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...

The adoption of copula functions is suggested in order to price bivariate contingent claims. Copulas enable the marginal distributions extracted from vertical spreads in the options markets to be imbedded in a multivariate pricing kernel. It is proved that such a kernel is a copula function, and...

This paper provides a closed-form Value-at-Risk (VaR) for the net exposure of an annuity provider, taking into account both mortality and interest-rate risk, on both assets and liabilities. It builds a classical risk- return frontier and shows that hedging strategies - such as the transfer of...

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...

We analyze theoretically banks choice of organization and leverage in branches or subsidiaries in the presence of organizational and financial synergies, government bailouts, bankruptcy costs and varying correlations between risk-factors. The social efficiency of banks’ choices are analyzed as...

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...

On the premise that pension provision in Europe will dramatically change over the next few decades, this book concentrates on the funded component of pension wealth, and specifically on annuities – financial products that, on the basis of actuarial equivalence, allow the conversion of wealth...

The presence of any friction in financial markets qualitatively changes the nature of the optimization problem faced by an investor. It requires one to either act or do nothing, an issue which, of course, does not arise in frictionless situations. The investor considered here accumulates wealth...