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Forecasting conceivable interest rate market scenarios and significant losses on interest rate portfolios using mathematical optimization

Katsuhiro Tanaka (pwd5re227i***at***hotmail.co.jp)

Abstract: This study proposes a mathematical optimization programming model that simultaneously forecasts interest rate market scenarios and significant losses on interest rate market portfolios. The model includes three main components. A constraint condition is set using the Mahalanobis distance, which consists of innovation terms in a dynamic conditional correlation-generalized autoregressive conditional heteroscedasticity (DCC-GARCH) model that represent the risk factors (RFs) and the correlations between RFs. The Mahalanobis distance can be interpreted as an eclipse-type uncertainty, set in the field of mathematical optimization, and can be represented by a second-order cone. The objection function is set using the loss on a market portfolio, represented by delta, gamma, and vega. The results are as follows. The forecasting scenarios are conceivable when compared with high-risk data in historical periods, and the forecasting losses are significant over a period of 20 business days as uncertainty increases. The proposed model can provide more plausible solutions if the second-order cones are replaced by nonlinear programming and an original heuristic approach. It is expected that the findings of this study will be of interest to researchers and practitioners in the field of risk management and mathematical optimization.

Keywords: Risk management, Mathematical optimization, Stress test, Reverse stress test, Uncertainty set, Portfolio analysis.

Category 1: Applications -- OR and Management Sciences (Finance and Economics )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 01/10/2019
Entry Accepted: 01/10/2019
Entry Last Modified: 01/15/2019

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