Lee-Carter goes risk-neutral: an application to the Italian annuity market

We consider a class of stochastic intensities of mortality that generalizes the model proposed by Lee and Carter (1992), allowing general diffusions to drive the mortality time-trend. We analyze the stability of such class of intensities under measure changes and show how a risk-neutral version of the generalized Lee-Carter model can be employed for fair valuation purposes. We provide an example of model calibration based on the Italian annuity market

A pricing formula for delayed claims: Appreciating the past to value the future

We consider the valuation of contingent claims with delayed dynamics in a Black \& Scholes complete market model. We find a pricing formula that can be decomposed into terms reflecting the market values of the past and the present, showing how the valuation of future cashflows cannot abstract away from the contribution of the past. As a practical application, we provide an explicit expression for the market value of human capital in a setting with wage rigidity

Tra poesia e pittura: versi di Francesco Zannio per Giuseppe Salviati

Giuseppe Salviati, the painter Tuscan by birth but active in Venice between 1540 and 1575, is known for his remarkable achievements in the mathematics and astrology, and for his close connection with notable men of letters, humanists and literati. This article outlines his relationship with Francesco Zannio, a little-known but highly prolific poet and the author of an ecfrasis of Salviati’s paintings in Palazzo Ducale published in 1567. His corpus of poems is now increased by a newly rediscovered latin eulogy dedicated to Salviati, which praises his virtuosity and commends his mastery as a painter

The cost of counterparty risk and collateralization in longevity swaps

Derivative longevity risk solutions, such as bespoke and indexed longevity swaps, allow pension schemes and annuity providers to swap out longevity risk, but introduce counterparty credit risk, which can be mitigated if not fully eliminated by collateralization. We examine the impact of bilateral default risk and collateral rules on the marking to market of longevity swaps, and show how longevity swap rates must be determined endogenously from the collateral flows associated with the marking-to-market procedure. For typical interest rate and mortality parameters, we find that the impact of collateralization is modest in the presence of symmetric default risk, but more pronounced when default risk and/or collateral rules are asymmetric. Our results suggest that the overall cost of collateralization is comparable with, and often much smaller than, that found in the interest-rate swaps market (as a result of the offsetting effects of interest rate and longevity risks), which may then provide the appropriate reference framework for the credit enhancement of both indemnity-based and indexed longevity risk solutions.longevity swap; counterparty risk; default risk; collateral; marking-to-market

Los centros históricos latinoamericanos: estrategias de intervención, renovación y gestión. Periodo: 1980-2010

En el pasado, los centros históricos constituyeron toda la dimensión de las ciudades. Eran los lugares donde se desarrollaban las actividades políticas, económicas, sociales, religiosas y culturales de la sociedad, y en donde residía la mayor cantidad de la población. Contienen gran parte de la historia, además de ser testigos de los cambios y de las diversas crisis que se fueron produciendo. Dichas crisis han dejado huellas que se han visto reflejadas en su progresivo abandono. El deterioro de estas áreas, ha planteado la necesidad de iniciar procesos de intervención que han incorporado nuevas formas de gestión, con el propósito de adaptarlas a las nuevas demandas económicas, culturales y sociales. El artículo abordará el concepto de centro histórico, los mecanismos y resultados identificados en intervenciones latinoamericanas, y los casos de Quito y La Habana. Finalmente, se esbozarán recomendaciones enfocadas en la gestión de estos sectores clave de las ciudades.In the past, historical urban cores constituted the whole dimension of the cities. They were the place where political, economic, social, religious and cultural activities took place; they were also the place of residence for the major amount of the population. They contain great part of the history besides being witnesses of the changes and of the diverse crisis who were taking place. The crisis just mentioned have left his treads, which eventually were reflected in his progressive abandon. The deterioration of these areas has raised the need to initiate process´ of intervention that have been incorporating new forms of management, with the intention to adapt them to the new economic, cultural and social demands. The article will approach the concept of historic urban core, the mechanisms and outcomes identified in Latin American interventions, and the cases of Quito and La Habana. Finally, outlining recommendations focused on the management of these key areas of the cities.Peer Reviewe

Optimal Insurance with Counterparty Default Risk

We study the design of optimal insurance contracts when the insurer can default on its obligations. In our model default arises endogenously from the interaction of the insurance premium, the indemnity schedule and the insurer's assets. This allows us to understand the joint effect of insolvency risk and background risk on optimal contracts. The results may shed light on the aggregate risk retention schedules observed in catastrophe reinsurance markets, and can assist in the design of (re)insurance programs and guarantee funds

The Cost of Counterparty Risk and Collateralization in Longevity Swaps

Derivative longevity risk solutions, such as bespoke and indexed longevity swaps, allow pension schemes, and annuity providers to swap out longevity risk, but introduce counterparty credit risk, which can be mitigated if not fully eliminated by collateralization. We examine the impact of bilateral default risk and collateral rules on the marking to market of longevity swaps, and show how longevity swap rates must be determined endogenously from the collateral flows associated with the marking-to-market procedure. For typical interest rate and mortality parameters, we find that the impact of collateralization is modest in the presence of symmetric default risk, but more pronounced when default risk and/or collateral rules are asymmetric. Our results suggest that the overall cost of collateralization is comparable with, and often much smaller than, that found in the interest rate swaps market, which may then provide the appropriate reference framework for the credit enhancement of both indemnity-based and indexed longevity risk solutions

A Trend-Change Extension of the Cairns-Blake-Dowd Model

This paper builds on the two-factor mortality model known as the Cairns-Blake-Dowd (CBD) model, which is used to project future mortality. It is shown that these two factors do not follow a random walk, as proposed in the original model, but that each should instead be modelled as a random fluctuation around a trend, the trend changing periodically. The paper uses statistical techniques to determine the points at which there are statistically significant changes in each trend. The frequency of change in each trend is then used to project the frequency of future changes, and the sizes of historical changes are used to project the sizes of future changes. The results are then presented as fan charts, and used to estimate the range of possible future outcomes for period life expectancies. These projections show that modelling mortality rates in this way leaves much greater uncertainty over future life expectancy in the long term

Managing Capital Market Risk for Retirement

We offer an overview of solutions available to pension plans to manage capital market risk in order to meet their obligations. We outline the main drivers behind the evolution of asset-liability management (ALM) for pension plans and the emergence of liability-driven investment (LDI) in the last decade. We look at some of the most popular pension de-risking tools and at recent innovations prompted by the Global Financial Crisis. We offer examples based on the rise of cross-asset correlation, the use of hybrid products to mitigate tail risk, and the increasing relevance of counterparty risk mitigation tools such as collateralization. We conclude by outlining some of the main challenges ahead, including developments in pension regulation, centralized clearing of over-the-counter (OTC) instruments, and risk taking incentives in delegated asset management for long term retirement obligations

Keeping Some Skin in the Game: How to Start a Capital Market in Longevity Risk Transfers

The recent activity in pension buyouts and bespoke longevity swaps suggests that a significant process of aggregation of longevity exposures is under way, led by major insurers, investment banks, and buyout firms with the support of leading reinsurers. As regulatory capital charges and limited reinsurance capacity constrain the scope for market growth, there is now an opportunity for institutions that are pooling longevity exposures to issue securities that appeal to capital market investors, thereby broadening the sharing of longevity risk and increasing market capacity. For this to happen, longevity exposures need to be suitably pooled and tranched to maximize diversification benefits offered to investors and to address asymmetric information issues. We argue that a natural way for longevity risk to be transferred is through suitably designed principal-at-risk bonds