Comparison of Selected Advanced Numerical Methods for Greeks Calculation of Vanilla Options

Option valuation has been a challenging issue of financial engineering and optimization for a long time. The increasing complexity of market conditions requires utilization of advanced models that, commonly, do not lead to closed-form solutions. Development of novel numerical procedures, which prove to be efficient within various option valuation problems, is therefore worthwhile. Notwithstanding, such novel approaches should be tested as well, the most natural way being to assume simple plain vanilla options under the Black and Scholes model first; because of its simplicity the analytical solution is available and the convergence of novel numerical approaches can be analyzed easily. Here, we present the methodological concepts of two relatively modern numerical techniques, i.e., discontinuous Galerkin and fuzzy transform approaches, and compare their performance with the standard finite difference scheme in the case of sensitivity calculation (a so-called Greeks) of plain vanilla option price under Black and Scholes model conditions. The results show some interesting properties of the proposed methods.