Equity linked securities(ELS) are securities whose returns on investment are tied to the returns of individual stocks or equity indices. It is important to calculate theoretical prices and Greeks of ELS because they have a significant impact on decision-making of investor and hedging strategy of the issuer. In finance, Monte-Carlo simulation(MC) and partial differential equations are being used for financial derivatives pricing. Among the partial differential equation approaches, the finite difference method(FDM) is the most used numerical method to solve Black-Scholes equation. As one of the finite difference methods, operator splitting method(OSM) is mainly used to solve a multidimensional Black-Scholes equation. In this paper, we apply physics-informed neural network(PINN) to the multidimensional Black-scholes equation and calculate theoretical price of a step-down ELS which has two underlying assets. Then we compare with the price with OSM and MC. Also, we calculate Greeks of ELS with PINN and compare those of OSM.
