Risk management using principal curvature

Abstract

Risk management is recently very important in financial market. However, well-known risk measurements are not efficient as duration, convexity etc. They are limited to use measuring risk. We suggest principal curvature in mathematics. We show the difference between convexity and principal curvature by proof of principal curvature. And there are three methods to compute principal curvature, direction in this article. It can measure risks have got two risk factors. We compute some numerical examples and bonds. Thus we can get directions of risk factors that has got maximum and minimum losses.