How To Create A Financial Simulation Model

Inside the operating theatre

Financial simulation, which was rare just 10 years ago, is now a common practice, routinely used in pricing and risk measurement. However, understanding the computing processes involved can be difficult. Thus, guaranteeing the reliability of the model is left entirely to the developer, i.e., software houses and designers. Thus a doctor-patient like relationship develops between the user and the developer. However the patient cannot be indifferent to what is done when he/she is under the knife.

This article outlines some of the possible causes that might lead to "malpractice" in financial modeling, from the mathematical point of view.

1. Designing the model with too few degrees of freedom

The relationships among multiple probability swing factors can be expressed in terms of linear algebra, by real symmetric matrix. (Figure 1). The yellow portions of the diagram are a dense matrix (non-zero area), in a financial context these areas as sometimes referred to as "systematic risk." A skyline matrix is a matrix type that includes multiple dense matrices, its shape is typical of a probability swing model. The degrees of freedom are defined by the length of one edge of real symmetric matrix, (i.e., the number of dimensions of the matrix). A probability equation is built by placing the included dense matrix and the probability variable (which depends on the diagonal component) on the right side (Figure 2). The same method applies not only to financial issues but also to other simulation fields such as structural analysis. Are you with us? Do not worry too much if you have a little difficulty following.

Now, let's go into the main subject. Handling larger degrees of freedom requires a more complicated technique called numerical calculation. This often drives the developer to decrease the degrees of freedom intentionally to simplify the calculation. The once popular RiskMetrics is one of these models (Figure 3). Looking at the worst examples of this kind of shortcutting, there are even models that use only one probability variable to express more than 3,000 individual stocks.

Even global regulations knowingly permit the use of fewer degrees of freedom. It is very simple to outsmart the regulations - just create a spread position in the portion with fewer degrees of freedom. It is dangerous to believe that "Using the BIS-conforming VaR in the risk management is a silver bullet."

2. Instability in trigonometric decomposition operations

I think that the financial community, dominated by materialists and the primacy of results, uses maths in a way that is far sloppier than that of physicists, who are themselves often teased by mathematicians. When I think about my own days working in a bank, there is much to reflect upon.

In the process of simulation, as opposed to the above dense matrix, square root operation in terms of a unit variant and conversion to an L*L^t format, i.e. trigonometric decomposition, is necessary. However, when the Cholesky decomposition (often introduced in entry-level handbooks) is used, if the computations deals with lots of financial sequences in which individual figures are prone to move in the same direction, (e.g., short-term interest rates), errors may be encountered during the calculation. This sort of model sometimes produces confusing figures. It is neither strong nor robust, in the technical sense of the word. Systems that have this sort of problem generate more and more errors as the calculation is repeated. Such systems make daily review of the correlation coefficient impossible.

To cut a long story short, as you study beyond the beginner's guide, you will realize that L*D*L^t format conversion followed by an L*L^t format is the best way to operate the matrix.

3. Overuse of variance reduction techniques

Variance reduction techniques reduce errors as perceived by the observer. However, it has serious side effects related to disturbance of the inter-sequence correlation (multi-correlation) and quasi-random cycle (Figure 2). Therefore the results are prone Type I error ("the rash person's error") leading one to wonder how on earth the developer in question managed to get a PhD. For example, I was once rendered speechless by someone from a famous risk management corporation who strongly insisted that "With a quasi-random sequence, it is possible, with tens of thousands of portfolios, to measure the risk coupled with market and credit events, by running less than 5000-time simulations."

From the nature of a numerical simulation, a usable level of precision can only be achieved after ten thousand or so runs for a single event measurement, for multiple events further simulations are necessary. Regarding the enormous sums involved for a newly-merged bank, vast amounts of preparation are needed, even with the latest PC server capable of completing 100,000-time calculation in 17 hours,(obtained from the simultaneous calculation of the credit VaR, CVaR, risk contribution, OLAP, and DM/MTM on a 4-CPU Linux server).

[An elegant PDF chart created using 100,000-time simulations and variance reduction techniques]

[An XY plot of credit diversification benefit created using 100,000-time simulation and variance reduction techniques]

After-purchase inspection recommended

Coronary bypassing, once regarded as an extremely difficult operation, is now routine, over 90% success rate, and the heart surgeon may be blamed if his patient died upon operation. Likewise, the enormous fees paid in the past for a 'specialist' to carry out model audits now seem questionable. As when purchasing a home, the quality of financial models and systems must, in the end, be evaluated the users themselves.