Financial Risk Calculation

Problem Statement

We now build up on our knowledge from the blog entry Delay Propagation in a Sequential Task Chain and use the knowledge as well as the C code that was developed in that blog post in order to tackle a problem from project risk management. We want to examine which outcomes are possible based on a set of risks and their possible monetary impact on our project. The assumption in our example is though that all risks are independent from each other.
The questions we are going to ask are of the type:

• What is the probability that our overall damage is less than x €?
• What is the probability that our overall damage is higher than x €?
• …

Source Data

We use the following risks below. Different from traditional risk tables, we do not have only 2 outcomes per risk (“Risk does not materialize.” and “Risk materializes.”), but we have an n-ary discrete outcome for each risk (“Risk does not materialize.”, “Risk materializes with damage A and probability a%”, “Risk materializes with damage B and probability b%”, …). This allows a finer grained monetary allocation of each risk.

We can calulate that the expected value of the damage is 1,026,000 € by adding up the expected damages of the individual, independent risks.

Solution

Our approach will use the discrete convolution and take leverage of the C file faltung.c. However, in contrast to the example in the blog entry Delay Propagation in a Sequential Task Chain, we face the problem that our possible outcomes (the individual damage values) are a few discrete values spread over a large interval. Hence, the program faltung.c. must be modified unless we want to eat up the whole system memory with unnecessarily large arrays of float numbers. Therefore, the upgraded version (faltung2.c) uses a struct to capture our input and output vectors, and the modified sub-routine convolution() iterates through all possible combinations of input vectors and stores the resulting struct elements in the output vector. We also need a helper funtion that checks if a struct with a certain damage value already exists (function exists()). We do not sort our output vector until before printing it out where we use qsort() in connection with compare_damage() to get an output with increasing damage values. In addition to the probability distribution, we now generate values for a probability curve (accumulated probabilities) which will help us to answer the questions of the problem statement.
Our input values now are reflected in 3 input vectors in the file input_monetary.dat and looks like this:

When we evaluate this input with our C program, we get the following output:

The second problem statement (“What is the probability that our overall damage is higher than x €?”) is determined with the same approach. However, rather than directly using the value on the axis Accumulated Probability, we have to subtract that one from 1.00. The result is then the probability that the resulting damage is higher than x.

Downloads and Hints

• You can download the source code of faltung2.c from https://caipirinha.spdns.org/~gabriel/Blog/faltung2.c. The source code is in Unix format, hence no CR/LF, but only LF. It can be compiled with gcc -o {target_name} faltung2.c. The C program is a demonstration only; no responsibility is assumed for damages resulting from its usage.
• The sample input file input_monetary.dat is available at https://caipirinha.spdns.org/~gabriel/Blog/input_monetary.dat and can be read with a standard text editor. If is also in Unix format (only LF).
• The Excel tables and visualizations are available at https://caipirinha.spdns.org/~gabriel/Blog/PM%20Blog%20Tables.xlsx.