Abstract
We study the value of European security derivatives in the Black-Scholes model, when the underlying asset 𝛏 is approximated by random walks 𝛏(𝑛). We obtain an explicit error formula, up to a term of order 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 𝛏(𝑛), for which option values converge at a speed of 𝒪(𝑛⁻³/² ).
