Polynomials in Quant Finance: Example

Polynomials can be used in a variety of areas of quant finance however today we are discussing how to use them to fill in data. Often our data comes with different levels of granularity. If we are filling in one or two missing values, there are easier methods however if we are changing granularity of an entire data series we can use polynomials. The general steps are:

1) Fit the polynomial.
2) Use the polynomial to pull values at the new desired spacing.
3) Fit a model to the data to get the forecast.

As with everything we do in quantitative finance there are assumptions that must be made. These assumptions are risks and selecting the best method for a specific scenario is a part of managing that risk. One assumption being made with polynomials is that the unknown data between the known data points is monotonic. This is a slightly better assumption than using averages which has the assumptions of monotonic and linearity. A more complex method would be to use distributions to generate random data between the data points however determining this distribution is challenging and often not known in cases where we have less granular data. This complex method would fall under stochastic methods.


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