The Mathematics of Financial Modelingand Investment Management

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23-RiskManagement Page 755 Wednesday, February 4, 2004 1:13 PM


Risk Management 755

Clearly banks must show the ability to measure risk which the Fed-
eral Reserve prescribes measuring as VaR. The Federal Reserve then
controls the quality of a bank’s ability to forecast adverse movements. If
adverse movements occur more frequently than anticipated by a given
bank’s risk management system, then that bank is obliged to increase its
liquid reserve. The implications of these new regulations from both the
business and the macroeconomic points of view will be analyzed in the
coming years.

SUMMARY


■ Diversification and risk transfer through financial engineering are the
key tools of risk management.
■ Estimating the shape of loss distributions is central to modern financial
risk management.
■ A market is complete if every possible contingency can be traded.
■ In a complete market, risk can be perfectly hedged.
■ Multivariate geometric diffusion models are complete.
■ Stochastic volatility models are not complete, but can be completed.
■ If risk does not exist in aggregate, it can be eliminated; if it exists in
aggregate, it can only be transferred.
■ Off-the-shelf market and credit risk models are commercially available.
■ Risk can be measured in numerous ways: unexpected loss, value-at-
risk, expected shortfall, and sensitivities.
■ Client demand and management push are behind the growing use of
risk management in investment management.
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