Standard fixed-income applications make a larger and larger use of the multi-curve framework to price products and hedge risks. For whatever reason this is the case, it is useful to know how to implement such a framework.
We have already talked about multi-curves in the past. Here we gave a list useful references and here we illustrated the mean features of risk metrics and sensitivity patterns. In this blog, we describe how to design the multi-curve framework. We do not claim that this is the only way or the best way. This is one possible way, which however turned out to work quite well within our system and happened to be easily integrated into our library.
Code snippets that will be shown below have been developed in C# using Visual Studio. Continue reading
Just before year end we put out our paper, titled "Review of Lattice Construction Methods"!
This paper extends the generalized procedure for building trees for short rates by Hull & White. A generalization for any mean and standard deviation of the underlying short rate model is presented. In addition we review the methodologies for constructing lattice models and give a step-by-step explanation on how to construct trinominal trees. We apply the formalism to some explicit examples of various complexity.
Full text can be found here
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
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