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In this paper, we implement and test two types of market-based models forEuropean-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 MonteCarlo samples of future paths of implied volatility surfaces. These paths andthe surfaces themselves are free of arbitrage, and are constructed in a waythat is consistent with the past and present values of implied volatility. Weuse a real market data to estimate the parameters of these models and conductan empirical study, to compare the performance of market-based models with theperformance of classical stochastic volatility models. We choose the problem ofminimal-variance portfolio choice as a measure of model performance and comparethe two tangent Levy models to SABR model. Our study demonstrates that thetangent Levy models do a much better job at finding a portfolio with smallestvariance, their predictions for the variance are more reliable, and theportfolio weights are more stable. To the best of our knowledge, this is thefirst example of empirical analysis that provides a convincing evidence of thesuperior performance of the market-based models for European options using realmarket data.

Simulation of Implied Volatility Surfaces via Tangent Levy Models