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A Stochastic Processes Toolkit for Risk Management

Damiano Brigo

Imperial College London - Department of Mathematics

Antonio Dalessandro


Matthias Neugebauer

Fitch Ratings Inc.

Fares Triki

Paris School of Economics, Pantheon Sorbonne University

November 15, 2007

In risk management it is desirable to grasp the essential statistical features of a time series representing a risk factor. This tutorial 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 behaviors. This paper does not aim at being exhaustive, but gives examples and a feeling for practically implementable models allowing for stylised features in the data. The reader may also use these models 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. We give some orientation on the initial choice of a suitable stochastic process and then explain how the process parameters can be estimated based on historical data. Once the process has been calibrated, typically through maximum likelihood estimation, one may simulate the risk factor and build future scenarios for the risky portfolio. On the terminal simulated distribution of the portfolio one may then single out several risk measures, although here we focus on the stochastic processes estimation preceding the simulation of the risk factors Finally, this first survey report focuses on single time series. Correlation or more generally dependence across risk factors, leading to multivariate processes modeling, will be addressed in future work.

Number of Pages in PDF File: 43

Keywords: Risk Management, Stochastic Processes, Maximum Likelihood Estimation, Fat Tails, Mean Reversion, Monte Carlo Simulation

JEL Classification: G32, C13, C15, C16

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Date posted: March 19, 2008 ; Last revised: October 5, 2008

Suggested Citation

Brigo, Damiano and Dalessandro, Antonio and Neugebauer, Matthias and Triki, Fares, A Stochastic Processes Toolkit for Risk Management (November 15, 2007). Available at SSRN: http://ssrn.com/abstract=1109160 or http://dx.doi.org/10.2139/ssrn.1109160

Contact Information

Damiano Brigo (Contact Author)
Imperial College London - Department of Mathematics ( email )
South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom
HOME PAGE: http://www.damianobrigo.it
Antonio Dalessandro
Independent ( email )
No Address Available
Matthias Neugebauer
Fitch Ratings Inc. ( email )
One state street plaza
New York, NY 10004
United States
Fares Triki
Paris School of Economics, Pantheon Sorbonne University ( email )
48 Boulevard Jourdan
Paris, 75014 75014
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