Luca Regis

Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk

This article provides natural hedging strategies for life insurance and annuity businesses written on a single generation or on different generations in the presence of both longevity and interest‐rate risks. We obtain closed‐form solutions for delta and gamma hedges against cohort‐based longevity risk. We exploit the correlation between the mortality intensities of different generations and hedge the longevity risk of one cohort with products on other cohorts. An application with UK data on survivorship and bond dynamics shows that hedging is effective, even when rebalancing is infrequent.

Basis Risk in Static versus Dynamic Longevity Risk Hedging

This paper provides a tractable, parsimonious model for assessing basis risk in longevity and its effect on the hedging strategies of Pension Funds and annuity providers. Basis risk is captured by a single parameter, that measures the co-movement between the portfolio and the reference population’s longevity. The paper sets out the static, full and customized swap-hedge for an annuity, and compares it with a dynamic, partial, and index-based hedge. We calibrate our model to the UK and Scottish populations. The effectiveness of static versus dynamic strategies depends on the rebalancing frequency of the second, on the relative costs, and on basis risk, which does not affect fully-customized, static hedges. We show that appropriately calibrated dynamic hedging strategies can still be reasonably effective, even at low rebalancing frequencies.

Natural Delta Gamma Hedging of Longevity and Interest Rate Risk

The paper presents closed-form Delta and Gamma hedges for annuities and death assurances, in the presence of both longevity and interest-rate risk. Longevity risk is modeled through an extension of the classical Gompertz law, while interest rate risk is modeled via an Hull-and-White process. We theoretically provide natural hedging strategies, considering also contracts written on different generations. We provide a UK-population and bond-market calibrated example. We compute longevity exposures and explicitly calculate Delta-Gamma hedges. Re-insurance is needed in order to set-up portfolios which are Delta-Gamma neutral to both longevity and interest-rate risk.

International Longevity Risk Pooling

This paper studies the problem of an insurance company that has to decide whether to expand her portfolio of policies selling contracts written on a foreign population. We quantify diversification across populations and cohorts using a parsimonious continuous-time model for longevity risk. We present a calibrated example, based on annuity portfolios of UK and Italian males aged 65–75. We show that diversification gains, evaluated as the reduction in the portfolio risk margin following the international expansion, can be non-negligible.

A Trade-off Theory of Ownership and Capital Structure

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.

Good and bad banks

In the recent financial crisis, reorganizations of distressed financial institutions following the good bank and bad bank model were discussed. In the context of a structural framework and under perfect information, we analyze endogenous capital structure choices of an arrangement constituted by a large regulated unit which manages the more secure assets of a bank and a smaller division - possibly unregulated - which gathers the more risky and volatile ones. We question whether such an arrangement is a priori optimal and whether financial institutions have private incentives to set up different risk-classes of assets in separate entities. We investigate the effect of intra-group guarantees on optimal leverage and expected default costs. Numerical results show that these guarantees can enhance group value and limit default costs when the firm separates its more secure from its more risky assets in regulated entities.