation of your results. In order to maximize your marks for presentation you may wish to consider issues such as: table size/readability, figure axis/formatting, grammar/spelling, and report structure. You may also wish to consider the use of executive summaries and appendixes, where appropriate.

Note that the main results and findings should be in the main body of the report.
Product code: Business Management-AW780
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