The first step is to create a library of coherent DISTs. Our
model illustrates this using two alternate DIST libraries, each
of 248 scenarios. The first uses historical returns; the second
an implied return distribution calibrated to market prices of
securities and options. Many other methods are available, and
appropriate for different purposes.
Once the library is created, making a new set of DISTs is
a trivial task and requires no extra work or coordination with
other business units. We specify only three market variables
and a single time horizon, but to the user a DIST is like any
other data element, and it is conceptually no more complicated to create a library with thousands of variables each with
thousands of paths over hundreds of time steps.
The DIST in our model representing 248 historical daily returns of the S&P is depicted in Figure 4 (below). Note that this
has two parts, a header and a body. The header contains the
name (SPX), along with the average, minimum and maximum
value, element count, type (double precision in this case) and
origin (i.e., where the DIST came from). The body contains
the 248 scenarios of the S&P, encoded into characters.
Figure 4: The Header and Body of a DIST
THE HEADER OF THE SPX DIST
<dist name=”SPX” avg=”- 5.35853769E-005” min=”-
9.03497961E-002” max=” 1.15800360E-001” count=”248”
type=”Double” origin=”Aaron Brown Oct. 09”>
THE BODY OF THE SPX DIST
EsEXWRPZAIUerhI2Cp8QTwsABv4QxQMCEK7//xILAAAcMhHb-
HUwMow Y6FdsL2QxvKhMQ0xinFnASoxvXB … BX1FQ0U0xVjEu-
MUhRPXFm0SaQAA</dist>
It is important to note that the DISTs in a library also capture the relationships between uncertainties. Traditionally, this
was accomplished using the concept of covariance, which is
not only non-intuitive, but cannot capture non-linear relationships such as optionality. This is where visualization helps.
Figure 5 (below) depicts a scatter plot matrix of the three
DISTs making up our historical price library. This plot, generated with only a few keystrokes using the JMP software package from SAS Institute, displays the relationships between
the values of SPX (S&P), CLV9 (Oil) and TYZ9 (Treasuries).
Note that by clicking on a point in any graph, that scenario is
highlighted in each of the other graphs. Thus we see that an
exceptionally high return on TYZ9 does not correspond to
The trend toward consolidated risk modeling is developing indepen-
dently along multiple tracks. The list of resources below is not exhaus-
tive, but does cover several facets of this new approach as we see it.
Technological change rarely occurs in a vacuum. The evolution of the
light bulb, the power grid and electrical instrumentation, for example,
were tightly intertwined. An analogous process is happening in model-
ing risk.
Simulation illuminates uncertainty and risk, much as the light bulb il-
luminates darkness. Probability distributions drive simulation, much as
electricity powers light bulbs. Statistical visualization validates the in-
puts and outputs of simulation models, much as voltmeters and amme-
ters allow monitoring to ensure a safe, consistent source of electricity.
Keeping this in mind, the resources listed here fall into three catego-
ries: standards, simulation and visualization.
Standards
Probability Management
( www.ProbabilityManagement.org)
ProbabilityManagement.org is responsible for developing and main-
taining the DIST data type. It features information on the DIST for-
mat, as well as articles on probability management and downloadable
models that perform interactive simulation in Excel. These include the
model described in this article and other financial and inventory mod-
els. Visitors can also find a demo of the application deployed at Royal
Dutch Shell.
EconSML
( www.soa.org/professional-interests/technology/tech-
scenario-file-format.aspx)
EconSML is a file format being developed by the technology section
of the Society of Actuaries to share stochastically generated sets of
economic scenarios. EconSML aims to provide a higher level of meta
data concerning scenario libraries than the DIST, but does not include
compression. Since both EconSML and the DIST are XML based,
it is easy to envision a synergy in which DISTs might some day be
embedded in EconSML.
Simulation
@RISK( www.palisade.com)
This was the first commercial spreadsheet-based Monte Carlo pack-
age, and is still a leader in the field. Developed by Palisade Corpo-
ration, which was founded in 1984, @RISK is currently part of the
Decision Tools Suite, a set of integrated powerful analytical tools for
Excel. Although @RISK does not yet support DISTs directly, it is easy
to adapt and has been used in this manner in at least one industrial
application.
