Encyclopedia of Financial Models III

Value-at-Risk

STOYAN V. STOYANOV, PhD

Professor of Finance at EDHEC Business School and Head of Research for EDHEC Risk Institute-Asia

SVETLOZAR T. RACHEV, PhD, Dr Sci

Frey Family Foundation Chair-Professor, Department of Applied Mathematics and Statistics, Stony Brook University, and Chief Scientist, FinAnalytica

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: A risk measure that has been widely accepted since the 1990s is the value-at-risk (VaR). In the late 1980s, it was integrated by JP Morgan on a firmwide level into its risk-management system. In the mid-1990s, the VaR measure was approved by regulators as a valid approach to calculating capital reserves needed to cover market risk. The Basel Committee on Banking Supervision released a package of amendments to the requirements for banking institutions, allowing them to use their own internal systems for risk estimation. In this way, capital reserves, which financial institutions are required to keep, could be based on the VaR numbers computed internally by an in-house risk management system. Generally, regulators demand that the capital reserve equal the VaR number multiplied by a factor between 3 and 4. Thus, regulators link the capital reserves for market risk directly to the risk measure. In practice, there are several approaches for estimating VaR.

In this entry, we cover the most commonly used risk measure used by financial institutions: value-at-risk (VaR). We comment on its ...