A diffusion approximation for the riskless profit under selling of discrete time call options

A discrete time model of a financial market is considered. We focus on the study of a guaranteed profit of an investor which arises when the stock price jumps are bounded. The limit distribution of the profit as the model becomes closer to the classical model of the geometric Brownian motion is established. It is of interest that in contrast with the discrete approximation, no guaranteed profit occurs in the approximated continuous time model. -- asymptotic uniformity ; weak convergence in Skorokhod Space D[0, 1].