Beyond VaR: Triangular Risk Decomposition (pdf)

Beyond VaR: Triangular Risk Decomposition

This paper describes triangular risk decomposition, which provides a useful, geometric view of the relationship between the risk of a position and that of the portfolio. We review triangular decomposition for the case of the parametric, or delta-normal, Value-at-Risk (VaR), which assumes that changes in a portfolio’s value are normally distributed with mean zero. We then generalize it for the c...

DECOMPOSITION METHOD FOR SOLVING FULLY FUZZY LINEAR SYSTEMS

In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. This paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix S and a fuzzy triangular matrix T.

Estimating Value-at-risk with a Precision Measure by Combining Kernel Estimation with Historical Simulation

We thank seminar participants at the OCC and the 1996 Chicago Fed Bank Structure Conference for their comments. We also thank Rene Stulz for comments and suggestions and Amy Crews for guidance concerning kernel estimation. The views expressed herein are those of the authors and do not necessarily represent the views of the Chase Manhattan Bank or any of its staff or of the Office of the Comptro...

Thoughts on VaR and CVaR

Value at Risk (VaR) is an important issue for banks since its adoption as a primary risk metric in the Basel Accords and the requirement that it is calculated on a daily basis. VaR calculates maximum expected losses over a given time period at a given tolerance level. Conditional Value at Risk (CVaR) measures extreme risk. It calculates the risk beyond VaR. Relative industry risk measurement is...

Risk Management Beyond VaR presented at the 2013 Financial Markets Conference