ACCURATE AND EFFICIENT COMPUTATIONS FOR THE GREEKS OF EUROPEAN MULTI-ASSET OPTIONS

Abstract

This paper presents accurate and efficient numerical methods for calculating thesensitivities of two-asset European options, the Greeks. The Greeks are important financialinstruments in management of economic value at risk due to changing market conditions. Theoption pricing model is based on the Black–Scholes partial differential equation. The model isdiscretized by using a finite difference method and resulting discrete equations are solved bymeans of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effectof high-order discretizations. For Rho and Vega, we develop an accurate and robust automaticalgorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate theperformance of the proposed algorithm for calculating the Greeks. The results show that thenew treatment gives automatic and robust calculations for the Greeks.