Consider a risk position X whose performance is influenced by a certain risk factor Y , a situation that calls for conditional risk measurement. We propose the conditional higher moment risk measure, which provides a flexible framework for risk assessment by incorporating a given scenario for Y , a confidence level, and the decision-maker’s risk aversion. We conduct an extreme value analysis of this risk measure to quantify how an extreme scenario of Y exacerbates the risk position of X . This analysis yields several asymptotic estimators, for which we establish asymptotic consistency and validate them via simulation studies. Finally, we conduct empirical studies to examine the impact of precipitation risk on building damage, as well as the spillover effect of a substantial decline in the U.S. S&P 500 Index on the U.K. FTSE 100 Index. • The conditional higher moment (CoHM) risk measure is proposed for risk assessment. • Bivariate regular variation is used to model both heavy tails and tail dependence. • Construct four estimators for CoHM and establish their asymptotic consistency. • Conduct extreme value analysis to assess the impact of underlying risk factors. • Empirically test insurance precipitation risk and financial spillover effects.
Tang et al. (Wed,) studied this question.