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...

We introduce a method for the approximation of a lognormal stock price process by a Cox, Ross and Rubinstein (CRR) type of binomial scheme, which allows to reach arbitrary speed of convergence of order O(n^{-(N/2)}), for any integer N>0.