محاسبات حاشیه ارزش بازار تحت هزینه روش سرمایه در چارچوب نردبان زنجیره ای بیزی

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 tt itself depends on the increase in the MVM between tt and t+1t+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.

Solvency II is creating a new approach to regulate capital requirements by quantifying risks and is giving incentives for companies to develop good risk management practices. It will be based on economic principles for the measurement of assets and liabilities and capital requirements will depend directly on this. In particular it introduces the market consistent economic (solvency) balance sheet and two points in time are considered to calculate the Solvency II Capital Requirement (SCR): the current balance sheet and the balance sheet at the end of the year. The main components of this balance sheet are the Market Value of Assets (MVA) and the Fair Value of Liabilities (FVL) consisting of the sum of two components: the Best Estimate valuation of Liabilities (BEL) and the Market Value Margin (MVM).

We now consider the case where the cash flows are discounted for the calculations of the reserves, the SCRs and the MVM, following the Solvency II framework. The Fair-Value of Liabilities for accident year i at time t is still defined as the sum of the Best Estimate valuation of Liabilities (BEL(d) i,t ) and the Market Value Margin (MVM(d) i,t ) of this accident year, but the SCR(d) i,t and the MVM(d) i,t are now given by the two simultaneous equations