而對於保險公司來講, 由於資本市場(Capital Market)的規模遠大於保險業的資本, 它對大規模天災的忍受度(損害賠償)也遠大於保險業本身. 因而保險公司將保險金融產品化,由投資人(銀行, 基金)一起分攤利潤及風險,也是一件非常合理的事.
既然買家跟賣家都找齊了, 爲什麼市場還未普遍呢? 最大的兩個原因就是,定價(pricing)困難,以及缺乏可用的指數(index).
由於underlying的保險契約本身並沒有可交易的市場, 加上其事件發生的分布並不是"常態分布", 今天常見的定價技巧如Black & Scholes並無法幫上忙.
現在市面上只有一種相關的指數, 叫做 CSFB Longevity Index 瑞士信貸長壽指數
, 那是一個好的開始, 不過並不夠, 它並沒有不同人群分類(人種, 居住的, 年齡等...)的資料. 另外,我們還需要有公信力的,各地方的天災指數, 交通安全指數, 等等. 來讓金融契約有一個遵循的規範.
longevity swaps and longevity structured notes
"Insurance Derivatives: A Hidden Market"
"The Grave Problem of Longevity Risk"
"Insurance Derivatives: A Hidden Market"
Hurricane Katrina and the fears of avian flu have brought new attention to the risks faced by the insurance industry, and to ways of transferring some of these risks to the capital markets. Overall, the issuance of insurance-linked securities – from property catastrophe bonds to those that fund life insurance reserves – is on the rise. While the vast majority of publicly disclosed transactions have been in the form of fixed income instruments, the growth in the general insurance-linked securities market has generated a renewed interest in insurance derivatives.
A financial derivative is a security whose price depends on the value of an underlying asset or assets. While the underlying assets for most derivatives include financial instruments ranging from common stocks to foreign exchange rates, there are also derivatives based on seemingly non-financial “assets” such as the amount of rainfall at a particular location. Insurance derivatives, a growing class of derivative instruments, are designed to help insurance companies hedge their exposure to insurance losses. In most cases, they are used as a protection against catastrophic losses such as those caused by a hurricane or an earthquake. As other derivatives, in addition to hedging, insurance derivatives could be used by investors for speculative purposes or to improve portfolio diversification.
While the first insurance derivatives were developed by the Chicago Board of Trade (CBOT) almost a quarter century ago, acceptance of these products has been very slow. In fact, the CBOT had to stop trading in insurance options due to the low trading volume. After that false start, there was very limited activity in insurance derivatives for a number of years.
The resurgence of insurance derivatives is part of the general trend of using capital markets solutions to solve insurance industry problems. Turning to the capital markets makes particular sense in managing catastrophic risk. After all, capital markets are vastly larger than the total capital of the insurance industry, and could more easily absorb catastrophic losses.
A simple example of an insurance derivative is an option that gives its buyer the right to a cash payment if a specific index of insured earthquake losses reaches a specified level (“strike price”). Alternatively, the index might be based not on the level of losses, but on the severity of the catastrophic event.
Since there is no traded underlying asset, the payment trigger for the insurance derivatives could be dependent on the actual losses suffered by an insurer, on an index based on aggregate losses suffered by the insurance industry, or on a parametric index based on physical characteristics of a catastrophic event. In transferring to the capital markets risk based on actual losses of an insurance company, a cat bond structure is usually utilized. The other two trigger types (i.e., industry losses index and parametric index) are used in insurance derivatives contracts. While they introduce some basis risk for the insurer, investors generally prefer them due to the lack of moral hazard and the inherently greater objectivity of using an index.
In theory, an insurance company could use a combination of index-based derivative contracts to create a hedge corresponding almost perfectly to its portfolio of insurance risk. This would minimize the basis risk – that is, the risk that insurance derivative payout would not mirror the loss exposure of the insurance company. In practice, the market development is very far from the point where such index-based derivatives are available and actively traded. However, the basis risk concerns might be overblown since in most cases the risk portfolio of an insurance company is strongly correlated with an index when a catastrophe strikes. To determine the right index and strike price – that is, trigger point – requires that risk exposure be better understood and more extensively modeled. In the aftermath of hurricane Katrina this analysis is being undertaken at many insurance and reinsurance companies.
In some cases, it makes sense to use an insurance risk swap. Of publicly disclosed transactions, a good example is a catastrophe swap between Swiss Re and the Japanese insurer Mitsui Sumitomo. In this swap, the risk of a typhoon in Japan was exchanged by Mitsui for the risk of a North Atlantic hurricane and a European windstorm. The transaction improved risk diversification for both parties.
Industry Loss Warranties (ILWs), a better-known insurance derivative product, are usually structured as binary options, with the trigger being a certain level of losses suffered by the insurance industry in aggregate as a result of a natural catastrophe. If the trigger is hit, a specified payment is made to the buyer of the protection. The trigger is based on an index such as, for example, the PCS ® index of catastrophe wind losses in the United States. An unusual feature of these contracts is that sometimes the protection buyer has the option to buy another ILW at a predetermined price if the first one has been “used up” due to a catastrophe. This feature comes from the reinstatement clause commonly found in insurance and reinsurance contracts.
It is rare to see any underlying other than an index, except in more complicated structures that could involve issuance of equity or some other action in addition to, or instead of, the cash payout expected in derivatives. Such instruments, usually not falling under the traditional definition of derivative contracts, could include giving an insurance company an option to issue preferred stock (or another security) at a predetermined price should a certain catastrophic event take place. This gives the insurance company access to capital when it is most needed.
Most insurance derivatives are custom contracts designed to hedge the risk exposure of a specific insurance company. The need to customize the contracts is a significant barrier to the development of this marketplace. The market is largely illiquid and the number of investors limited. On the positive side, the growth in this market could be facilitated by the recent decision by one of the players to become a market maker in ILWs.
It is important to note that insurance risk is not part of the realm of Black and Scholes. Not only is there no trading in the underlying, but the outcome distribution does not follow the assumptions of the Black-Scholes model. The distribution almost always has a very fat right tail. Consequently, pricing of insurance derivatives is more akin to pricing insurance contracts than traditional financial derivatives. For natural catastrophes, pricing is driven by the same catastrophe models that are used in evaluating catastrophe bonds. While these models have been criticized for inaccuracy, they still present the best available way to determine both the frequency of catastrophic events such as hurricanes and earthquakes, and the severity of their impact on insurance company losses. The natural hazard modeling firms introduced significant changes and improvement to the models in the aftermath of hurricane Katrina. In some cases, Extreme Value Theory could be utilized in pricing to account for the skewness of the distribution.
While the use of insurance derivatives so far has been limited to property insurance risk, the life insurance industry has its own unique types of insurance risk that could be hedged using derivative instruments. Death, like taxes, is still certain, but its timing is not. Credit Suisse has recently introduced an index that tracks the level of mortality rates of the U.S. population. Based on government data, the Credit Suisse Longevity Index SM is intended to establish a reference point for mortality rates and expected lifetimes of the general population in the U.S. As such, the index could be used as a basis for creating derivative instruments. Credit Suisse designed the index to enable the structuring and settlement of longevity swaps and longevity structured notes.
It is uncertain whether the index, which is based on the general population, would adequately reflect the mortality experience of a life insurance company. The insurance company might find the basis risk too high for a hedge based on this index to be effective. At the same time, however, the introduction of the index is a very positive step toward creating a measurable mortality yardstick for both the insurance industry and the investor community. Introduction of derivative instruments based on a mortality index would allow better hedging by the insurance industry while at the same time making a new and different type of security available to the investor community.
As in the case of insurance derivatives based on property catastrophe risk, an insurance company has a choice between using a straight mortality or longevity derivative, and a fixed income instrument similar to a catastrophe bond. We have seen three public deals where the risk of extreme changes in mortality rates was transferred from insurance companies to the capital markets by using a bond structure. In these bonds, the main risk was perceived to be that of a pandemic causing a sharp rise in mortality rates. The choice between using derivatives and fixed income instruments in hedging is a complicated one, with the decision also depending on such factors as the basis risk, investor demand, regulatory and rating agency treatment, and legal and accounting considerations.
Pension funds and issuers of annuity contracts also have a significant stake in the levels of mortality and longevity. If not fully reflected in funding assumptions, the fact that people are living longer increases defined benefit pension liabilities and might lead to underfunding. An insurance derivative based on longevity and mortality rates could be used as a hedge against such a mismatch between pension fund assets and liabilities.
Insurance derivatives offer one more tool for insurance companies to protect against risk and for investors to optimize their portfolios. The market has a strong potential for fast growth, but its future depends on the ability of insurance derivatives to effectively compete with other risk transfer instruments, including both alternative capital markets solutions and reinsurance.
"The Grave Problem of Longevity Risk"
There are worse things in life than death. For Woody Allen, it was the prospect of spending an evening with an insurance salesman. However, many insurance companies and pension funds face a prospect that is even more dire: the risk that their annuity and pension holders will live too long – or, more precisely, the risk that these people will on average live longer than anticipated.
Mary Hardy provided a nice discussion of this problem in one of her recent FEN columns (Hardy 2005), where she pointed out that life expectancy for men aged 60 is more than five years’ longer in 2005 than it was anticipated to be in mortality projections made in the 1980s. This means five more years of pension, which is good news for the pensioner, but is potentially catastrophic for the pension provider who failed to anticipate the longevity improvement.
This problem threatens the solvency of the life and pensions industries, and some idea of its magnitude can be appreciated from the fact that the amounts exposed to longevity risk in the UK pensions industry alone were estimated to be £2,520 billion (about U.S. $4,424 billion) at the end of 2003 (Pensions Commission 2005) – or nearly £40,000 (or U.S. $70,000) for every man, woman and child in the UK.
Financial institutions exposed to longevity risk therefore need ways to manage it, but have traditionally been hampered by a dearth of suitable hedging instruments – in particular by the absence of longevity derivatives. However, this state of affairs is changing, and the first such derivatives – survivor or longevity bonds – were proposed by Blake and Burrows in 2001. These took the form of annuity bonds whose annual coupon payments were tied to the survivorship index of some reference population. As members of this population gradually died off, the coupon payments would gradually fall, and Blake and Burrows suggested that such a bond might be a useful hedge for the annuity book of a life company. Before long, other longevity derivatives were also being proposed, including longevity swaps, options and futures, and there were the usual debates about their relative merits for different longevity risk management problems.
Besides giving insurance companies and pension funds means of hedging longevity risk, longevity derivatives also offer other interested parties the opportunity to acquire it. The most obvious counterparties are capital market investors who would be keen to acquire longevity exposure because longevity risks have low correlations with more conventional risk factors. This means that longevity risks have low beta – the capital markets’ Holy Grail – and makes them potentially very attractive investment opportunities.
Financial institutions have also started to issue longevity derivatives. In December 2003, Swiss Re offered a three-year mortality bond whose principal payment was tied to an international mortality index. This bond offered investors a generous floating coupon payment in return for accepting the risk of a reduced principal payment in the event of a catastrophic mortality deterioration such as that associated with the Spanish flu pandemic of 1918. This bond allowed Swiss Re to lay off some of its extreme mortality risk and was well received by investors.
A second longevity bond was then announced in November 2004 by BNP Paribas. This was a 25-year annuity bond to be issued by the European Investment Bank (EIB), whose coupon payments were tied to a survivorship index of English and Welsh males aged 65 in 2002. This bond was targeted at life companies and pension funds wishing to hedge their annuity books and was similar in concept to the bonds proposed by Blake and Burrows. However, this second bond fared less well with investors and was withdrawn for redesign a year later.
During the last several years, a market for longevity swaps has also started to develop, and in December 2005 CS announced the CSFB Longevity Index, which aims to provide a benchmark longevity index against which longevity derivatives of various kinds can be calibrated.
We also know from our own discussions with practitioners that a number of financial institutions have plans to issue further longevity derivatives, but most institutions are extremely sensitive about giving any details away, especially after the failure of the EIB/BNP bond issue – which was all the more embarrassing because of the fanfare associated with the bond’s initial announcement.
Thus, longevity markets are beginning to develop, but progress so far has been mixed.
Ready to take off?
The controversy over longevity derivatives is also starting to heat up nicely. This became very apparent when a paper on longevity derivatives by the present authors (Blake et al 2006) was presented to a meeting of the Institute of Actuaries in London in February 2006. The meeting was very well attended (which attests to the interest in the topic) and led to a lively discussion, but the majority of the audience was sceptical. Perhaps the most critical reaction came from a participant who said the paper amounted to “little more than rearranging the lifeboats on the Titanic” and went on to suggest that the crisis in pensions, caused by low yields and too much longevity, could be solved by the actuarial profession pushing the case for higher interest rates.
However, no one in their right minds would ever suggest that longevity derivatives are a solution for the all past mistakes – the inadequate provisioning, low returns, bad risk management and so on – that have produced the current pensions crisis. Longevity derivatives cannot rectify all these problems, but still have their uses as risk management tools. We would also argue against the actuarial profession lobbying for higher interest rates; monetary policy should be geared towards price-level stability for the good of the economy as a whole and should not be manipulated to suit the convenience of annuity markets. Basic monetary economics also suggests that raising interest rates would also be counterproductive, as it would lead to lower inflation and possible deflation, which would create market pressures leading to even lower market interest rates down the road.
Instead, we would suggest that what is now needed is for participants in the longevity risk business to learn from experience – in particular, to learn from the failure of the EIB/BNP bond and to learn from the experience of other derivatives markets. One problem with the EIB/BNP bond was that it is capital intensive; it requires a high degree of upfront capital commitment for the degree of protection it offered. This particular problem can be ameliorated by looking for ways of increasing leverage so the bond provides more protection for less capital. We would also speculate that a second problem seems to have been basis risk – that the bond would provide a relatively poor hedge for a typical annuity book because the bond’s reference population was insufficiently correlated with the population underlying a typical annuity book. However, there are many possible solutions to this sort of problem and they need to be carefully explored.
It is also important to learn from the experience of other derivatives markets, such as the markets for credit and property derivatives. These markets experienced their own problems, and many of these are comparable to those now faced by the longevity derivatives market – problems of leverage, basis risk, the valuation methodology to use in incomplete markets, liquidity, getting the “right” benchmark indices, mitigating counterparty credit risk and so on. There may also be other problems more specific to longevity risk markets, such as getting trustees to take responsibility for longevity risk management, concerns about reinsurance capacity and so forth.
Broadly speaking, the experience of other derivatives suggests that “teething” problems of one sort or another – including widespread initial scepticism and occasional costly “failures” – are only to be expected and are part and parcel of the process of capitalist experimentation and “creative destruction” – institutional “details” matter and take time to sort out. However, these problems are being addressed, and the fact that investment banks and other financial institutions are investing a lot of their time and effort into solving them suggests that the market for longevity products is about to enter a new and more mature stage of development. Indeed, we would go further and suggest that longevity may well be the next big frontier for financial derivatives. The lesson for derivatives dealers? Eat, drink and be merry, for tomorrow we die . . . or, there again, we might die some other day instead.
For More Reading
Blake, D., A.J.G. Cairns and K. Dowd. 2006. “Living with mortality: longevity bonds and other mortality-linked securities.” Presented to the Institute of Actuaries in London, February 27, 2006. Last accessed March 7, 2006, at http://www.actuaries.org.uk/files/pdf/sessional/fac_sm20060116.pdf.
Blake, D. and W. Burrows. 2001. “Survivor bonds: helping to hedge mortality risk.” Journal of Risk and Insurance. 68: 339-348.
Dowd, Kevin, Blake, D., A.J.G. Cairns and P. E. Dawson. 2006. “Survivor Swaps.” Journal of Risk and Insurance. 73(1): 1-17.
Hardy, Mary. 2005. “A matter of life and death.” Financial Engineering News. 46: 17, 20. Last accessed March 7, 2006, at http://www.fenews.com/fen46/topics_act_analysis/topics-act-analysis.htm.
Lin, Y. and S. H. Cox. 2005. “Securitization of mortality risks in life annuities.” Journal of Risk and Insurance. 72: 227-252.
Pensions Commission. 2005. A New Pensions Settlement for the 21st Century. Last accessed at http://www.pensionscommission.org.uk/publications/2005/annrep/annrep-index.asp.