Corridor implied volatility and the variance risk premium in the Italian market

Corridor implied volatility introduced in Carr and Madan (1998) and recently implemented in Andersen and Bondarenko (2007) is obtained from model-free implied volatility by truncating the integration domain between two barriers. Corridor implied volatility is implicitly linked with the concept that the tails of the risk-neutral distribution are estimated with less precision than central values, due to the lack of liquid options for very high and very low strikes. However, there is no golden choice for the barriers levels’, which will probably change depending on the underlying asset risk neutral distribution. The latter feature renders its forecasting performance mainly an empirical question. The aim of the paper is twofold. First we investigate the forecasting performance of corridor implied volatility by choosing different corridors with symmetric and asymmetric cuts, and compare the results with the preliminary findings in Muzzioli (2010b). Second, we examine the nature of the variance risk premium and shed light on the information content of different parts of the risk neutral distribution of the stock price, by using a model-independent approach based on corridor measures. To this end we compute both realised and model-free variance measures which accounts for drops versus increases in the underlying asset price. The comparison is pursued by using intra-daily synchronous prices between the options and the underlying asset.corridor implied volatility, variance swap, corridor variance swap, variance risk

The skew pattern of implied volatility in the DAX index options market

The aim of this paper is twofold: to investigate how the information content of implied volatility varies according to moneyness and option type and to compare the latter option based forecasts with historical volatility in order to see if they subsume all the information contained in the latter. We run a horse race of different implied volatility estimates: at the money and out of the money call and put implied volatilities and average implied that is a weighted average of at the money call and put implied volatilities with weights proportional to trading volume. Two hypotheses are tested: unbiasedness and efficiency of the different volatility forecasts. The investigation is pursued in the Dax index options market, by using synchronous prices matched in a one minute interval. The results highlight that the information content of implied volatility has a humped shape, with out of the money options being less informative than at the money ones. Overall, the best forecast is at the money put implied volatility: it is unbiased (after a constant adjustment) and efficient, in that it subsumes all the information contained in historical volatility.implied Volatility; volatility Smile; volatility forecasting; option type

The skew pattern of implied volatility in the DAX-index options market

The aim of this paper is twofold: to investigate how the information content of implied volatility varies according to moneyness and option type, and to compare option-based forecasts with historical volatility in order to see if they subsume all the information contained in historical volatility. The different information content of implied volatility is examined for the most liquid at-the-money and out-of-the-money options: put (call) options for strikes below (above) the current underlying asset price, i.e. the ones that are usually used as inputs for the computation of the smile function. In particular, since at-the-money implied volatilities are usually inserted in the smile function by computing some average of both call and put implied ones, we investigate the performance of a weighted average of at-the-money call and put implied volatilities with weights proportional to trading volume. Two hypotheses are tested: unbiasedness and efficiency of the different volatility forecasts. The investigation is pursued in the Dax index options market, by using synchronous prices matched in a one-minute interval. It was found that the information content of implied volatility has a humped shape, with out-of-the-money options being less informative than at-the-money ones. Overall, the best forecast is at-the-money put implied volatility: it is unbiased (after a constant adjustment) and efficient, in that it subsumes all the information contained in historical volatility

American option pricing with imprecise risk neutral probabilities: from plain intervals to fuzzy sets

The aim f this paper is to price an American style option when there is uncertainty on the underlying asset volatility

Risk-asymmetry indices in Europe

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

Asymmetric Semi-Volatility Spillover in a Nonlinear Model of Interacting Markets

This paper develops an heterogeneous agents model with fundamentalists and chartists trading in two different speculative markets. It examines whether investors’ behaviour is related to the volatility and its dynamics. We find that investors’ heterogeneity in price trends and trading strategies can significantly explain asymmetry in semi-volatility transmission

Construction and properties of volatility indices for Austria, Finland and Spain

The volatility index of the Chicago Board Options Exchange (VIX) is the first to have been introduced and it has attracted international imitators world-wide since it is considered as a barometer of investor fear. The aim of the paper is threefold. First, by following the VIX methodology, we construct a volatility index for three European countries (Austria, Finland and Spain) that do not have yet that piece of market information for investors. Second, we investigate the properties of the new volatility indices. In particular, we test their ability to act as fear indicators and as predictors of future returns. Moreover, we shed light on the term structure of the proposed volatility indices, by computing spot and forward implied volatility indices for different time to maturities (30, 60 and 90 days). Our results indicate that volatility indices are useful not only for investors to improve their trading decisions, but also for policy makers to choose the appropriate economic measure to guarantee stability in the market

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