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 15-20 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

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