Papers by Luca Gambarelli
This paper analyzes the role of the VSTOXX volatility index as a measure of risk for the EU stock... more This paper analyzes the role of the VSTOXX volatility index as a measure of risk for the EU stock market. Employing daily data from 2007 to 2017, we study and contrast the properties of the VSTOXX index in various market conditions. Moreover, to investigate the information content of each country-specific index for the VSTOXX, we exploit the Ordered Weighted Averaging (OWA) operator, which provides a flexible aggregation procedure ranging between the minimum and the maximum of the input values. The VSTOXX index can correctly measure the volatility risk only for France and Germany, while the results depend on the period under investigation for the other countries. Moreover, VSTOXX acted more like an OR-like measure than an AND-like measure of volatility for the EU stock markets and represented an average for the EU volatility only during periods of extreme volatility.
The aim of this paper is to assess the existence and the sign of moment risk premia. To this end,... more 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.
The aim of this paper is to assess the existence and the sign of moment risk premia. To this end,... more 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.
The aim of this paper is to assess the existence and the sign of moment risk premia. To this end,... more 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. Corresponding author: Department of Economics and CEFIN, University of Modena and Reggio Emilia, Viale Berengario 51, 41121 Modena (I), Tel. +390592056771, email [email protected],ORCID iD: 0000-0003-0738-6690.
The Chicago Board Options Exchange (CBOE) SKEW index is designed to capture investors’ fear in th... more The Chicago Board Options Exchange (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...
Multinational Finance Journal, 2018
The aim of this paper is to propose a simple and unique measure of risk that subsumes the conflic... more 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. (JEL: G13, C02)
The measurement of volatility is of fundamental importance in finance. The standard market practi... more 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.
The objectives of this study are threefold. First, we investigate the properties of a skewness in... more The objectives of this study are 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 contemporaneous linear relationship among skewness, volatility and returns. Third, we provide evidence on the information content of skewness on future returns, which is highly debated in the literature. Fourth, we investigate the Italian market, where a skewness index is not traded yet. The methodology we propose for the construction of the Italian skewness index is applicable also to other European and non-European countries characterized by a limited number of option traded. Several results are obtained. First, in the Italian market the skewness index acts as measures of market greed, as opposed to market fear, namely that it measures more investors’ excitement than investors’ fear. Second, for almost 70% of the daily observations, th...
The aim of this paper is to propose a simple and unique measure of risk, that subsumes the confli... more 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 (RAX). The risk-asymmetry index (RAX) plays a crucial role in predicting future returns, since it subsumes all the information embedded in both the Italian skewness index ITSKEW and the Italian volatility index (ITVIX). The RAX 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 n...
The aim of this paper is to investigate the potential of fuzzy regression methods for computing a... more 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.
Applied Economics, 2020
ABSTRACT The aims of this study are twofold. First, to determine the sign and magnitude of the sk... more 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.
Quantitative Finance and Economics, 2017
Measurement of volatility is of paramount importance in finance because of the effects on risk me... more 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 volatility of positive returns from that of negative returns beyond standard market volatility. The aim of corridor implied volatility and some combinations of them information about investors' sentiment and in prediction of market returns under crisis and the European debt crisis) market and covers the 2005-2014 period. the highest information content about contemporaneous market return options in measuring current sentiment 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.
Fuzzy Optimization and Decision Making, 2020
The aim of this paper is to investigate the potential of fuzzy regression methods for computing m... more 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 of market 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.
Journal of Banking & Finance, 2020
International Journal of Information Technology & Decision Making, 2018
The measurement of volatility is of fundamental importance in finance. Standard market practice a... more 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 adopt fuzzy regression methods in order to include all the available information from option prices, and to obtain an informative volatility index. In fact, the obtained fuzzy volatility indices 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 to select a representative value within this interval. Moreover, we investigate the occurrence of truncation and discretization errors in volatility index computation by adopting an interpolation-extrapolation method. We also test the forecasting power of each volatility index on future r...
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Papers by Luca Gambarelli