Forward-looking Monte Carlo simulations have emerged as a powerful tool for banks seeking to manage enterprisewide risk, particularly interest rate option risk.
Despite the growing acceptance of Monte Carlo simulation and tools that use it, such as our company's Radar system, the technique has come under recent criticism.
These criticisms, while possibly relevant to the Wall Street trading- room environment, do not apply to the kind of risk management that banks are most likely to need as they manage their business on Main Street.
Here, bankers are most concerned with understanding the behavior and potential value of a product or portfolio based on potential changes in interest rates, not with their next short-term trading decision.
Two basic criticisms of the Monte Carlo simulation have been expressed in these pages (Oct. 11).
First, critics charge that Monte Carlo simulation does not produce a sufficiently accurate price for financial instruments such as prepayable mortgages or deposits subject to early withdrawal.
Second, critics charge that Monte Carlo simulation suffers from inaccuracy in valuation due to the sampling error inherent in the technique.
Actually, for both of these criticisms they concede that Monte Carlo simulation can produce results with the desired accuracy, but they complain that doing so requires thousands of iterative simulations-far too many to be practical.
All of these criticisms are flawed.
The first criticism focuses solely on the price of an instrument-a single number-which is calculated as the mean from all the Monte Carlo iterations conducted.
The banker, however, is seeking much more information: an entire distribution of the potential values from all the scenarios, not just a single mean price.
The shape of that distribution, which is almost never symmetrical, reveals essential information about the nature of the embedded risk in the instrument.
This information is completely missing in Wall Street's price-only orientation.
The criticism that Monte Carlo simulation takes too long simply fails to take into account two important advances:
Mathematical variance reduction techniques, which dramatically reduce the number of scenarios needed to produce accurate values.
The dramatic improvement in mainstream computer processing, which compresses the time required to a very practical range.
These criticisms are rooted in the trader's buy/sell mind-set, but the instruments being modeled with Monte Carlo techniques by integrated banks are not generally traded in the Wall Street sense.
Rather than concern about the price of a product, bankers most want to understand how their customers will be motivated to act on their options, such as the option to prepay a mortgage in the event that interest rates change.
To gather this kind of information, the Monte Carlo approach is ideal because it dependably places a numerical value on the customer's incentive to act.
The criticisms of Monte Carlo analysis are valid only for one class of instruments: American price-driven options where there is no dependable driver for the random behavior Monte Carlo depends on.
Even then, techniques are available to allow the use of Monte Carlo approaches with reasonable-if not extreme - accuracy.
In any case, these price-driven derivative instruments make up an insignificant portion of Main Street banking's balance sheet.
We certainly don't dispute the need for accurate value-at-risk analysis.
However, the key wild card in the banker's value-at-risk analysis is the problem of interest rate fluctuation and how consumers will respond to their options under various scenarios.
A shift in interest of just a few basis points can trigger a string of actions that quickly reduces the current income and future value of an entire portfolio of bank products.
Therefore the bank manager, faced with the need to introduce new products quickly to meet market conditions or counter competitive threats, needs to understand the full range of possible outcomes based on potential consumer reactions to interest rate changes.
The wrong decision can put the bank in the situation where the very success of a new product may be overloading the bank with unacceptably high levels of risk.
For instance, a successful credit card promotion that uses a very low extended introductory rate to attract a large amount of new customers could backfire if interest rates rapidly increase.
That's the challenge of life on Main Street.
In addition, bank managers are concerned with the risk embedded in the bank's whole product line-the entire balance sheet rather than a single portfolio. Value-at-risk analysis, therefore, must be done enterprisewide, because different parts of the balance sheet will be affected differently by the same interest rate shifts.
The value-at-risk assessment of a single product will be different when that analysis is correlated to other products-the well-known "portfolio effect." As a result, value-at-risk analysis in the bank requires a much more strategic view than one typically finds on the trading room floor where specialized desks predominate.
In the banking environment almost every department has portfolios that are affected by interest rate shifts. Only rarely is a banker concerned with a single mean net present value (or average value) for the products he or she deals with. Rather, these bankers need to understand the range of values under different possible scenarios and the potential rate environments that produce these values.
With that understanding, he or she can act today in an informed manner- perhaps by changing product prices or parameters to minimize the likelihood of adverse future outcomes.
Monte Carlo simulation, performed this time as part of a "what if" exercise, is the perfect tool for choosing the optimal path.
Rather than mislead the banker with an inaccurate price, then, Monte Carlo delivers exactly what bank managers need-information appropriate for strategically viewing a bigger picture and for making confident decisions about the future.
Let us also address the second criticism: inaccuracy in pricing due to sampling error inherent in the Monte Carlo technique.
It is possible to achieve a precise figure with a Monte Carlo simulation, the critics concede, but doing so requires thousands of iterations of the simulation.
This once was a valid complaint. However, considerable progress in the area of variance reduction techniques, which significantly reduce the need to run an excessive number of simulations, fully addresses this concern.
Convergence to value, using well-established techniques such as antithetic variables or Sobol sequences, requires no more than a few hundred simulations, not the thousands the critics claim.
In addition, on today's affordable computers those hundreds of scenarios can be done as quickly or as frequently as required.
This makes Monte Carlo simulation entirely practical for even the most precise analyses.
Our company's tests suggest that as you follow successive Monte Carlo scenarios, you can easily observe the decreasing changes in mean value and reliably determine the convergence point at which further differences become insignificant.
That convergence occurs over dozens to hundreds of iterations, not the thousands critics claim. Since the smallest difference in which we will be interested in any case is 1/32 of a dollar (even if you are a Wall Street trader), there is almost never a need for more than a few hundred simulations.
For trading room situations where value-at-risk analysis might be run every day, Monte Carlo may not be the most efficient approach.
Meanwhile, for enterprisewide risk management, the bank may only need to run Monte Carlo simulation across its entire balance sheet on a weekly or monthly basis. Here the benefits of the greater amount of information provided-the entire distribution of potential values rather than a precise price-still make Monte Carlo the preferred approach.
The issue, in the end, comes down to Wall Street versus Main Street, with Monte Carlo clearly falling on the side of Main Street, where most bankers operate.
