# Introduction

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

# Intuitions From The Multi-Curve Framework

### How can we hedge within the multi-curve framework?

Let’s consider a simplified case. Our building blocks will be swaps only of various tenors and maturities with the following purposes:

• Discounting instruments: we use 1-month tenor swaps of various maturities to construct the discounting curve.
• Tenor instruments: we use 3-months, 6-months and 12-months tenor swaps to construct the forward curves. We denote them as 3M, 6M and 12M.

The exact swap data are given in the attached spreadsheets [a] and [b]. In particular:

• the Data tab contains details of the input data and convention used in the calculation;
• the Rows tab contains the matrix with the PV01s/IV01s of all the input instruments as rows;
• the Columns tab contains the actual PV01/IV01 matrices as the transpose of the matrix in the previous tab;
• our notation in these examples is that all the curves are ordered by discounting type (the first one is always the discounting curve) and increasing tenors.

# Review of Lattice Construction Methods

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

# Finance: Between Testing and Regulations

Last July 8th we hosted our second meet up. The announced topics were Testing and Regulations, however the event was mostly testing. In a way, it has been very exciting to organise it, mainly because of some last-minute changes that affected the whole program. In fact, one of the speaker was sick and could not attend, and on top of that a few unexpected technical problems arose at the MixTup venue as well. Eventually everything worked fine and all the efforts made during the few days and hours before the event contributed to the success of the evening.

The chairman of the event was my colleague Jorrit-Jaap de Jong (Ugly Duckling), who entertained the audience, introduced the speakers, and reminded everybody of the purposes of the FEN evenings (which you can read in the ad of our introductory meeting here). The two talks were essentially on testing. The first speaker was our financial engineer Michele Maio (Ugly Duckling) who introduced various testing techniques and good practices such as test driven development and automated testing (mostly focusing on Excel and FitNesse). Michele used the programming language C#. The second speaker was Mert Aybat (Connectis). Mert had an extremely nice "live" and interactive presentation on how to use Mocks when testing complicated projects with many dependencies, and he definitely showed his competence in testing. Mert used Java and Mockito as tools of choice.

The crowd present to the meeting also deserves some comment. Besides the people who attended our first meeting, we were happy to see many new faces who joined this second event, coming both from the software and the finance industries.  They all stimulated the discussions that arose during the presentations: thanks to them the flow of information was not in one direction only.

What will happen in the future?

It is important for us to keep track of what we want to achieve and what the FEN events are all about, namely: sharing knowledge, creating an intellectual stimulating environment, meeting like-minded people, discussing trends and hot topics in finance, and networking. In order to move forward, events are planned every couple of month, and the next one will be in autumn when everybody is back from summer vacations. We will keep the current format, which has been successful so far: hosting two talks within an informal environment with topics related to software, finance, and financial engineering.

Requests

To make the FEN community larger, it is crucial that everybody is active. That's why we would like to reminder everybody that anybody is welcome to join. Moreover, as Jorrit mentioned during this event:

• we are always looking for speakers, so if anybody is interested to talk at next event please let us know;
• we are also looking for locations, so if anybody would like to organise the next event with use by booking a seminar room in his/her bank or institution please let us know;
• we are always looking forward to growing our community, so please share it with your network.

# FEN Event - July 2014

## Amsterdam - July 8 2014, 19:00 @ MixTup

Financial Engineering Netherlands (FEN) is a community of specialists in software and in the financial sector that everybody can join and consult.

The next FEN event will be held on July 8 and the topic will be about

### "Finance Between Testing and Regulations".

The speakers for this evening are:

Paramita Banerjee (ING) **
Paramita is a business analyst at ING. Her predominant focus has been on operationlizing change solution within global investment banks normally representing AML and Front-Office interests, and her specialties are requirement elicitation and analysis and process modelling. She is an expert in the international banking and international finance sectors.

Mert Aybat  (Connected Information Systems - Connectis)
Mert is a software engineer at Connectis. He has a strong quantitative (PhD in particle physics) background as well as an exhaustive international experience (he has lived and worked in many countries, such as US, Switzerland, Netherlands, etc.). His current work is in the area of information technology in general, and his specialty is information security.

The Talks

• Paramita Banerjee: Basel III on Stress Testing & Backtesting **
• Mert Aybat: Advanced Testing with Mocks: Theory and Practice

No prior knowledge of finance and/or financial engineering and/or testing will be required.

Registration
Via the Meet-up website. Please register asap.
If you have already registered but you are not able to come anymore, please let us know.

Space-time Coordinates
MixTup, Ferdinand Bolstraat 8, 1072 LJ Amsterdam (map).  Doors open at 19:00.

Blog

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** Paramita was sick during the actual event, so she could not attend. She was replaced by the Duckling Michele Maio (who also spoke at our opening event):

• Michele Maio: Automated Testing in Finance

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# 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

# Test Driven Development for Financial Engineers

On the evening of last April 24th at the Ugly Duckling office in Amsterdam we celebrated the birth of our new series of events for financial engineers. We called it Financial Engineering Netherlands, and we hope we will create a community of specialists that everybody can join and consult.

The aims of Financial Engineering Netherlands are

• to bring together experts with similar passions, who are willing to improve themselves by sharing their knowledge with others, keeping the topics within the interest range of financial engineers, and hence including testing, programming, technology, finance, mathematical finance, etc. as subjects of discussion;
• to create an intellectually stimulating and social environment, where people can discuss about trends, problems, progress and achievements in any of the above-mentioned fields, in order to find what really matters in our work and discover how we can improve ourselves in a collaborative way.