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Longevity bond pricing models: an application to the Italian annuity market and pension schemes
No full textLongevity Bond Pricing Models: an Application to the Italian Annuity Market and Pension Schemes
No full textThe paper focuses on the securitization of longevity risk through mortality-linked securities. Alternative
mortality-linked securities have been proposed in literature (see Cairns-Blake-Dowd (2006)) and among
these we considered the longevity bond as the most appropriate to hedge longevity risk. The paper aims
at comparing two different approaches used for the pricing of mortality-linked securities: one based
on the Wang transform and the other based on the classical arbitrage-free pricing framework used for
financial derivatives.
The pricing models are applied to the Italian annuity market. We underline the critical features of each
method mainly due to the incompleteness of the mortality securities market and to the lack of a secondary
annuity market in Italy, necessary to calibrate the considered pricing approaches. Each approach
is applied to the case study adopting a Lee-Carter log-bilinear model to represent the evolution of mortality.
Finally, we calculate the risk adjusted market price of a longevity bond with constant fixed coupons
Pricing S-forwards via the Risk Margin under Solvency II
No full textThe paper focuses on the securitization of longevity risk via longevity-linked securities. Among the ones
proposed in the literature, we consider the S-forward, an agreement between two counterparties to exchange at
the maturity a fixed survival-dependent payment for a payment depending on the realized survival of a given
cohort of individuals. S-forwards are up to now the most prevalent securities in the longevity market. Major
problems are encountered in the pricing of these derivatives, mainly due to the incompleteness of the longevity
market which does not allow to find a unique market price of risk. We propose here a method to find a maximum
market price for longevity risk depending on the risk margin implicit in the calculation of the technical provisions
as defined in the Solvency II project. We adopt the Cairns-Black-Dowd model to represent the evolution of
mortality over time, that combined with the information on the risk margin permits us to calculate upper limits
for the risk-adjusted survival probabilities, the market price of longevity risk and the S-forward prices. Numerical
results can be extended for the pricing of other longevity-linked-securities
Is judgement of line orientation selectively impaired in right brain damaged patients?
No full textThe judgement of line orientation test (JLOT) is widely used to assess visuo-spatial processing. Most neuropsychological studies have shown that on this task right hemisphere damaged (RHD) patients are significantly more impaired than left hemisphere damaged (LHD) patients, suggesting a dominant role of the right hemisphere in discriminating line orientation. To investigate whether other factors can affect performance on JLOT, a modified version of the test, consisting of the 30 original test items and their mirror images, was employed. In Experiment 1 normal participants were more accurate in discriminating the left lines of the original items, and the right lines of the mirror-reversed items, thus indicating that in original JLOT the stimulus arrays comprise lines on the left side that are easier to judge than lines on the right. In Experiment 2, RHD patients with visual neglect were significantly more impaired than patients without neglect, who performed similarly independently from the side of the lesion. Among patients without neglect, however, LHD patients were more accurate than RHD patients without neglect with the original items, but produced more errors than RHD patients without neglect when faced with the mirror-reversed items. Overall, the results of the present study suggest that the greater impairment on standard JLOT shown by RHD patients has to be interpreted as the by-product of the presence of visual neglect, which is more frequent following right hemisphere damage, and of the uneven distribution of the stimulus lines, which are easier to discriminate in the left space. The clinical and theoretical implications of the results are discussed
Pricing Basic Survivor Swaps
No full textThis paper aims to give a contribution on the current debate about
the pricing of longevity-linked securities. The main problem arises from the incompleteness
of their market and the diculties to nd a unique market price of
risk. We study the possibility to get the market price of longevity risk through
the risk margin implicit in the technical provisions evaluation under the Solvency
II regulation. The model is used to nd a maximum price for the xed payer of a
basic survivor swap
On longevity risk securitization and solvency capital requirements in life annuities
No full textIn the current work we analyze two mortality-linked securities and try to
price them coherently with the Solvency II framework. We consider a vanilla survivor
swap and a survivor option. The mortality index underlying these derivatives
is built on the survivors of a specific cohort of individuals. Although extensively discussed,
it does not exist yet a satisfactory methodology for pricing these products.
At the root of the problem lies the incompleteness of the market of longevity-linked
securities. Innovative solutions continue to be presented. Moving from the consideration
that the market price of longevity risk is intrinsic in the risk margin computed
for the same risk, some authors suggest using the risk margin to price longevity risk.
We follow suggestions to price vanilla survivor swap and survivor option
The securitization of longevity risk in pension schemes: the case of Italy
No full textThis chapter focuses on the securitization of longevity risk in pension
schemes through mortality-linked securities. Among the alternative
mortality-linked securities proposed in the literature, we considered a
longevity bond and a vanilla survivor swap as the most appropriate hedging
tools.
The analysis refers to the Italian market adopting a Poisson Lee–Carter
model to represent the evolution of mortality. We describe the main features
of longevity bonds and survivor swaps and the critical issue of the
pricing models due to the incompleteness of the mortality securities market
and to the lack of a secondary annuity market in Italy, necessary to
calibrate the pricing models. For pricing purposes, we refer to the risk
neutral approach proposed by Biffis et al. (2005). Finally, we calculate the
risk-adjusted market price of a longevity bond with constant fixed coupons
and of a vanilla survivor swap
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