The paper addresses the question of the calculation of the current value of the mathematical provi-sion and moulds it in a deterministic and stochastic scenario, using a proper term structure of inter-est rates estimated by means of a Cox-Ingersoll-Ross model. It provides a complete and original year-by-year evaluation model for the business performance, and a closed solution for the current evaluation of the reserve, together with a comprehensive insight into the dynamics of the reserve connected to the selection of a defined term structure of interest rates. Moreover, the calculation of the VaR of the mathematical provision is prospected as risk measure useful to appreciate also the evaluation rate risk. Future research prospects concern the selection of the stochastic process used to describe the dynamics of the interest rates and the possible managerial and regulatory applica-tion of a VaR measure. The modelling has been applied, as an exemplification, to a life annuity portfolio but it can be easily replicated for any kind of policy and any kind of portfolios even non homogeneous.
The current value of the mathematical provision: a financial risk prospect
SIBILLO, Marilena;
2007-01-01
Abstract
The paper addresses the question of the calculation of the current value of the mathematical provi-sion and moulds it in a deterministic and stochastic scenario, using a proper term structure of inter-est rates estimated by means of a Cox-Ingersoll-Ross model. It provides a complete and original year-by-year evaluation model for the business performance, and a closed solution for the current evaluation of the reserve, together with a comprehensive insight into the dynamics of the reserve connected to the selection of a defined term structure of interest rates. Moreover, the calculation of the VaR of the mathematical provision is prospected as risk measure useful to appreciate also the evaluation rate risk. Future research prospects concern the selection of the stochastic process used to describe the dynamics of the interest rates and the possible managerial and regulatory applica-tion of a VaR measure. The modelling has been applied, as an exemplification, to a life annuity portfolio but it can be easily replicated for any kind of policy and any kind of portfolios even non homogeneous.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
