Towards a skewness index for the Italian stock market

The present paper is a first attempt of computing a skewness index for the Italian stock market. We compare and contrast different measures of asymmetry of the distribution: an index computed with the CBOE SKEW index formula and two other asymmetry indexes, the SIX indexes, as proposed in Faff and Liu (2014). We analyze the properties of the skewness indexes, by investigating their relationship with model-free implied volatility and the returns on the underlying stock index. Moreover, we assess the profitability of skewness trades and disentangle the contribution of the left and the right part of the risk neutral distribution to the profitability of the latter strategies. The data set consists of FTSE MIB index options data and covers the years 2011-2014, allowing us to address the behavior of skewness measures both in bullish and bearish market periods. We find that the Italian SKEW index presents many advantages with respect to other asymmetry measures: it has a significant contemporaneous relation with both returns, model-free implied volatility and has explanatory power on returns, after controlling for volatility. We find a negative relation between volatility changes and changes in the Italian SKEW index: an increase in model-free implied volatility is associated with a decrease in the Italian SKEW index. Moreover, the SKEW index acts as a measure of market greed, since returns react more negatively to a decrease in the SKEW index (increase in risk neutral skewness) than they react positively to an increase of the latter (decrease in risk neutral skewness). The results of the paper point to the existence of a skewness risk premium in the Italian market. This emerges both from the fact that implied skewness is more negative than physical one in the sample period and from the profitability of skewness trading strategies. In addition, the higher performance of the portfolio composed by only put options indicates that the mispricing of options is mainly focused on the left part of the distribution

The properties of a skewness index and its relation with volatility and returns

The objective of this study is threefold. First, we investigate the properties of a skewness index in order to determine whether it captures fear (fear of losing money), or greed in the market (fear of losing opportunities). Second, we uncover the combined relationship among skewness, volatility and returns. Third, we provide further evidence and possible explanations for the relationship between skewness and future returns, which is highly debated in the literature. The stock market investigated is the Italian one, for which a skewness index is not traded yet. The methodology proposed for the construction of the Italian skewness index can be adopted for other European and non-European countries characterized by a limited number of option prices traded. Several results are obtained. First, we find that in the Italian market the skewness index acts as measures of market greed, as opposed to market fear. Second, for almost 70% of the daily observations, the implied volatility and the skewness index move together but in opposite directions. Increases (decreases) in volatility and decreases (increases) in the skewness index are associated with negative (positive) returns. Last, we find strong evidence that positive returns are reflected both in a decrease in the implied volatility index and in an increase in the skewness index the following day. Implications for investors and policy makers are drawn

The Risk-Asymmetry Index

The aim of this paper is to propose a simple and unique measure of risk, that subsumes the conflicting information in volatility and skewness indices and overcomes the limits of these indices in correctly measuring future fear or greed in the market. To this end, we exploit the concept of upside and downside corridor implied volatility, which accounts for the asymmetry in risk-neutral distribution, i.e. the fact that investors like positive spikes in returns, while they dislike negative ones. We combine upside and downside implied volatilities in a single asymmetry index called the risk-asymmetry index (\u734\u723 .(\u73aThe risk-asymmetry index \u123a\u734\u723\u73a\u123b plays a crucial role in predicting future returns, since it subsumes all the information embedded in both the Italian skewness index \u72b\u735\u736\u727\u72d \u739and the Italian volatility index (\u72b\u738\u736\u72b .(\u73aThe \u734\u723 \u73aindex is the only index that is able to indicate (when reaching very high values) a clearly risky situation for the aggregate stock market, which is detected neither by the \u72b\u738\u736\u72b \u73aindex nor by the \u72b\u735\u736\u727\u72d \u739index

Moment Risk Premia and the Cross-Section of Stock Returns

The aim of this paper is to assess the existence and the sign of moment risk premia. To this end, we use methodologies ranging from swap contracts to portfolio sorting techniques in order to obtain robust estimates. We provide empirical evidence for the European stock market for the 2008-2015 time period. Evidence is found of a negative volatility risk premium and a positive skewness risk premium, which are robust to the different techniques and cannot be explained by common risk-factors such as market excess return, size, book-to-market and momentum. Kurtosis risk is not priced in our dataset. Furthermore, we find evidence of a positive risk premium in relation to the firm’s size

Forecasting and pricing powers of option-implied tree models: Tranquil and volatile market conditions

The aims of this paper are twofold. First, to investigate the accuracy of different option-implied trees in pricing European options in order to assess the power of implied trees in replicating the market information. Second, to compare deterministic volatility implied trees and stochastic implied volatility models (Bakshi et al. (2003)) in assessing the forecasting power of implied moments on subsequently realised moments, and ascertaining the existence, magnitude and sign of variance, skewness, and kurtosis risk-premia. The analysis is carried out using the Italian daily market data covering the period 2005-2014. This enables us to contrast the pricing performance of implied trees and to assess the magnitude and sign of risk premia in both a tranquil and a turmoil period. The findings are as follows. First, the pricing performance of the Enhanced Derman and Kani (EDK, Moriggia et al. 2009) model is superior to that of the Rubinstein (1994) model. This superiority is stronger especially in the high volatility period due to a better estimation of the left tail of the distribution describing bad market conditions. Second, the Bakshi et al. (2003) formula is the most accurate for forecasting skewness and kurtosis, while for variance it yields upwardly biased forecasts. All models agree on the signs of the risk premia: negative for variance and kurtosis, and positive for skewness, but differ in magnitude. Overall, the results suggest that selling (buying) variance and kurtosis (skewness) is profitable in both high and low volatility periods

Role of zinc and α2macroglobulin on thymic endocrine activity and on peripheral immune efficiency (natural killer activity and interleukin 2) in cervical carcinoma

Decreased natural killer (NK) activity as well as interleukin 2 (IL-2) are risk factors for the progression of cervical carcinoma. NK activity and IL-2 may be thymus controlled. Plasma levels of active thymulin, a zinc-dependent thymic hormone (ZnFTS), are reduced in cancer because of the low peripheral zinc bioavailability. Zinc and thymulin are relevant for normal immune functions. α2-Macroglobulin is an inhibitor of matrix metalloproteases (MMPs) against invasive tumour proliferation. Because α2-macroglobulin has a binding affinity (Kd) for zinc that is higher than does thymulin, it may play a key role in immune efficiency in cancer. Plasma samples of 22 patients (age range 35–60 years) with locally advanced squamous cervical carcinoma and with FIGO stage Ib2–IIb were examined. They showed reduced active thymulin, decreased NK activity and IL-2 production, increased soluble IL-2 receptor (sIL-2R) and augmented α2-macroglobulin in the circulation, whereas plasma zinc levels were within the normal range for age. Significant positive correlations were found between zinc or active thymulin and α2-macroglobulin (r = 0.75, P< 0.01, r = 0.78, P< 0.01, respectively) in cancer patients. In vitro zinc increases IL-2 production from peripheral blood mononuclear cells (PBMCs) of cancer patients. These data suggest that an increase in α2-macroglobulin, which competes with thymulin for zinc binding, may be involved in causing a thymulin deficit with a consequent decrease of IL-2 and NK cytotoxicity. Thus, physiological zinc treatment in cervical carcinoma maybe restores impaired central and peripheral immune efficiency. © 1999 Cancer Research Campaig

Testing the predictive ability of corridor implied volatility under GARCH models

YesThis paper studies the predictive ability of corridor implied volatility (CIV) measure. It is motivated by the fact that CIV is measured with better precision and reliability than the model-free implied volatility due to the lack of liquid options in the tails of the risk-neutral distribution. By adding CIV measures to the modified GARCH specifications, the out-of-sample predictive ability of CIV is measured by the forecast accuracy of conditional volatility. It finds that the narrowest CIV measure, covering about 10% of the RND, dominate the 1-day ahead conditional volatility forecasts regardless of the choice of GARCH models in high volatile period; as market moves to non volatile periods, the optimal width broadens. For multi-day ahead forecasts narrow and mid-range CIV measures are favoured in the full sample and high volatile period for all forecast horizons, depending on which loss functions are used; whereas in non turbulent markets, certain mid-range CIV measures are favoured, for rare instances, wide CIV measures dominate the performance. Regarding the comparisons between best performed CIV measures and two benchmark measures (market volatility index and at-the-money Black–Scholes implied volatility), it shows that under the EGARCH framework, none of the benchmark measures are found to outperform best performed CIV measures, whereas under the GARCH and NAGARCH models, best performed CIV measures are outperformed by benchmark measures for certain instances