2023/06/14 by Tobias Behrens, Behrens, Tobias, Gero Junike +2 · 1 citation
Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #FOS: Economics and business #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2306.08421
openalex publication_date 2023/06/14 · openalex created_date 2023/06/17 · openalex updated_date 2026/07/28
The Greeks Delta and Gamma of plain vanilla options play a fundamental role in finance, e.g., in hedging or risk management. These Greeks are approximated in many models such as the widely used Variance Gamma model by Fourier techniques such as the Carr-Madan formula, the COS method or the Lewis formula. However, for some realistic market parameters, we show empirically that these three Fourier methods completely fail to approximate the Greeks. As an application we show that the Delta-Gamma VaR is severely underestimated in realistic market environments. As a solution, we propose to use finite differences instead to obtain the Greeks.