The Mathematics of Financial Modelingand Investment Management

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23-RiskManagement Page 745 Wednesday, February 4, 2004 1:13 PM


Risk Management 745

ket plunges, so only small optimization adjustment is possible. There-
fore there are natural limits to the size of coverage that can be offered.
On the other hand, in the case of interest rates if one entity loses
another gains and risk transfer is effective.
In fact, the elimination of interest rate risk forms the bulk of risk
management. According to the U.S. Office of the Controller of the Cur-
rency Quarterly Derivatives Report, interest rate derivatives made up
86% of all derivative contracts in the second quarter of 2003. Foreign-
exchange contracts were the second-largest category of derivatives,
making up about 11% of all derivatives in the same period while equity,
commodity, and credit derivatives made up about 3% of all contracts.
Note that the size of the bond and equity markets are comparable. The
huge notional volume of interest rate derivatives is partially due to for-
mal duplication of traded contracts. For instance, in a number of cases,
instead of selling a swap agreement it might be easier to create a new
swap agreement with opposite cash flows. Formal duplication, however,
is possible just because there is no risk in aggregate.
The situation would be different for an entity that had the ability to
make reliable forecasts. Banks as well as industrial firms hedge interest
rates because they do not feel sufficiently comfortable with interest rate
forecasts. Unable to make sufficiently safe bets they prefer to eliminate
the risk. Hence the huge market for covering interest rates fluctuations.

RISK MODELS


A risk model is a mathematical model of prices, returns, rates, and even-
tually other quantities that allows one to determine the probability dis-
tribution of the total value of portfolios held by a financial institution.
Many different models have been proposed in different areas of finan-
cial risk. Let’s discuss each of them.

Market Risk
Perhaps the best known model of market risk is RiskMetrics, initially
proposed by JP Morgan in 1994 and now commercialized by the Risk-
Metrics Group. Over 100.000 physical copies of the RiskMetrics soft-
ware are now in use at banks and asset management firms.^4

(^4) Information on the company and technical details on the product are available and
can be downloaded from the RiskMetrics Group web site http://www.riskmetrics.com.
Since inception JPMorgan has made technical details on the product broadly avail-
able. The RiskMetrics Group has continued this practice.

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