Provision For Equality-Linked Liabilities


An easy way for the insurer to manage the liability from options embedded
in equity-linked contracts is to buy options, equivalent to those they have sold, from third parties. This is equivalent to reinsuring the entire risk;
indeed, reinsurers have been involved in selling such options to insurers. As with reinsurance, the insurer is likely to pass on a substantial proportion
of the expected profit on the contracts along with the risk. Also, (as with
reinsurance) the insurer must be aware of the counterparty risk; that is, the
risk that the option provider will not survive to the maturity date, which may be decades away. For some markets, such as that for segregated fund contracts in Canada, reinsurers and other option providers are increasingly unwilling to provide the options at prices acceptable to the insurers.

Dynamic Hedging

As mentioned in the section on equity-linked insurance and options, the
Black-Scholes analysis provides a risk management strategy for option
providers; use the Black-Scholes equation to find the replicating portfolio. The portfolio will change continuously, so it is necessary to recalculate
and adjust the portfolio frequently. Although the Black-Scholes equation
contains some strong assumptions that cannot be realized in practice, the
replicating portfolio still manages to provide a powerful method of hedging the liability. Most of the academic literature relating to equity-linked insurance assumes a dynamic-hedging management strategy. See, for example, Boyle and Schwartz (1977), Brennan and Schwartz (1975, 1979), Bacinello and Ortu (1993), Ekern and Persson (1996), and Persson and Aase (1994); these papers appear in actuarial, finance, and business journals. Nevertheless, although the application by actuaries in practice of financial economic theory to the management of embedded options is growing, in many areas it is still not widely accepted.

The Actuarial Approach

In the mid 1970s the ground-breaking work of Black, Scholes, and Merton
was relatively unknown in actuarial circles. In the United Kingdom, however, maturity guarantees of 100 percent of premium were a common
feature of the unit-linked contracts, which were then proving very popular
with consumers. The prolonged low stock market of 1973 to 1974 had
awakened the actuaries to the possibility that this benefit, which had been
treated as a relatively unimportant policy “tweak” with very little value or risk, constituted a serious potential liability. The then recent theory of
Black and Scholes was considered to be too risky and unproven to be used for unit-linked guaranteed maturity benefits by the U.K. actuarial
profession. In 1980, the Maturity Guarantees Working Party (MGWP) suggested, instead, using stochastic simulation to determine an approximate distribution for the guarantee liabilities, and then using quantile reserving to convert the distribution into a usable capital requirement. The quantile reserve had already been used for many years, particularly in non-life insurance. To calculate the quantile reserve, the insurer assesses an appropriate quantile of the loss distribution, for example, 99 percent. The present value of the quantile is held in risk-free bonds, so that the office can be 99 percent certain that the liability will be met. This principle is identical to the (VaR) concept of finance, though generally applied over longer time periods by the insurance companies than by the banks.


There are several issues that are important for actuaries and risk managers
involved in any area of policy design, marketing, valuation, or risk management of equity-linked insurance. The following are three main considerations: What price should the policyholder be charged for the guarantee benefit? How much capital should the insurer hold in respect of the benefit through the term of the contract? How should this capital be invested? Much work in equity-linked insurance has focused on pricing without very much consideration of the capital issues. But the three issues are crucially interrelated. For example, using the option approach for pricing maturity guarantees gives a price, but that price is only appropriate if it is suitably invested (in a dynamic-hedge portfolio, or by purchasing the
options externally). Also, as we shall see in later chapters, different risk
management strategies require different levels of capital (for the same level
of risk), and therefore the implied price for the guarantee would vary. The approach of this book is that all of these issues are really facets of the same issue. The first requirement for pricing or for determination of capital requirements is a credible estimate of the distribution of the liabilities, and that is the main focus of this book. Once this distribution is determined, it can be used for both pricing and capital requirement decisions. In addition, the liability issue is really an asset-liability issue, so the estimation of the liability distribution depends on the risk management decision.

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