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