Scenario analysis for derivatives portfolios via dynamic factor models
File(s)
Accepted version
Author(s)
Haugh, Martin
Ruiz Lacedelli, Octavio
Type
Journal Article
Abstract
A classic approach to financial risk management is the use of scenario analysis to stress test portfolios. In the case of an S&P 500 options portfolio, for example, a scenario analysis might report a P&L of −$1m in the event the S&P 500 falls 5% and its implied volatility surface increases by 3 percentage points. But how accurate is this reported value of −$1m? Such a number is typically computed under the (implicit) assumption that all other risk factors are set to zero. But this assumption is generally not justified as it ignores the often substantial statistical dependence among the risk factors. In particular, the expected values of the non-stressed factors conditional on the values of the stressed factors are generally non-zero. Moreover, even if the non-stressed factors were set to their conditional expected values rather than zero, the reported P&L might still be inaccurate due to convexity effects, particularly in the case of derivatives portfolios. A further weakness of this standard approach to scenario analysis is that the reported P&L numbers are generally not back-tested so their accuracy is not subjected to any statistical tests. There are many reasons for this but perhaps the main one is that scenario analysis for derivatives portfolios is typically conducted without having a probabilistic model for the underlying dynamics of the risk factors under the physical measure P. In this paper we address these weaknesses by embedding the scenario analysis within a dynamic factor model for the underlying risk factors. Such an approach typically requires multivariate state-space models that can model the real-world behavior of financial markets where risk factors are often latent, and that are sufficiently tractable so that we can compute (or simulate from) the conditional distribution of unstressed risk factors. We demonstrate how this can be done for observable as well as latent risk factors in examples drawn from options and fixed income markets. We show how the two forms of scenario analysis can lead to dramatically different results particularly in the case of portfolios that have been designed to be neutral to a subset of the risk factors.
Date Issued
2020-01-29
Date Acceptance
2019-11-22
Citation
Quantitative Finance, 2020, 20 (4), pp.547-571
ISSN
1469-7688
Publisher
Taylor & Francis (Routledge)
Start Page
547
End Page
571
Journal / Book Title
Quantitative Finance
Volume
20
Issue
4
Copyright Statement
© 2020 Informa UK Limited, trading as Taylor & Francis Group. This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 29 Jan 2020, available online: https://www.tandfonline.com/doi/full/10.1080/14697688.2019.1698757
Identifier
https://www.tandfonline.com/doi/full/10.1080/14697688.2019.1698757
Subjects
Social Sciences
Science & Technology
Physical Sciences
Business, Finance
Economics
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Business & Economics
Mathematics
Mathematical Methods In Social Sciences
Risk management
Filtering
Scenario analysis
Multi-factor models
TERM STRUCTURE
SELECTION
ROBUST
01 Mathematical Sciences
14 Economics
15 Commerce, Management, Tourism and Services
Finance
Publication Status
Published online
Date Publish Online
2020-01-29