Comparison of Certain Models and Results of Stochastic Financial Mathematics with Real Data

Certain probabilistic models for the logarithmic increments of stock prices are compared with real data. It is shown that all these models are essentially inadequate because of the statistical instability of the observed data. Nevertheless, theoretical results on option hedging are confirmed (to unexpectedly high accuracy) by hedging simulations using real price data. This fact is explained by comparatively small fluctuations of the volatility of prices, which are the main source of imbalance (i.e. the hedging inaccuracy).