IV. METODOLOGÍA
4.3 Definición y operacionalización de variables
8. valseg, life insurance - financial asset
9. valpenseg = valor + valseg, pension scheme - financial asset,
10. odeuhog,
7.2. Multiple Imputation (MI)
The key point to note for MI is, if the research interest is a point estimate of mean, median, regression parameter (denoted by Q for example), for each of the five implicates, the MI estimate Q¯ = 15
ÿ5 i=1
Qˆi. The variance of this estimate ¯Q has two components:
1. Within imputation sampling variance W , the average of the five variance estimates (Vˆi): W= 15ÿ5
i=1
(Vˆi)
2. Between imputations variance that reflects the variability due to imputation uncertainty:
B = 14q5i=1(Qˆi≠ ¯Q)2
Total variance of ¯Q then can be written as T =W + (65)B.
Alternatively, to obtain MI estimates, it may be possible to do the following: If only mean of the statistics are of interest, instead of analyzing the five implicates separately, one can construct a complete dataset by combining the five implicates successively. This is equivalent to construct a unique dataset with 5 times of the actual number of respondents. The calculation can be done by dividing the weight variables (facine3, discussed immediately below) by five, and calculate the desired statistic. Carlin et al. (2003) (79) describes the procedure for analysis using MI dataset by STATA.
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Part III.
Gauging basis risk of longevity risk solutions
119
Chapter 8
Introduction
Background Being the first country to witness the development of both pension liability buy-in/outs and longevity-linked securities, UK has become one of the most important global centers of pension longevity markets during the past two decades. In today’s low interest rate regime, coupled with slow recovery of asset prices to pre-crisis period, as well as stable, long-term longevity improvement, pension schemes may face large funding deficits. On the other hand, Solvency II regulatory reform has created uncertainties to measurement of pension scheme’s balance sheet, which motivates pension industry to adopt a de-risking strategy. These factors all contribute to the historical peak of the global pension risk transfer market in the past decade. According to Aon Hewitt (2015) (103), by the end of 2014, the global pension risk transfer market has grown to the size of £35 billion, with £22 billion of these transactions being longevity swaps (£8.8bn in 2013), and bulk annuities reached around £13.2 billion (£7.8bn in 2013). Bulk annuities, or buy-in/outs transactions are indemnity-based solutions which allow the pension sponsors to transfer part or all pension liabilities to a buyer, usually a specialty insurance company. Through these instruments, pension schemes sell their liabilities outwards by paying a buy-out premium. An alternative hedging solution for the pension schemes is to implement their own Asset-Liability Management (ALM) strategy, with longevity swaps being part of it to hedge the unfavourable longevity improvements. Currently there are mainly two types of longevity derivatives: Among the recent market transactions of longevity securities, the majority of those transactions are bespoke, or customised, indemnity-based longevity swaps that hedge the longevity risks of specific pension schemes or annuity providers’ portfolios, which are similar to the annuity reinsurance offered in the reinsurance markets currently1. The other type of longevity swaps are linked to a population index such as the LifeMetrics index developed by JP Morgan (see Coughlan et al (2007)(112)). They are referred to as the indexed-based, or standardized longevity swaps. Please see Tables A.0.1 A.0.2 and A.0.3 in Appendix for a list of recent longevity transactions.
1It is worth noting that the fundamental difference between the bespoke longevity swap and a traditional reinsurance contract is that the longevity swaps are usually backed up by collateral, whereas reinsurances are not. The lack of collateral associated with the traditional annuity reinsurance contracts are possibly due to the fact that longevity risk transfer through reinsurance programme is part of the global de-risking strategy of the pension plans or annuity providers, before the innovation of longevity swaps
120
8.1 Bespoke v.s. index-based longevity swaps 121
8.1. Bespoke v.s. index-based longevity swaps
Early examples of bespoke, or customized longevity swaps are the transactions agreed between Babcock International and Credit Suisse in 2009. The cash flows exchanged between the hedgers (pension plans and annuity providers, etc) and the hedge suppliers (specialty (re)insurers, in-vestment banks and hedge fund etc.) are designed to match exactly the survival index of the hedgers’ pensioners/annuitants portfolio. To sum up, the advantages of the bespoke longevity swaps are significant: They provide a perfect hedge to the longevity risk hedgers. However, the costs associated with setting up such transactions are usually high. This is because the hedge suppliers need to put up substantial regulatory capital to ensure the pension liabilities can be met with a high probability. At the same time, the hedge suppliers expect the buy-out price includes a premium relative to the longevity risks being transferred. Moreover, these bespoke securities are viewed as static, buy-and-hold hedges that sit on the hedgers’ balance sheets which do not generate further market transactions.
In contrast, the other type of longevity securities is index-based, or index-linked, standard-ized longevity swaps. For example, pension sponsors can structure such longevity swaps by combining several q-forwards (112) designed by JP Morgan. These instruments exchange cash flows between the hedgers and hedge suppliers that linked to a broader index (e.g. a national population), usually larger and more reliable than the hedgers’ portfolios. This design makes the index-based transactions more transparent, and easier to manage and structure, which induces lower set-up cost and better liquidity than the bespoke ones. Moreover, some pension scheme is too large to hedge with bespoke solutions. This makes indexed longevity hedge is currently the most practical and only available solution for hedging the longevity risk associated with deferred pensions and deferred annuities, as well as those super large schemes. Moreover, the specialist longevity insurance companies may use indexed longevity swaps to hedge their exposure instead of purchasing reinsurance as a cost-effective solution.
Nonetheless, the disadvantages of these index-based longevity hedge are obvious, which is the mismatch of the survival experience between the hedgers’ own portfolios and the reference popu-lation, which would cause mismatch of cash flows. The index-based hedges are imperfect, leaving a residual amount of risk that cannot be hedged. This specific risk is called basis risk.