A stochastic processes toolkit for risk management: Mean reverting processes and jumps
Abstract
In risk management it is desirable to grasp the essential statistical features of a time series representing a risk factor. this paper aims to introduce a number of different stochastic processes that can help in grasping the essential features of risk factors, describing different asset classes or behaviours. the paper does not aim to be exhaustive, but gives examples and a feeling for practically implementable models, allowing for stylised features in the data. these models can also be used as building blocks to build more complex models, although, for a number of risk management applications, the models developed here suffice for the first step in the quantitative analysis. the broad qualitative features addressed here are fat tails and mean reversion. the introduction, the general framework and fat tails have been addressed in the authors’ paper published in vol. 2, no. 4 of the journal. this paper deals with mean reversion both on its own and jointly with fat tails.
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Author's Biography
Damiano Brigo is Managing Director of Fitch Solutions' Quantitative Innovation team and Visiting Professor at Imperial College London's Department of Mathematics. His work has been published in top journals for mathematical finance, systems theory, probability and statistics, and he has also written a field reference book on stochastic interest rate modelling. Damiano is Managing Editor of the International Journal of Theoretical and Applied Finance, a member of the Fitch Academic Advisory Board, and has been a charter member of Risk Who's Who since 2007. Damiano obtained a PhD in stochastic filtering with differential geometry in 1996 from the Free University of Amsterdam, following a BSc in mathematics with honours from the University of Padua.
Antonio Dalessandro holds a PhD in mathematics from Imperial College London and is research associate at the University of Geneva's Department of Econometrics. From 2001 to 2004 he worked as a researcher at CERN and INFN in Geneva. He has a first-class honours MSc in electrical engineering from the Politecnico di Bari, and his research interests include probability, functional analysis, optimisation and high frequencies trading.
Matthias Neugebauer is Senior Director of Fitch Ratings' structured credit group. His responsibilities include criteria development and credit market research, including design and development of the portfolio credit model. Prior to this, he worked with the company's European quantitative research team. He holds a master's degree in finance and economics from Durham University and an engineering degree from Technical University Cottbus. He also holds a master's degree in mathematical finance from Oxford University.
Fares Triki obtained an engineering diploma from a French grande école, an MSc in finance from CNAM Paris, and a DEA diploma in economics from Paris Sorbonne University with summa cum laude distinction. After working for multinational consulting firms, he joined the Fitch Ratings Quantitative Financial Research team with the role of risk assessment and valuation of various financial products. Fares is now a macro finance expert at the financial stability directorate of Banque de France and is also a PhD student at the Paris School of Economics. His research areas include risk modelling and international economics and finance.
Citation
Brigo, Damiano, Dalessandro, Antonio, Neugebauer, Matthias and Triki, Fares (2010, January 1). A stochastic processes toolkit for risk management: Mean reverting processes and jumps. In the Journal of Risk Management in Financial Institutions, Volume 3, Issue 1. https://doi.org/10.69554/FFOR6336.
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