engleski

Non-structural approach to implied moments extraction

Moments of the future prices and returns are not observable, but it is possible to measure these unknown parameters indirectly. Moreover, a set of option prices with the same maturity but with different exercise prices are used to extract implied probability distribution of the underlying asset at the expiration date. Implied probability distribution is riskneutral in the absence of arbitrage. The goal of this paper is to extract market expectations from option prices and to investigate which of the non-structural models for estimating risk- neutral density (RND) give the best fit. Nonstructural models assume that only dynamics in prices is known. Mixture of two log-normals (MLN), Edgeworth expansions and Shimko’s model, i.e. the representatives of parametric, semiparametric and nonparametric approaches respectively, are compared. Previous researches are inconclusive about the superiority of one approach over the others. This paper contributes to finding which approach dominates. The model that fits data better than the others is used to describe moments of the probability distribution. The sample covers one-year data for DAX index options. The results are compared through models and maturities. All models give better short-term forecasts. In pairwise comparison, MLN is superior to the other approaches according to mean squared errors and Diebold Mariano test.

Edgeworth expansions ; implied moments ; mixture of two log-normals ; Shimko’s model

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