Abstract
Moments of future prices and returns are not observable, but it is possible to measure them indirectly. 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. The aim is to obtain market expectations from options and to investigate which non-structural model for estimating implied probability distribution gives the best fit. Non-structural models assume that only dynamics in prices is known. Mixture of two log-normals (MLN), Edgeworth expansions and Shimko’s model (representatives of parametric, semiparametric and nonparametric approaches respectively) are compared. Previous researches are inconclusive about the superiority of one approach over the others. This article contributes to finding which approach dominates. The best fit model is used to describe moments of the implied 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 other approaches according to mean squared errors and Diebold-Mariano test in the observed period for DAX index options.
Highlights
Market participants, both small individual investors and big institutional investors, are interested in forecasting variance and mean and other unknown moments since they provide important information in portfolio management
The results show that the short-run forecasts yield better results with smaller mean square error (MSE), i.e., within each estimated model (MLN, Edgeworth expansions (EE) and s model (SM)) the null hypothesis of DM test can be rejected in favour of onesided alternative
Non-structural models assume that only dynamics in prices is known
Summary
Both small individual investors and big institutional investors, are interested in forecasting variance and mean and other unknown moments since they provide important information in portfolio management. Non-structural approaches yield a description of the implied probability distribution without completely describing the price dynamics They can be parametric, semiparametric and nonparametric. Some papers indicate that there is no significant difference between the models (Jackwerth, 1999), while some give the advantage to certain parametric (Duca & Ruxanda, 2013; Jondeau et al, 2007; Santos & Guerra, 2015), semiparametric (Coutant, Jondeau, & Rockinger, 2001; Flamouris & Giamouridis, 2002; Xiao & Zhou, 2017) and nonparametric models (Aparicio & Hodges, 1998; Benavides & Mora, 2008; Bliss & Panigirtzoglou, 2002; Jondeau & Rockinger, 2000) These papers do not always compare all non-structural models and or do it only for the in-the-sample testing, while neglecting the out-ofsample predictive accuracy. This article contributes to the existing literature in several ways It reveals at which maturity horizon the prediction of implied probability distribution is most accurate given by the ‘best’ non-structural model.
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