Due to better healthcare and a safer living environment, the average life expectancy in the developed world has been increasing. For life insurance companies this uncertainty creates ‘longevity risk’ – one of their major risks. They can use longevity swaps to hedge the possibility of people living longer. Can longevity swaps create value too?

Under Solvency II, all risks that cannot be hedged away against zero or low costs are classified as non-hedgeable. Because a deep, liquid market with instruments to hedge longevity risk doesn’t exist, longevity risk is one of them. Despite the Solvency II classification, life insurers can still use longevity swaps to hedge their longevity risk. This leads to the following questions: how does a longevity swap impact the balance sheet and capital requirements? Can value be created with the use of longevity swaps? And is the market value margin impacted by the longevity swap?

Regulators require that life insurers hold capital. The minimum required amount of capital is called the Solvency Capital Requirement (SCR) and is based on individual SCRs for each risk, e.g. market risk, credit risk, longevity risk, etc. The total SCR is not equal to the sum of the SCRs because of diversification effects. Equation 1 gives the basic SCR formula:

Besides holding a minimum amount of capital, Solvency II also requires that insurers must present their balance sheet at market value. As most of the assets on the balance sheet of insurers are marketable securities, this is straightforward, but for the liabilities this is more difficult. One of the fundamental principles of market consistent valuation is to value the insurance liabilities at ‘fair value’, i.e. the amount for which a liability is settled, between knowledgeable, willing parties in an arm’s length transaction. In order to get a market consistent value of the liabilities the expected (best estimate) liability cash flows are discounted at the risk free rate.

This approach misses a key risk for the hypothetical buyer: the uncertainty of the insurance liabilities. Therefore next to holding assets to meet the liabilities, the buyer needs to raise and hold capital. The compensation for raising and holding capital for the liabilities is called the market value margin (MVM), or risk margin, and applies only to non-hedgeable risks: if a buyer can transfer a risk associated with the liabilities into the market, he would not have to hold capital to support it. Another non-hedgeable risk is operational risk. Under the Solvency II framework, the MVM is calculated as the discounted value of the costs of the future SCRs, see Equation 2.

Currently the cost of capital (CoC) under Solvency II is set at 6%. Visually the balance sheet including the MVM and the SCR is presented in Figure 2.

*Figure 2: Payout pattern and Cost of Capital over time for the longevity risk SCR*

Note that the SCR does not impact the balance sheet, but is measured against the amount of available capital. In other words, the amount of equity must be higher that the SCR.

The example is based on an insurance company with 100 assets and a best estimate of the liabilities of 70. It is assumed that the risk profile of the insurance company consists only of market risk, longevity risk and other non-hedgeable risks. For those the SCR is given as 10, 5 and 5 respectively. With correlations prescribed by Solvency II, this adds up to a total SCR of 14.58. Under the assumption that the SCRs in the future are always proportional to the best estimate, the MVM equals 3.95.

The structure of a longevity swap is in essence similar to an interest rate swap, consisting of a floating leg and a fixed leg. The fixed leg contains payments based on the agreed survival rate (agreed at the swap initiation) and the floating leg contains payments based on the actual survival rate. The survival rate is the percentage of the population that has not died after a certain period.

As the longevity swap market is an undeveloped market, the swaps have a very illiquid nature. Together with the imbalance between the buyers and the sellers of these swaps, this means that the buyers of longevity swaps have to pay a premium.

The market value of a longevity swap is equal to the premium and in this example it is assumed to be equal to the MVM solely based on longevity risk. For the insurer, this results in an arbitrage-free, consistent pricing method.

Entering a longevity swap decreases (or removes, in the case of a perfect hedge) longevity risk and therefore decreases the longevity SCR. This reduces the overall SCR and increases the free equity. This SCR reduction is for the lifetime of the longevity swap.

The question that remains: is the MVM also affected, due to the SCR reduction of longevity risk? The definition of the MVM provides the answer to this question. In principle you cannot assume that the MVM is affected by a longevity swap, because you cannot assume that the reference entity takes over the longevity swap in an arm’s length transaction. The hedge is not low- or zero-cost because there is still a premium to be paid.

Because the MVM is not affected, value creation by a longevity swap can only come from capital relief over the lifetime of the swap. Value creation is defined as the difference between the value of the created free equity and the costs of entering the longevity swap. Using Equation 2, the arbitrage-free price of the swap is derived as the total discounted future cost of capital for the longevity risk SCR, based on a typical payout pattern. This is graphically illustrated in Figure 2. In our example the price of the swap is 2.50, and the total SCR decreases to 12.25. Note that the SCR decreases by less than 5 as a result of the diversification effect in the square root formula.

The capital relief is based on the current and future decreases of the SCR and the cost of capital. It is calculated using the formula in Equation 3, in which SCRt ^{unhedged }is the SCR without the longevity swap and SCRt ^{hedged }is the SCR including the longevity swap.

The table below shows the balance sheet after the purchase of the longevity swap:

The value destruction in the example is equal to -1.45 (2.50 – 1.05). Note that the amount of value creation/ destruction depends heavily on the underlying assumptions such as the underlying SCR correlations, the SCR proportions between the different risk types and the value of the longevity swap.

Since the MVM is not affected, value creation is only possible if the capital relief is greater than the cost of the longevity swap. Due to the illiquid nature of longevity swaps, they require large premiums. In addition the diversification effects, the correlations between SCRs in Solvency II, ensure that the reduction in total SCR is less than the hedged longevity SCR. Although there can be other, valid reasons to use longevity swaps, they do not create value for life insurance companies in the Solvency II world of today.

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