Forecasting plausible scenarios and losses in interest rate targeting using mathematical optimization

Abstract

This study proposes a mathematical optimization model for simultaneously forecasting plausible market scenarios and portfolio losses. Interest rates, volatilities and correlation coefficients can be modeled by the DCC-GARCH. A constraint condition is set by the Mahalanobis distance for deciding an acceptable range of change in interest rates. An objective function is set as a hypothetical market portfolio loss from delta, gamma and vega. The mathematical optimization model becomes a nonlinear programming problem for which it is difficult to find appropriate solutions. Therefore, the study introduces an original heuristic approach for preventing the signs of solutions from unintentionally becoming inverse. The study finds that, compared to a stressful scenario in Japan, the forecasting scenarios and losses are plausible.