stochastic formulas. Instead of using average values, the numeric sheet is based on individual scenarios from the DISTs,
which may be selected with a scroll bar. The stochastic sheet
has formulas, each of which results in a full DIST of possible outcomes (cells C6 through C9) and which can be used
to compute statistics like volatility and VaR, plot histograms
and other displays. Furthermore, they may be combined with
other DISTs to drive additional interactive simulations.
Finally, we have added six derivative instruments that allow
the user to test potential hedges. The amounts and strike prices
are in cell D11 through E16. As with the buttons that switch
between pricing assumptions, changing these cells instantly
results in all 248 scenarios being run through the stochastic
sheet, which drives the average portfolio value and histogram
and risk gauge.
Probability Management and the CPO
Whereas risk management has traditionally been viewed as a
single function, as pointed out by Cambridge’s Scholtes (and
others), it would be beneficial to decompose it into independent activities that could be aggregated. We now describe how
the DIST data type might facilitate this process.
The concept of probability management was defined in
2006, as a variant of data management in which objects being managed are probability distributions (stored as scenarios)
rather than numbers.
9 The DIST makes these ideas far more
practical than envisioned just three years ago, but they still
cannot be maintained like numeric data, or lumped under
standard data management practices. Instead, due to the interrelationships between the variables, DIST libraries must be
maintained centrally by a “chief probability officer” (CPO).
Typically, the CPO will not be an individual, but rather represents one of the hats worn by the CRO or CFO. Statistical
and econometric skills will be required, as well as managerial
and leadership ability.
The CPO must maintain and update the DIST library.
Some DISTs, such as stress tests, might be reviewed quarterly;
historical simulation DISTs can be adjusted daily, while those
calibrated to market data might be continuously updated. If
the positions held by the business units can be priced from the
existing DIST library, no coordination is required. To the extent new variables are required, the CPO needs to verify and
model the interrelationships between the new and the existing
variables. This is easier said than done, and should be viewed
as an ongoing journey rather than a destination.
For example, suppose the Bhutan branch wants to start trad-
ing Yak butter futures. It has analyzed the stand-alone risks of
the business, but Yak butter prices are not in the existing DIST
library. We do not yet have good information about its return
distribution, nor how it relates to the world economy. So we
start with a best guess and maintain some formal stress testing
for this and other uncertainties. As we gather more data and
have more time to analyze things, our Yak butter DIST more
accurately reflects both the distribution of price and its relationships to the other DISTs in the library.
Business Units
Each business unit is responsible for maintaining models to
estimate the P&L impact of any set of scenarios stored as
DISTs. Risk controllers and model validation groups will
oversee the quality of these programs, and part of the new
product approval process is to create and validate an acceptable model.
In our sample model, the desk positions are all simple
enough to be evaluated in short spreadsheet formulae. In
practice, some positions will require coded macros, and others might have to be run on powerful servers. Often it will be
useful to have approximate simple models for some applications, but allow the user to specify a complete computation
when required.
Given the DIST library and P&L models, any user can
pull together sophisticated reports, dashboards and metrics
quickly and easily. The sample model took half an hour to
create, and used a low-cost package. The point is that this
process may be scaled up, not by constructing a single tremendous model, but by having hundreds of business units
with thousands of positions each building their pricing models in parallel.
Only ordinary spreadsheet tools with simulation add-ins
are used. There are several competing software packages
on the market, and the cost of the most expensive would be
rounding error in any risk IT budget.
Asking the Right Question
The core idea we are promoting is the standardization and
packaging of probability information in a form that may be
aggregated to create consolidated risk models. Just as the
spreadsheet took corporate information out of a mainframe
guarded by white-coated specialists and put it on everyone’s
desktop, the DIST has the potential to disperse elements of
the risk management process.
It has been said that a simulation is only as accurate as the
