The model underwent extensive testing and is regularly being run through an exhaustive suite of unit and regression tests. The model results include intrinsic value and schedule, and extrinsic valuation and Greeks (if requested). Correctness of intrinsic optimization can usually be deduced by inspecting the results. The ultimate test for extrinsic calculation accuracy is to see if the hedge implied by the model performs well. For this, we performed extensive back-testing over multiple years with storage contracts of different parameters.

It is true that in some simple cases it is straightforward for a person with experience in numerical optimization and Monte Carlo simulations to put together a storage model in Matlab (or Python, Julia, etc.) However, from experience we found that there are plenty of edge cases where such models fail. Then, the originally straightforward self-coded model becomes a multi-year support headache. In more complex cases things get out of hand quite quickly, requiring significant resources to debug, test and maintain the code. We spent hundreds of hours to ensure that our model is robust, accurate and very fast.

Even if you are an experienced quant who can overcome these obstacles and you have a mandate from your company to develop an in-house model, we encourage you to use our model to help you debug and double check your code.

On the numerical side, the main contributors to speed are adaptive interpolation and per-path optimization. Adaptive interpolation allows us to build interpolants with a minimal number of points while still achieving the required precision. Per-path optimization (using only forward looking information) is based on recent research that shows that the method produces near-optimal solutions. Unlike other methods, per-path optimization methods are highly parallelizable, which allows us to use all cores of modern processors efficiently.

The model is coded in C++. From a programming perspective, the main contributors are precise memory management and ensuring that as many calculation as possible moved outside of the innermost loops. Precise memory management allows us to avoid unnecessary allocations and deallocations that have big performance impact. Additionally, it also ensures a compact memory footprint, which allows for the calculations to stay inside CPU cache.

The resulting calculation engine is very fast. For example, one year back-testing of Delta and Vega hedging (requiring the calculation of storage value, 12 Deltas and 12 Vegas every business day for a year) takes less than two minutes on our 16 core, 3.2 GHz PC. The web based model is somewhat slower as it is hosted in the cloud and each calculation is using up to 4 cores.