A European option general first-order error formula

Abstract

We study the value of European security derivatives in the Black–Scholes model when the underlying asset \(\xi\) is approximated by random walks \(\xi^{(n)}\). We obtain an explicit error formula, up to a term of order \(\mathcal{O}(n^{3/2})\), which is valid for general approximating schemes and general payoff functions. We show how this error formula can be used to find random walks \(\xi^{(n)}\) for which option values converge at a speed of \(\mathcal{O}(n^{3/2})\). doi:10.1017/S1446181113000254