Computation of market risk measures with stochastic liquidity horizon

Gemma Colldeforns-Papiol, Luis Ortiz-Gracia

    Research output: Contribution to journalArticleResearch

    3 Citations (Scopus)

    Abstract

    © 2018 Elsevier B.V. The Basel Committee of Banking Supervision has recently set out the revised standards for minimum capital requirements for market risk. The Committee has focused, among other things, on the two key areas of moving from Value-at-Risk (VaR) to Expected Shortfall (ES) and considering a comprehensive incorporation of the risk of market illiquidity by extending the risk measurement horizon. The estimation of the ES for several trading desks and taking into account different liquidity horizons is computationally very involved. We present a novel numerical method to compute the VaR and ES of a given portfolio within the stochastic holding period framework. Two approaches are considered, the delta–gamma approximation, for modelling the change in value of the portfolio as a quadratic approximation of the change in value of the risk factors, and some of the state-of-the-art stochastic processes for driving the dynamics of the log-value change of the portfolio like the Merton jump–diffusion model and the Kou model. Central to this procedure is the application of the SWIFT method developed for option pricing, that appears to be a very efficient and robust Fourier inversion method for risk management purposes.
    Original languageEnglish
    Pages (from-to)431-450
    JournalJournal of Computational and Applied Mathematics
    Volume342
    DOIs
    Publication statusPublished - 1 Nov 2018

    Keywords

    • Expected shortfall
    • Liquidity risk
    • Market risk
    • Shannon wavelets
    • Stochastic liquidity horizon
    • Value-at-Risk

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