Forecasting scenarios from the perspective of a reverse stress test using second-order cone programming

Katsuhiro Tanaka

Abstract

This paper proposes a model for forecasting scenarios from the perspective of a reverse stress test using interest rate (JGB10Y yield), equity (Nikkei 225) and foreign exchange (US$/U) data. The model consists of

(i) a constraint with error terms of dynamic conditional correlation–generalized autoregressive conditional heteroscedasticity (DCC–GARCH) for expressing risk factors (RFs) located in an acceptable range, where the acceptable range is determined by the Mahalanobis distance, which consists of error terms of DCC–GARCH and the correlation between one RF and another RF; and

(ii) maximization of the objection function, which is the loss of market portfolio (ie, minimization of the difference of a market portfolio). I also show that

(i) forecasting scenarios identified by this model are valid in terms of expressing very stressful data, which documents that some financial institutions may be in default, and that there is a mostly distributed multivariate normal distribution; and

(ii) this model can be solved by formulating second-order cone programming, which is standard in the field of mathematical optimization programming.

I expect this paper will be of interest to researchers and practitioners in the fields of stress testing and risk management.