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Risk Management in Environment Production and Economy Part 12

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 99.9 99.5 and 99 worst-case loss scenarios for the corporation become 450.69 434.64 and 414.88 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 99.9 and 99.0 worst case losses grows to 1131.8 931.4 and 464.1 424.6 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 151.5 95.95 and 55.55 respectively. New economic capital hybrid approach becomes 301.75 so that AEHP 301.75 - 299.73 2.02. Increasing the size of the network division by 1 implies an increase in the economic capital for market basis and operational risk to 45.45 38.38 and 25.25 respectively. The total economic capital becomes 300.11 so that EnT 300.11 - 299.73 0.38. The numbers for telecommunication is AErc 300.33 - 299.73 0.60. The economic capital allocation gains are therefore divided between hydropower .