We consider a Black-Scholes type equation arising on a pricing model for a multi-asset option with general transaction costs. The pioneering work of Leland is thus extended in two different ways: on the one hand, the problem is multi-dimensional since it involves different underlying assets; on the other hand, the transaction costs are not assumed to be constant (i.e. a fixed proportion of the traded quantity). Using an iterative method, we prove the existence of solutions for the corresponding initial-boundary value problem. Moreover, we develop a numerical scheme that allows to find a sequence of approximate solutions. We apply this method on a specific multi-asset derivative and we obtain the option price under different pricing scenarios.
↧