Nuova ricerca

LUCA GAMBARELLI

CULTORE DELLA MATERIA presso: Dipartimento di Economia "Marco Biagi"

DOCENTE A CONTRATTO presso: Dipartimento di Economia "Marco Biagi"


Home | Curriculum(pdf) | Didattica |


Pubblicazioni

2021 - The skewness index: uncovering the relation with volatility and market returns [Articolo su rivista]
Elyasiani, 2. E.; Gambarelli, L.; Muzzioli, S.
abstract


2021 - The skewness index: uncovering the relationship with volatility and market returns [Articolo su rivista]
Elyasiani, E.; Gambarelli, L.; Muzzioli, S.
abstract

The SKEW index of the Chicago Board Options Exchange (CBOE), launched in February 2011, measures the tail risk not fully captured by the VIX index. In this paper we introduce, for the first time, a skewness index for the Italian stock market (ITSKEW) and investigate the pairwise and trilateral relations of this index with volatility and market returns. The results are compared with those of the US market. Data for the period 3 January 2011 to 29 December 2017 are used and three main results are found. First, in both the US and the Italian markets, the skewness index acts as a measure of market greed, as opposed to market fear, in the sense that it captures investor excitement to a larger extent than investor fear. Second, increases in the skewness index are related to returns with high significance in the Granger causality test, while the reverse is not the case. Last, volatility and skewness may give conflicting signals. When skewness and volatility indices move in the same direction, investors should rely on volatility because it has a stronger influence on market returns. The implications for investors and policy-makers are outlined.


2020 - Moment risk premia and the cross-section of stock returns in the European stock market [Articolo su rivista]
Elyasiani, Elyas; Gambarelli, Luca; Muzzioli, Silvia
abstract

This article investigates whether volatility, skewness, and kurtosis risks are priced in the European stock market and assess the signs and the magnitudes of the corresponding risk premia. To this end, we adopt two approaches: a model-free approach based on swap contracts, and a model-based approach built on portfolio-sorting techniques. A number of results are obtained. First, stocks with high exposure to innovations in implied market volatility (skewness) exhibit low (high) returns on average. Second, the estimated premium for bearing market volatility (skewness) risk is negative (positive), robust to the two approaches employed, and statistically and economically significant. Third, in contrast with studies on the US stock market, we identify the existence of a size premium in the European stock market: small capitalization stocks earn higher returns than high capitalization stocks.


2020 - Option implied moments obtained through fuzzy regression [Articolo su rivista]
Muzzioli, Silvia; Gambarelli, Luca; De Baets, Bernard
abstract

The aim of this paper is to investigate the potential of fuzzy regression methods for computing more reliable estimates of higher-order moments of the risk-neutral distribution. We improve upon the formula of Bakshi et al. (RFS 16(1):101–143, 2003), which is used for the computation ofmarket volatility and skewness indices (such as the VIX and the SKEW indices traded on the Chicago Board Options Exchange), through the use of fuzzy regression methods. In particular, we use the possibilistic regression method of Tanaka, Uejima and Asai, the least squares fuzzy regression method of Savic and Pedrycz and the hybrid method of Ishibuchi and Nii.We compare the fuzzy moments with those obtained by the standard methodology, based on the Bakshi et al. (2003) formula, which relies on an ex-ante choice of the option prices to be used and cubic spline interpolation.We evaluate the quality of the obtained moments by assessing their forecasting power on future realized moments. We compare the competing forecasts by using both the Model Confidence Set and Mincer–Zarnowitz regressions. We find that the forecasts for skewness and kurtosis obtained using fuzzy regression methods are closer to the subsequently realized moments than those provided by the standard methodology. In particular, the lower bound of the fuzzy moments obtained using the Savic and Pedrycz method is the best ones. The results are important for investors and policy makers who can rely on fuzzy regression methods to get a more reliable forecast for skewness and kurtosis.


2020 - The use of option prices to assess the skewness risk premium [Articolo su rivista]
Elyasiani, E.; Gambarelli, L.; Muzzioli, S.
abstract

The aims of this study are twofold. First, to determine the sign and magnitude of the skewness risk premium (SRP) in the Italian index option market using two procedures: (i) skewness swap contracts, (ii) option trading strategies consisting of positions in options and their underlying assets. Second, to investigate the term structure of the SRP for 30, 60 and 90-day maturities to provide investors with a proper time horizon for profitable skewness trading strategies. Several results are obtained. First, the SRP, defined as the difference between the physical and the risk-neutral skewness, is positive and statistically and economically significant. These findings indicate that the SRP does exist, it is positive in sign, and it can be quantified. Second, the SRP is higher in magnitude for short-term maturity (€35 for the 30-day maturity) and lower for 60-day and 90-day maturities (both about €27). Third, skewness trading strategies confirm our finding of a positive and economically significant SRP. Fourth, a strategy that sells out-of-the-money puts is more profitable for medium-term maturities compared to short-term maturities. A strategy that takes a long position on out-of-the-money calls, and a short position on out-of-the-money puts, yields a higher return, if near-term options are used.


2019 - Risk-asymmetry indices in Europe [Working paper]
Gambarelli, Luca; Muzzioli, Silvia
abstract

The objectives of this study are threefold. First, we introduce for the first time a skewness index (SKEW) for each European country. Second, we compute an alternative measure of asymmetry (RAX) based on corridor implied volatilities to assess whether it outperforms the standard skewness index in measuring tail risk. Third, we investigate the properties of the proposed indices by uncovering the contemporaneous linear relationship among skewness, volatility, and returns and the information content of skewness on future returns, which is highly debated in the literature. Last, we propose two aggregate indices of asymmetry to monitor the risk of the EU financial market as a whole. To deal with the limited availability of option-based data for European countries, that represent the main obstacle for the construction of such indices in the EU, we delineate a country-specific procedure. Several results are obtained. First, all the asymmetry indices are on average higher than 100, indicating that the risk-neutral distribution is in general left-skew for the 12 EU countries under investigation. Second, the relation between changes in asymmetry indices and contemporaneous market returns in positive, indicating that asymmetry indices are not able to capture the same fear effect captured by volatility indices. Third, the results for the relationship between asymmetry and volatility (future returns) are mixed both in terms of magnitude and significance and do not allow us to delineate general conclusions. Last, the aggregate asymmetry index based on the RAX methodology is the only one able to forecast future negative returns for all the EU countries in our dataset when it reaches very high levels.


2019 - Towards a fuzzy index of skewness [Capitolo/Saggio]
Muzzioli, Silvia; Gambarelli, L.; De baets, Bernard
abstract

The aim of this paper is to investigate the potential of fuzzy regression methods for computing a measure of skewness for the market. A quadratic version of the Ishibuchi and Nii hybrid fuzzy regression method is used to estimate the third order moment. The obtained fuzzy estimates are compared with the one provided by standard market practice. The proposed approach allows us to cope with the limited availability of data and to use all the information that is present in the market. In the Italian market, the results suggest that the fuzzy-regression based skewness measure is closer to the subsequently realized measure of skewness than the one provided by the standard methodology. In particular, the upper bound of the Ishibuchi and Nii method provides the best forecast. The results are important for investors and policy makers who can rely on fuzzy regression methods to get a more reliable forecast of skewness.


2018 - INDICES FOR FINANCIAL MARKET VOLATILITY OBTAINED THROUGH FUZZY REGRESSION [Articolo su rivista]
Muzzioli, Silvia; Gambarelli, Luca; De Baets, Bernard
abstract

The measurement of volatility is of fundamental importance in finance. Standard market practice adopted for volatility estimation from option prices leads to a considerable loss of information and the introduction of an element of arbitrariness in the volatility index computation. We propose to resort to fuzzy regression methods in order to include all the available information from option prices and obtain an informative volatility index. In fact, the obtained fuzzy volatility indices do not only offer a most possible value, but also a lower and an upper bound for the interval of possible values, providing investors with an additional source of information. We also propose a defuzzification procedure in order to select a representative value within this interval. Moreover, we investigate the occurrence of truncation and discretization errors in the volatility index computation by resorting to an interpolation-extrapolation method. We also test the forecasting power of each volatility index on future realized volatility.


2018 - The Risk-Asymmetry Index as a New Measure of Risk [Articolo su rivista]
Elyasiani, E.; Gambarelli, L.; Muzzioli, S.
abstract

The aim of this paper is to propose a simple and unique measure of risk that subsumes the conflicting information contained in volatility and skewness indices and overcomes the limitations of these indices in accurately measuring future fear or greed in the market. To this end, the concept of upside and downside corridor implied volatility, which accounts for the asymmetry in the risk-neutral distribution, is exploited. The risk-asymmetry index is intended to capture the investors’ pricing asymmetry towards upside gains and downside losses. The results show that the proposed risk-asymmetry index can play a crucial role in predicting future returns, at various forecast horizons, since it subsumes the information embedded in both the volatility and skewness indices. Furthermore, the risk-asymmetry index is the only index that, at very high values, possesses the ability to clearly highlight a risky situation for the aggregate stock market.


2018 - The properties of a skewness index and its relation with volatility and returns [Working paper]
Elyasiani, E.; Gambarelli, L.; Muzzioli, Silvia
abstract

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.


2018 - The use of option prices in order to evaluate the skewness risk premium [Working paper]
Elyasiani, E.; Gambarelli, L.; Muzzioli, Silvia
abstract


2017 - The information content of corridor volatility measures during calm and turmoil periods [Articolo su rivista]
Elyasiani, E.; Gambarelli, L.; Muzzioli, S.
abstract

Measurement of volatility is of paramount importance in finance because of the effects on risk measurement and risk management. Corridor implied volatility measures allow us to disentangle the volatility of positive returns from that of negative returns, providing investors with additional information beyond standard market volatility. The aim of the paper is twofold. First, to propose different types of corridor implied volatility and some combinations of them as risk indicators, in order to provide useful information about investors’ sentiment and future market returns. Second, to investigate their usefulness in prediction of market returns under different market conditions (with a particular focus on the subprime crisis and the European debt crisis). The data set consists of daily index options traded on the Italian market and covers the 2005-2014 period. We find that upside corridor implied volatility measure embeds the highest information content about contemporaneous market returns, claiming the superiority of call options in measuring current sentiment in the market. Moreover, both upside and downside volatilities can be considered as barometers of investors’ fear. The volatility measures proposed have forecasting power on future returns only during high volatility periods and in particular during the European debt crisis. The explanatory power on future market returns improves when two of the proposed volatility measures are combined together in the same model.


2017 - Towards a Fuzzy Volatility Index for the Italian Market [Relazione in Atti di Convegno]
Muzzioli, Silvia; Gambarelli, Luca; De Baets, Bernard
abstract

The measurement of volatility is of fundamental importance in finance. The standard market practice adopted for the computation of a volatility index imposes to discard some option prices quoted in the market, resulting in a considerable loss of information. To overcome this drawback, we propose to resort to fuzzy regression methods in order to include all the available information and obtain an informative volatility index for the Italian stock market.


2016 - Fear or greed? What does a skewness index measure? [Working paper]
Elyasiani, E.; Gambarelli, L.; Muzzioli, S.
abstract

The ℎ ℎ (CBOE) SKEW index is designed to capture investors’ fear in the US stock market. In this paper we pursue two objectives. First, we investigate the properties of the CBOE SKEW index in order to assess whether it captures fear or greed in the market. Second, we introduce and compare three measures of asymmetry of the Italian index options return distribution. These measures include: (i) the CBOE SKEW index adapted to the Italian market (we call it ITSKEW) and (ii) two model-free measures of skewness based on comparison of a bear and a bull index. Finally, we explore the existence and sign of the skewness risk premium. Several results are obtained. First, the Italian skewness index (ITSKEW) presents many advantages compared to the two model-free measures: it has a significant contemporaneous relation with market index returns and with model-free implied volatility. Both the ITSKEW and the CBOE SKEW indices act as measures of market greed (the opposite of market fear), since returns react positively to an increase in the skewness indices. Trading strategies show that the Italian market is characterized by a significant positive skewness risk premium.


2016 - Moment Risk Premia and the Cross-Section of Stock Returns [Working paper]
Elyasiani, E.; Gambarelli, L.; Muzzioli, S.
abstract

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.


2016 - The Risk-Asymmetry Index [Working paper]
Elyasiany, E.; Gambarelli, L.; Muzzioli, S.
abstract

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 (ܴܣ .(ܺThe risk-asymmetry index ሺܴܣܺሻ plays a crucial role in predicting future returns, since it subsumes all the information embedded in both the Italian skewness index ܫܵܶܧܭ ܹand the Italian volatility index (ܫܸܶܫ .(ܺThe ܴܣ ܺindex 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 ܫܸܶܫ ܺindex nor by the ܫܵܶܧܭ ܹindex.


2015 - Towards a skewness index for the Italian stock market [Working paper]
Elyasiani, E.; Gambarelli, L.; Muzzioli, S.
abstract

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.