Tham khảo tài liệu 'risk management in environment production and economy part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Market Risk Management with Stochastic Volatility Models 209 diversification effects lowering the total economic capital to approximately 305 as the new risk measure for the corporation as a whole. Capital requirements at and 99 worst-case loss scenarios for the corporation become and respectively for the normal distributions case. For the student-t distribution with two four degrees of freedom illustrating a medium an extreme heavy tail case the excess and worst case losses grows to and respectively. Fig. 15. Distributions of VaR and CVaR for Normal and Student-t distributions ÕE The diversification benefits are to be allocated by an amount xi to the ith business unit ổxi where E is the total risk capital and xi is the investment in the ith business unit. By using the Euler s theorem we ensure that the total of the allocated capital is E. Euler s theorem says 210 Risk Management in Environment Production and Economy v -V õ VaR VaR . . xi T-i x 1 I 1 oxi where N is the number of components. We can therefore set Ci d VaR 8xi xi where Ci is the component VaR for the ith component. We define AEi as the increase in the total risk capital when we increase xi by Axi. A discrete approximation for the amount allocated to business unit i becomes where Prob u x . When we increase Ay the size of the hydropower generation by 1 its economic capital amounts for market basis and operational risk increases to and respectively. New economic capital hybrid approach becomes so that AEHP - . Increasing the size of the network division by 1 implies an increase in the economic capital for market basis and operational risk to and respectively. The total economic capital becomes so that EnT - . The numbers for telecommunication is AErc - . The economic capital allocation gains are therefore divided between hydropower .
