Market Value Margin calculations under the Cost of Capital approach within a Bayesian chain ladder framework

- In the SII framework, insurance companies need to calculate the BEL and the MVM.
- The Cost-of-Capital approach is used.
- There exists an intricate circularity dependency between MVM and SCR.
- We consider a Bayesian log-normal chain ladder model.
- We give exact and accurate approximate analytic formulas for MVMs.

In the Solvency II framework, insurance companies need to calculate the Best Estimate valuation of Liabilities (BEL) and the Market Value Margin (MVM) for non-hedgeable insurance-technical risks. The Cost-of-Capital approach defines the MVM as the present value of the current and future Solvency Capital Requirement (SCR) of the non-hedgeable risks to protect against adverse developments in the run-off of the insurance liabilities. However the SCR at time t itself depends on the increase in the MVM between t and t+1. Hence there exists an intricate circularity dependency between both quantities. In this paper we present exact and accurate approximate analytic formulas for MVMs within a Bayesian log-normal chain ladder framework.