A Cost-of-Capital Risk Margin Formula for Nonlife Insurance Liabilities

A Bayesian Markov chain Monte Carlo (MCMC) stochastic loss reserve model provides an arbitrarily large number of equally likely parameter sets that enable one to simulate future cash flows of the liability. Using these parameter sets to represent all future outcomes, it is possible to describe any future state in the model’s time horizon including those states necessary to calculate a cost-of-capital risk margin. This paper shows how to use the MCMC output to (1) calculate the risk margin for an “ultimate” time horizon; (2) calculate the risk margin for a one-year time horizon; and (3) analyze the effect of diversification in a risk margin calculation for multiple lines of insurance.