Quantifying Model Performance

A model/hedging performance is relatively poorly covered in the literature. This is particularly valid for general portfolios including both vanilla and exotic instruments. Practitioners generally use so called \pnl explain which measures whether portfolio price movements can be explained by changes in risk factors for corresponding sensitivities. It gives, however, relatively little information about the model performance. In this paper, we address the problem under a new angle of the payoff replication along the whole portfolio life and come up with a metric which can classify different hedging strategies, in both relative and absolute ways.We confirm our theoretical results with numerical experiments. Initially we generate scenarios using the Heston model: the obtained numerical classification of different hedging strategies naturally agrees with a common sense. Moreover, this classification remains valid for all the Heston evolution scenarios (Monte Carlo paths) with tiny exceptions. Subsequently, we repeat these tests using real market data. Contrary to previous finding in the literature, we conclude that more sophisticated models, such as the Heston model, do in fact outperform simpler models, such as the Black-Scholes model, according to the metric introduced in this paper. These results contradict previous findings in the literature, so we supplement our numerical tests with the corresponding P\&L explained results. In accordance with the literature, the latter metric cannot identify more sophisticated models as performing better than simple models, however the metric introduced in this paper can