Modeling Stock Index Returns using Semi-Parametric Approach with Multiplicative Adjustment

In this paper we utilize a semi-parametric approach with multiplicative adjustment to estimate the distributions for a series of stock index returns including developed and emerging economies. The semi-parametric approach has potential improvements over both pure parametric and non-parametric estimators. Firstly, in the case where the parametric model is misspecified so that the parametric estimator for the true density is usually inconsistent, the semi-parametric estimator can still be consistent with the true density. Secondly, in comparison with the kernel density estimator, the semi- parametric estimator can result in bias reduction as long as the parametric model can capture some roughness feature of the true density function, whereas the two estimators have the same asymptotic variance. The simulation results show that the proposed approach has good finite sample performance compared with non-parametric approach. We apply the approach to the empirical data of a series of stock index returns and find support for it in each of the markets under consideration.