  A basic model in financial mathematics was introduced by Black, Scholes and
Merton in 1973 (BSM model). A classical discrete approximation in distribution
is the binomial model given by Cox, Ross and Rubinstein in 1979 (CRR model).
The BSM and the CRR models have been used for example to price European call
and put options. Our aim in this work is to give a strong (almost sure,
pathwise) discrete approximation of the BSM model using a suitable nested
sequence of simple, symmetric random walks. The approximation extends to the
stock price process, the value process, the replicating portfolio, and the
greeks. An important tool in the approximation is a discrete version of the
Feynman--Kac formula as well. It is hoped that such a discrete pathwise
approximation can be useful for example when teaching students whose
mathematical background is limited, e.g. does not contain measure theory or
stochastic analysis.
