The Need for Financial Models
by Björn Palmgren
Against a background in insurance and finance and with my present
experience from supervision of the financial sector, I would like
to give an overview and some reflections on the role of mathematics
and statistics in finance. The emphasis will be on the need for
models and a discussion of what may make models useful. There
are other important areas, such as secure handling of information
and related questions covered by the field of cryptography and
protocols, which will be left out here.
Cash flows
One way to understand the need for financial models is to look
at what the financial sector is dealing with. What we see is as
customers are products and services offered by banks, securities
firms and insurance companies. The financial institutions receive
our deposits, savings and insurance premiums and offer management
of investments, loans, insurance cover and pensions. With a more
abstract description we could say that cash flows in and out are
handled by these institutions. What is more important is that
some of these cash flows may be uncertain at a given moment in
time. Certain cash flows may be of size that cannot be predicted
with certainty, such as the yield on bonds or equity. In particular,
some future cash-flows may turn out to be nil or non-existent,
due to the default of those who should provide this cash-flow,
or due to that the conditions for payment will not be satisfied,
eg in insurance when no damage covered by the insurance contract
occurs.
Uncertainty and stability
It is the duty of the financial institution to find a balance
or at least an acceptable level of imbalance between the cash
flows that it manages. This balance is a condition for the fulfilment
of liabilities to customers and the corresponding goal of stability
of the financial sector motivates special legislation for the
financial sector and a system of authorisation, monitoring and
supervision. It is the uncertainty about this balance, subject
to financial and operational risk, that is one of the motivations
for an increasing interest in financial models of use for achieving
this balance or stability. Talking of risk, it is worth mentioning
the other side of the coin, opportunity. Opportunity is another
good reason for trying to understand the financial processes using
financial models, at least as a complement to everything else
that is of value for success in the financial sector: information,
knowledge and competence in the field.
Having identified uncertainty as a characteristic feature of financial
activity, we turn next to aspects for managing it. Here it would
seem reasonable to make some distinction between methods, tools
and models, although they are quite intertwined. For the moment
we will, however, make no particular efforts to keep these aspects
apart. Instead we will look closer at the types of uncertainty
or risk that may occur and put them into a wider context, in order
to be able to say something non-trivial about the usefulness and
need for financial models.
Horizons
It is important to bear in mind that the practical use of models
should be judged with reference to some decision situation or
context. Such a context necessarily depends on some horizon or
period within which decisions have to be made. This aspect of
horizon has consequences for the choice of model for describing
the uncertainty or risk. Many processes in industry have a need
for reactions or decisions in real time or at least with a relatively
short horizon for decisions or monitoring. Similar processes do
occur in certain financial markets, such as different kind of
trading activities. Most other financial activities work, however,
with considerably longer horizons, ranging from days and weeks
to months and years. With a longer horizon and less frequent data
it may be problematic to use models that were designed to handle
continuous or highly frequent processes, mainly because the underlying
reality will be too unstable or inhomogeneous to fit into such
a model. This highlights another aspect of the use of models.
Will they be used for predictions or will they rather be used
for descriptions of experience or projections of assumptions made
about the future? For processes in real time there is a need for
models with predictive power for at least a very near future.
There is a need for financial models in situations where there
is little hope of safe prediction, for several reasons. The process
modelled may be poorly understood or just intrinsically inhomogeneous.
The process may be depending on unpredictable market behaviour
or external events, resisting any attempt to find a truthful model.
For this reason it is important to realise that many if not most
financial models cannot be used as sharp predictive instruments.
There are, however, a number of other respectable uses of financial
models. These include projections of assumptions made, assessment
of possible uncertainty, risk or opportunity, including different
kinds of sensitivity analysis and calculation of buffers or margins
that may be needed to compensate for adverse developments, ie
when things do not go your way. Such approaches are of importance
for defining regulatory minimum capital requirements and for capital
allocation and performance measurement.
Some models and methods
With the background given I would finally like to mention some
concrete approaches that seem to be fruitful for further research.
A general reference that gives a critical overview of a part of
this vast field is ‘Risk Management and Analysis, Vol. 1’ edited
by Carol Alexander, Wiley 1998.
It is a general experience that a deep understanding of the phenomenon
to be modelled is the best starting point. Models with elements
of market behaviour satisfy this requirement to a certain extent.
The assumption of no arbitrage has been fruitful for the area
of stochastic financial calculus, including models for derivative
instruments. These models are used in pricing and are put to the
test there.
Still, actual behaviour may differ from theoretical assumption.
In such fields as credit or counterparty risk there seems to be
room for more analysis. First there is a need to link default
risk to properties of the debtor. Much have been done in credit
scoring where the law of large numbers seems to be working, but
there are several areas where default is relatively scarce or
comes in batches. There is a need to sort out risk determining
factors and find more frequent proxies for default. Given sufficient
and relevant data this is an area for statistical analysis, including
cluster analysis and various kind of structure-finding methods.
There are connections with non-life insurance, which faces similar
problems for pricing insurance risk, but usually with more statistics
available. The increasing capacity of computers makes certain
methods or approaches more practical than before. One example
is methods based on the Bayesian approach that can be combined
with empirical data rather than subjective a priori information.
Here we have eg credibility methods in insurance and the area
of stochastic simulation for Bayesian inference, known as the
Markov chain Monte Carlo approach.
Models describing inhomogeneous processes, especially rare or
catastrophic events are of interest, although there are limits
for what can be said in such cases. Information is scarce and
it may take a very long time to evaluate whether decisions based
on the models were correct. Extreme value theory can be explored
further, but perhaps best within the framework of sensitivity
testing rather than prediction.
When measuring the total exposure to risk of a financial entity,
it is clear that models should reflect various kinds of dependencies.
Such dependencies occur between consecutive periods of time and
between various types of activities. Models incorporating dynamic
control mechanisms can explain some of the dependencies over time.
In a more descriptive approach, there seems to be further work
to be done in finding and describing correlation between asset
types and, in case of insurance, correlation between types of
business. One area where such interactions are studied is the
area of asset liability models, where there is interaction between
the two sides of the balance sheet. Future development and experience
with such models can be expected.
Please contact:
Björn Palmgren - Chief Actuary Finansinspektionen, the Financial
Supervisory Authority of Sweden and a member of the Data Security
project at SICS
Tel: +46 8 787 80 00
E-mail: bjorn.palmgren@fi.se
