One-Year Volatility of Reserve Risk in a Multivariate Framework

The one-year prediction error (one-year MSEP) proposed by Merz and Wüthrich has become a market-standard approach for the assessment of reserve volatilities for Solvency II purposes. However, this approach is declined in a univariate framework. Moreover, Braun proposed a closed-formed expression of the prediction error of several run-off portfolios at the ultimate horizon by taking into account their dependency. This article proposes an analytical expression of the one-year MSEP obtained by generalizing the modeling developed by Braun to the one-year horizon with an approach similar to Merz and Wüthrich. A full mathematical demonstration of the formula has been provided in this paper. A case study is presented to assess the dependency between commercial and motor liabilities businesses based on data coming from a major international insurer.