financial library

Multi-Curve - Useful References

We have recently started the project of including the multi-curve framework into the UDFinLib, our own financial library. The topic is delicate, as it consists of both research and implementation at once.

After the 2007-2008 world financial crisis it became clear that the classical single-curve framework that had been used until then was not appropriate to value products and to hedge portfolio's positions. All of a sudden credit risk was an every day's topic, collateral margins exploded and the previously small spreads between different-tenor swaps (OIS vs Libor, 3M-tenor vs 6M-tenor) could not be neglected anymore. Single-curve building, which treated instrument with different tenors in the same way, had to be upgraded to multi-curve.

In a nutshell, the multi-curve framework amounts to construct one discount curve and many tenor curves. The discount curve is typically built with OIS instruments, which are the best approximation for the risk free rate. All the other tenor curve are built with instruments with homogeneous tenors. The most used tenors are 3M, 6M, 9M, 12M. Typically, the longer the tenor the riskier the trade and hence the higher the corresponding rate.

In this blog we give a non-exhaustive list of references that helped us in both understanding the multi-curve and designing the process.



Nice reading!

Interpolation methods and the Hagan-West paper

Interpolation is a very useful technique for extracting data when the available information does not come in a continuous form.

From a non-technical point of view, any inference or decision process (sometimes subconsciously) is based on a kind of interpolation or best fitting or regression of the available informations. We as people are normally quite good at generalising (often too fast) from the little amount of information that we have about other people, situations, or even numerical data. This is possible because our brain can recognise patterns and see trends in any kind of data. However, technically speaking, interpolation is more that just finding a trend.

Technically, we are often given a discrete set of data corresponding to a certain function which is known at specific points, or nodes (for example, we have made an experiment for specific input values and measured the outputs  corresponding to that input), and is otherwise unknown.  In principle this is a multi-dimensional problem, and the interpolating hyper-surface will give an idea of the missing information. In fact, even if it is true that such a hyper-surface can always be numerically constructed,  however the uniqueness issue remains. Given the same input data, many different constructions can be engineered, all satisfying to various -more or less realistic- criteria, and all passing through the same input points. Continue reading

UD Fin Lib

Ugly Duckling Finance is currently working on its financial library, UDFinLib. UDFinLib will appear soon and will be advertised on this blog and website. Everybody interested is therefore invited to come back later when it will be ready to use. In this blog post I would like to anticipate some of the features of the library.

The library comes in two parts: the core and the Excel Add-in. Continue reading