Approximations of Profit-and-Loss Distributions (A Numerical Approach for Evaluating VaR based on Extremal Measures)
Series
Risklab report
Type
work report
Date Issued
1995
Author(s)
Abstract
working report - Value functions (risk profiles) of financial instruments and the real distributions of risk factors are not available in analytically closed forms. These components have to be approximated. In this work, a new approach for risk measurement is introduced. The underlying methodology is based on the utilization of extremal measures for approximating the P&L distribution. A special class of "extremal measures" is employed which exploits the monotonicity of price sensitivities entailed by convexity. Clearly, in case the value functions have monotonous derivatives, the payoff-functions are convex or concave depending on whether a position is held short or long. The incorporated extremal measures provide approximations for both risk factor distribution and risk profiles, and allow for deriving an adequate approximation of the P&L distributions, in particual for appealing VaR-estimates. The basics of this approach are presented and first numerical results are tested against the currently apllied VaR-approaches and the simulation benchmarks established earlier in Allen (1994).
Language
English
HSG Classification
not classified
Refereed
No
Publisher
Institute for Operations Research, University of St. Gallen
Publisher place
St. Gallen, CH
Subject(s)
Division(s)
Eprints ID
7251