  In this paper, we implement and test two types of market-based models for
European-type options, based on the tangent Levy models proposed recently by R.
Carmona and S. Nadtochiy. As a result, we obtain a method for generating Monte
Carlo samples of future paths of implied volatility surfaces. These paths and
the surfaces themselves are free of arbitrage, and are constructed in a way
that is consistent with the past and present values of implied volatility. We
use a real market data to estimate the parameters of these models and conduct
an empirical study, to compare the performance of market-based models with the
performance of classical stochastic volatility models. We choose the problem of
minimal-variance portfolio choice as a measure of model performance and compare
the two tangent Levy models to SABR model. Our study demonstrates that the
tangent Levy models do a much better job at finding a portfolio with smallest
variance, their predictions for the variance are more reliable, and the
portfolio weights are more stable. To the best of our knowledge, this is the
first example of empirical analysis that provides a convincing evidence of the
superior performance of the market-based models for European options using real
market data.
