A Stochastic Processes Toolkit for Risk Management

DefaultRisk.com the web's biggest credit risk modeling resource.

Submit Your Paper

Fitch Ratings Jobs

[ Worldwide]

Post Your Résumé
For Recruiters

Featured Book

Interest Rate Models -- Theory and Practice: With Smile, Inflation and Credit, 2^nd Edition
by Damiano Brigo and Fabio Mercurio, Springer, (May 19, 2006), Hardcover, 981 pages

Training Discounted for DefaultRisk.com visitors only:

The Mathematics of Credit Derivatives: The Essential Credit Modelling and Pricing Companion
by Philipp J. Schönbucher,
WBS Training, August 2003, DVD / Interactive CD-ROM

Sponsor:
Shop at Amazon.com and support DefaultRisk.com

A Stochastic Processes Toolkit for Risk Management

by Damiano Brigo of Fitch-Solutions,
Antonio Dalessandro of Fitch-Solutions,
Matthias Neugebauer of Fitch-Solutions, and
Fares Triki of Fitch-Solutions

November 17, 2007

Abstract: 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.

JEL Classification: G32, C13, C15, C16.

AMS Classification: 60H10, 60J60, 60J75, 65C05, 65c20, 91B70.

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

Books Referenced in this Paper: (what is this?)