
RISK MANAGEMENT WITH
ACE™
Risk management is one of the most important aspects of daily
operations in any vital financial institution. Monte Carlo
simulation is a key tool. DEAR (Daily Earnings At Risk) does not
address adequately the longer term risk exposure. The covariance
approach can not capture the risk due to neither the nonlinear
derivative instruments in the portfolio, nor the extreme market
movements which are the most dangerous. Historical simulation may
provide some more information, but its implementation depends on the
choice of time series. We know that history will not simply repeat
itself. Depending only on historical simulation is like driving
forward by looking only the rear mirror. The only reliable and
complete survey of the potential risk landscape is the full Monte
Carlo VaR(Value At Risk) simulation of the future horizon.
In a sophistic risk management system, risk exposure calculation
on portfolios should provide VaR of various future time horizons for
certain confidence intervals, and take into account of the scenarios
involving large market movements, when correlation becomes less
predictable and extreme tails and gamma become important.
However the enormous amount of computation for such full
simulation can be prohibitive. In the first stage of such Monte
Carlo simulation, thousands risk neutral scenarios of interest
rates/exchange rates may be needed, involving dozens of correlated
market variables. Depending on the forwarding time horizon, which
may be from 10 days up to 1520 years, we may have 10~100 time
steps. Even after reduction by factor analysis, we could still have
a problem of thousands dimensions. For each scenario at each future
time, we need to evaluate each position of the entire trading book,
which may contain tens and hundreds of thousands transactions for a
major financial institution. This may amount up to a trillion
evaluations. Even for simple instruments with closed form
solutions and/or fast evaluation techniques, this may require up to
a hundred CPU hours. In the second stage of computation we need to
aggregate the data produced by the first stage, using accounting
netting rules and information on hundreds counter parties (and maybe
default probabilities, etc., for credit risk). In the third
stage we sort out the Monte Carlo data and make the histograms. The
computation time required for the second and third stages are
comparable to the first. Clearly, the time constraint is the most
concern to the risk management team. Such a daily astronomical
amount of computation can stretch the IT resource to its limit.
Traditional the only approach to this problem is to purchase
supercomputers, or multiply the computer installations, e.g. via
massive parallel processing. It requires proportionally multiples of
investment, multiplying floor spaces, IT human resource and
maintenance costs. For risk managers in most institutions, full
Monte Carlo is only a distant dream.
With Accelerated Convergence Expert™ (ACE™), the dream
becomes a reality. ACE can reduce the required number of sample
scenarios by a factor up to hundreds, while having better
distribution properties. Since the time spent on the second and
third stages of risk exposure calculation is roughly proportional to
the first, implementing ACE in Monte Carlo simulation can
drastically increase the overall speed of risk exposure computation,
up to tens of thousand times faster when ACE is also used in
speeding up the pricing of complex derivative instruments.
Implementing ACE does not require expensive hardware investment,
floor spaces and maintenance. Its power is perpetual. Smart
simulation is the smart approach.
ACE for Pricing and Trading
AAL (Advanced Analytics
Library)
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Analytics, Inc., AAI, the AAI logo, ACE, AAL
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