The paper illustrates the efficiency features of the Italian banking system through a review of the most important empirical studies over the last fifteen years. Particular emphasis is given to DEA (dynamic envelopment analysis) studies and to their capability to investigate economies of scale...

The paper presents closed-form Delta and Gamma hedges for an- nuities and death assurances, in the presence of both longevity and interest-rate risk. Longevity risk is modelled through an extension of the classical Gompertz law, while interest rate risk is modelled via an Hull-and-White process....

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...

Longevity risk transfer is a popular choice for annuity providers such as pension funds. This paper formalizes the trade-off between the cost and the risk relief of such choice, when the annuity provider uses value- at-risk to assess risk. Using first-order approximations we show that, if the...

This paper studies the hedging problem of life insurance policies, when the mortality and interest rates are stochastic. We focus primar- ily on stochastic mortality. We represent death arrival as the rst jump time of a doubly stochastic process, i.e. a jump process with stochastic intensity. We...

This paper examines a new model of credit risk measurement, the Variance Gamma- Merton one, which seems to be adequate for describing single default occurrence and default correlation in turbulent times. It is based on the notion of business time. Business time runs faster than calendar time...

In this paper we apply a copula function pricing technique to the evaluation of vulnerable options, i.e. options with counterpart risk. Using copulas enables to separate the specification of marginal distributions and the dependence structure of the events of exercise of the option and default...

Copula functions have proven to be extremely useful in describing joint default and survival probabilities in credit risk applications. We overview the state of the art and point out some open modelling issues. We discuss first joint default modelling in diffusion based structural models, then...

The most common approach for default dependence modelling is at present copula functions. Within this framework, the paper examines factor copulas, which are the industry standard, together with their latest development, namely the incorporation of sudden jumps to default instead of a pure...

In this note we use doubly stochastic processes (or Cox processes) in order to model the evolution of the stochastic force of mortality of an individual aged x. These processes have been widely used in the credit risk literature in modelling the default arrival, and in this context have proved...