Modeling the conditional distribution of financial returns with asymmetric tails

Abstract

Summary This paper proposes a conditional density model that allows for differing left/right tail indices and time‐varying volatility based on the dynamic conditional score (DCS) approach. The asymptotic properties of the maximum likelihood estimates are presented under verifiable conditions together with simulations showing effective estimation with practical sample sizes. It is shown that tail asymmetry is prevalent in global equity index returns and can be mistaken for skewness through the center of the distribution. The importance of tail asymmetry for asset allocation and risk premia is demonstrated in‐sample. Application to portfolio construction out‐of‐sample is then considered, with a representative investor willing to pay economically and statistically significant management fees to use the new model instead of traditional skewed models to determine their asset allocation.

A coupled component DCS-EGARCH model for intraday and overnight volatility

“…Finally, we note that although the conditional distribution of returns is symmetric about the mean, the unconditional distribution implied by our model may be asymmetric because of the conditional mean process and the asymmetric news impact curve that we allow for, He, Silvennoinen, and Teräsvirta (2008). Thiele (2019) consider some DCS models with asymmetric t-distributions, which might be a possible direction for future work.…”

Polynomial adjusted Student-t densities for modeling asset returns

“…3 It is well known that the PAG density is only suitable for return series with moderate kurtosis. The literature on this topic has developed very quickly during recent years, see, for instance, Wilhelmsson (2006), Komunjer (2007), Bali, Mo, and Tang (2008), Zhu and Galbraith (2011), Dendramis, Spungin, and Tzavalis (2014), Harvey and Sucarrat (2014), Liu, Li, and Ng (2015), Feunou, Jahan-Parvar, and Tédongap (2016), Kumar and Patil (2016), León and Ñíguez (2020) and Thiele (2020). Contributing to this line of research, we show that the PAST can be a good candidate for statistical analysis of financial returns and, in general, for fitting series with high levels of kurtosis.…”