regimes: from relatively fixed exchange rates in the 1950–1970 period, to relatively
floating exchange rates in the 1970s, to more managed floating rates in the 1980s and
1990s, to the abolition of exchange rates and the introduction of the European Cur-
rency Unit in 11 European countries in January 2002. Clearly, exchange rate behavior
and risk in a fixed exchange-rate regime will have little relevance to an FX trader or
market risk manager operating and analyzing risk in a floating-exchange rate regime.
This seems to confront the market risk manager with a difficult modeling problem.
There are, however, at least two approaches to this problem. The first is to weight
past observations in the back simulation unequally, giving a higher weight to the
more recent past observations.^28 The second is to use a Monte Carlo simulation ap-
proach that generates additional observations that are consistent with recent historic
experience. The latter approach in effect amounts to simulating or creating artificial
trading days and FX rate changes.
(b) Monte Carlo Simulation Approach. To overcome the problems imposed by a
limited number of actual observations, additional observations (in our example, FX
changes) can be generated. Normally, the simulation or generation of these additional
observations is structured so that returns or rates generated reflect the probability
with which they have occurred in recent historic time periods. The first step is to cal-
culate the historic variance—covariance matrix (∑) of FX changes. This matrix is
then decomposed into two symmetric matrices, AandA′. The only difference be-
tweenAandA′is that the numbers in the rows of Abecome the numbers in the
columns of A′. This decomposition^29 then allows us to generate “scenarios” for the
FX position by multiplying the A′matrix by a random number vector z: 10,000 ran-
dom values of zare drawn for each FX exchange rate.^30 TheA′matrix, which reflects
the historic correlations among FX rates, results in realistic FX scenarios being gen-
erated when multiplied by the randomly drawn values of z. The VARof the current
position is then caluculated as in Exhibit 8.7, except that in the Monte Carlo approach
theVARis the 500th worst simulated loss out of 10,000.^31
8.6 REGULATORY MODELS: THE BIS STANDARDIZED FRAMEWORK The develop-
ment of internal market risk models by FIs such as J.P. Morgan Chase was partly in
response to proposals by the Bank for International Settlement (BIS) in 1993 to
measure and regulate the market risk exposures of banks by imposing capital re-
quirements on their trading portfolios.^32 The BIS is a organization encompassing the
largest central banks in the world. After refining these proposals over a number of
years, the BIS (including the Federal Reserve) decided on a final approach to meas-
uring market risk and the capital reserves necessary for an FI to hold to withstand and
8 • 18 MARKET RISK(^28) See J. Boudoukh, M. Richardson, and X. R. Whitelaw, “The Best of Both Worlds: A Hybrid Ap-
proach to Calculating Value at Risk,” New York University Finance Department, Working Paper, 1998.
(^29) The technical term for this procedure is the Cholesky decomposition, where ∑=AA′.
(^30) Technically, let ybe an FX scenario; then yA′z. For each FX rate, 10,000 values of zare ran-
domly generated to produce 10,000 values of y. The yvalues are then used to revalue the FX position and
calculate gains and losses.
(^31) See, for example, J.P. Morgan, RiskMetrics, Technical Document, 4th ed., 1997.
(^32) BIS, Basel Committee on Banking Supervision, “The Supervisory Treatment of Market Risks,”
Basel, Switzerland, April 1993; and “Proposal to Issue a Supplement to the Basel Accord to Cover Mar-
ket Risks,” Basel, Switzerland, April 1995.