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.
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.
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.
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