Price of 5-year credit default swap (coupon=100) at the close of the market on , at 5:00 PM GMT (source: DataGrapple).

One Instrument: The CDS

The credit default swap (“CDS”) is a financial instrument enabling the transfer of an issuer’s credit risk between two investors. The CDS provides investors with a very simple, very liquid tool for hedging or investing. The price of a CDS is the market barometer for the risk of a borrower.

One Process: Arbitrage

Arbitrage is an investment technique that combines purchases and sales of financial instruments having offsetting risks. The net return on the portfolios thus combined is the arbitrage profit. The performance of arbitrage portfolios is not governed by the performance of the financial markets. Arbitrages are investment processes that use leverage – such investments are restricted to professional investors.

One Team: HC

Hellebore Capital (HC) is a management company specializing in credit derivatives arbitrage. Its technology gives HC the ability to operate in all the credit derivatives markets of Europe and North America. If you would like to learn more about HC and its products, you can create an account online. HC is regulated by the UK Financial Conduct Authority (“FCA”).

Research and Development

About Hellebore Capital's R&D

Hellebore Capital's R&D team focuses on credit default swap (CDS) time series modelling, both to define quantitative investment strategies or to design new risk management frameworks. The team has developed an expertise in clustering algorithms, a set of machine-learning techniques which clusters assets demonstrating similar behaviour. These techniques are providing resilient results despite noise and jumps characteristics of CDS time series. The team publishes some of its results and participates in various conferences on this topic. We think this is good practice to constantly challenge our ideas.

Among our current research themes:

  • Clustering multivariate representation of assets, for example combining stock returns and CDS prices for each company listed and traded in the CDS market;
  • Mathematical consistency and convergence properties of clustering many dependent random variables; and
  • Bayesian inference and clustering.

Hellebore Capital has established a partnership with the Ecole Polytechnique, France, and the team is currently hosting an intern from Imperial College, London.

Selection of published articles

Toward a generic representation of random variables for machine learning

This paper introduces a new representation of time series and an associated metric for clustering time series in homogeneous sets. The representation is applied to CDS time series. It essentially refines clusters of correlated assets by taking into account the marginal distribution of their returns. The method provides stable and reliable clusters.

A proposal of a methodological framework with experimental guidelines to investigate clustering stability on financial time series

This paper proposes a methodology to assess the robustness of clusters. Besides, it also aims to understand asset clustering invariants and to answer questions such as: "Are clusters the same using daily/weekly/monthly returns, using different maturities in the CDS term structure, both during bear and bull periods"?

Clustering Financial Time Series: How Long is Enough?

This paper also tackles the question of clustering stability, but from more of a theoretical point of view. We first show that the clustering methodology can be consistent. This means that the clusters obtained from the algorithm converge to the correct clusters. This also means that there is a minimum value of the time sample T (in practice, a minimum number of returns observed in the historical time series) required so that the clusters obtained are correct. We show that this minimum value T is strongly dependent of the clustering methodology. The challenge for us is then to find the clustering methodology which yields the smallest possible T. The smaller the T, the more relevant the applications of clustering financial time series can be.

Optimal Copula Transport for Clustering Multivariate Time Series

This paper contains several ideas and opens several research directions for us. We focus on (i) Understanding dependence between objects described by several time series; (ii) Defining new dependence coefficients which can robustly target specific dependence patterns; and (iii) Studying various geometries for copulas. We also explore issues such as the distance between these objects,  empirical 'ergodicity' and the rate of convergence of the clustering algorithms when the objects are described by several time series.

Past and Foreseen Conferences

We will give and gave talks at these machine learning conferences:

We also participate to various Machine Learning / Big Data / FinTech meetings in Paris and London:

Join Us

We propose internships on the following topics:
  • High Performance Computing for Machine Learning
  • Bayesian inference of market variables

Unsolicited applications from graduate students in math, physics, machine learning, financial engineering with strong computational skills are most welcomed.