The paper provides natural hedging strategies among death benefits and annuities written on a single and on different generations. It obtains closed-form Delta and Gamma hedges, in the presence of both longevity and interest rate risk. We present an application to UK data on survivorship and bond dynamics. We first compare longevity and financial risk exposures: Deltas and Gammas for longevity risk are greater in absolute value than the corresponding sensitivities for interest rate risk. We then calculate the optimal hedges, both within and across generations. Our results apply to both asset and asset-liability management.
We formulate, study and calibrate a continuous-time model for the joint evolution of the mortality surface of multiple populations. We model the mortality intensity by age and population as a mixture of stochastic latent factors, that can be either population-specific or common to all populations. These factors are described by affine time-(in)homogenous stochastic processes. Traditional, deterministic mortality laws can be extended to multi-population stochastic counterparts within our framework. We detail the calibration procedure when factors are Gaussian, using centralized data-fusion Kalman filter. We provide an application based on the mortality of UK males and females. Although parsimonious, the specification we calibrate provides a good fit of the observed mortality surface (ages 0-99) of both sexes between 1960 and 2013.
This paper determines the optimal ownership share held by a unit into a second unit, when both face a tax-bankruptcy trade-off. Full ownership is optimal when the first unit has positive debt, because dividends help avoid its default. Positive debt is, in turn, optimal when its corporate tax rate exceeds a threshold; and/or Thin Capitalization Rules place an upper limit on the debt level in the second unit, and/or the Volcker Rule bans bailout transfers to the second unit. Full ownership is no longer optimal only if there is a tax on intercorporate dividend. This theory rationalizes observations on multinationals, financial conglomerates and family groups.
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