Value-at-Risk Computation by Fourier Inversion with Explicit Error Bounds

TL;DR

This paper presents a method for computing value-at-risk using Fourier inversion with explicit error bounds, enabling automated parameter selection and faster computation compared to Monte Carlo methods.

Contribution

It introduces a systematic way to determine integration parameters based on data, ensuring error bounds and improving efficiency in risk calculations.

Findings

Method achieves faster computation than Monte Carlo for the same error tolerance.

Parameters for numerical integration are derived explicitly from data.

Applicable to normal and multivariate t-distributed risk factors.

Abstract

The value-at-risk of a delta-gamma approximated derivatives portfolio can be computed by numerical integration of the characteristic function. However, while the choice of parameters in any numerical integration scheme is paramount, in practice it often relies on ad hoc procedures of trial and error. For normal and multivariate $t$-distributed risk factors, we show how to calculate the necessary parameters for one particular integration scheme as a function of the data (the distribution of risk factors, and delta and gamma) \emph{in order to satisfy a given error tolerance}. This allows for implementation in a fully automated risk management system. We also demonstrate in simulations that the method is significantly faster than the Monte Carlo method, for a given error tolerance.