Financial Simulation Modeling in Excel

DISCUSSION ON ERRORS

The Hull-White tree method allows us to price options based on certain assumptions made about the characteristics of our underlying assets. When pricing an entire portfolio of derivatives using this method, it would be beneficial to understand how confident we are of the projected price. To accomplish this, we have to somehow characterize the accuracy of the tree itself. Unfortunately, this is nearly impossible since we have not yet developed a method for predicting the future. We just don't know what the actual price will be. Therefore, from the standpoint of our analysis, the answer we get is the actual answer and our error when using this model stems mainly from the number of time steps used in the analysis. Remember, as we increase the number of steps used, we also increase the accuracy of our result. At small-enough intervals, the answers will eventually converge; that is, the difference between finer and finer intervals will become negligible.

In an ideal situation where computational workload is a nonissue, we can run every simulation for every option in our portfolio with thousands of time steps each. However, this is not always practical in reality, as we must limit the number of steps used in order to produce results in a timely fashion. When we limit our simulation in this manner, the price we get will be a certain amount off from the actual price we would have gotten had we not limited our simulation. This difference is our error. Therefore, to ...