217 research outputs found
Corridor Implied Volatility and the Variance Risk Premium in the Italian Market
No full textCorridor 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
The skew pattern of implied volatility in the DAX-index options market
No full textThe 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
The pricing of options on an interval binomial tree. An application to the DAX-index option market
No full textThis paper implements a model setup in Muzzioli and Torricelli [Int. J. Intell. Syst. 17 (6) (2002) 577-594] for deriving implied trees and pricing options when the put-call parity is not fulfilled. The model basically extends Derman and Kani ́s [Risk 7 (2) (1994) 32-39], whereby call (put) prices are also used in the lower (upper) part of the tree thus exploiting the information content of both call and put prices. The DAX-index option market is chosen for this application because it is a relatively new European market where short-selling restrictions may induce put-call parity violations and the nature of the option (European) and of the underlying (dividends reinvested in the index) avoid some estimation problems. In order to test the pricing fit of the model, a non-linear optimisation procedure is proposed to estimate a unique implied tree which allows a comparison between the model prices, Derman and Kani ́s and market prices. The results suggest that the MT model improves the pricing
Towards a volatility index for the Italian stock market
No full textThe aim of this paper is to analyse and empirically test how to unlock volatility information from option prices. The information content of three option based forecasts of volatility: Black-Scholes implied volatility, model-free implied volatility and corridor implied volatility is addressed, with the ultimate plan of proposing a new volatility index for the Italian stock market. As for model-free implied volatility, two different extrapolation techniques are implemented. As for corridor implied volatility, five different corridors are compared.Our results, which point to a better performance of corridor implied volatilities with respect to both Black-Scholes implied volatility and model-free implied volatility, are in favour of narrow corridors. The volatility index proposed is obtained with an overall 50% cut of the risk neutral distribution. The properties of the volatility index are explored by analysing both the contemporaneous relationship between implied volatility changes and market returns and the usefulness of the proposed index in forecasting future market returns
Call and put implied volatilities and the derivation of option implied trees
No full textStandard methodologies for the derivation of implied trees from option prices are based on the validity of the put-call parity. Muzzioli and Torricelli (2002) propose a methodology which accounts for PCP violations. Based on this latter approach the present paper advances in two main directions. First we propose a different methodology in order to imply the interval of artificial probabilities at each node of the tree. Secondly, we perform an empirical validation of the implied tree obtained, both in the sample and out of sample, by using DAX index options data set covering the period from January 4, 1999 to December 28, 2000. Numerical results are compared with one of the most used standard methodologies, i.e. Derman and Kani’s. The results suggest that the estimation proposed, by taking into account the informational content of both call and put prices, highly improves both the in-the-sample fitting and the out-of-sample performance.Binomial Method; Put-Call Parity; Choquet Pricing; Interval Tree.
The optimal corridor for implied volatility: from calm to turmoil periods
No full textCorridor implied volatility is obtained from model-free implied volatility by truncating the integration domain between two barriers. Empirical evidence on volatility forecasting, in various markets, points to the utility of trimming the risk-neutral distribution of the underlying stock price, in order to obtain unbiased measures of future realised volatility (see e.g. [9], [3]). The aim of the paper is to investigate, both in a statistical and in an economic setting, the optimal corridor of strike prices to use for volatility forecasting in the Italian market, by analysing a data set which covers the years 2005-2010 and span both a relatively tranquil and a turmoil period
The relation between implied and realised volatility: are call options more informative than put options? Evidence from the DAX index options market
No full textThe aim of this paper is to investigate the relation between implied volatility, historical volatility and realised volatility in the Dax index options market. Since implied volatility varies across option type (call versus put) we run a horse race of different implied volatility estimates: implied call, implied put and average implied that is a weighted average of call and put implied volatility with weights proportional to traded volume. Two hypotheses are tested in the Dax index options market: unbiasedness and efficiency of the different volatility forecasts. Our results suggest that all the three implied volatility forecasts are unbiased (after a constant adjustment) and efficient forecasts of future realised volatility in that they subsume all the information contained in historical volatility
Option based forecasts of volatility: An empirical study in the DAX index options market
No full textOption based volatility forecasts can be divided into “model dependent” forecast, such as implied volatility, that is obtained by inverting the Black and Scholes formula, and “model free” forecasts, such as model free volatility, proposed by Britten-Jones and Neuberger (2000), that do not rely on a particular option pricing model. The aim of this paper is to investigate the unbiasedness and efficiency in predicting future realized volatility of the two option based volatility forecasts: implied volatility and model free volatility. The comparison is pursued by using intradaily data on the Dax-index options market. Our results suggest that Black-Scholes volatility subsumes all the information contained in historical volatility and is a better predictor than model free volatility
A note on the Pastor et al. (2021) model
No full textIn this paper, we revise the asset pricing model of Lubo ˇ s Pˇ astor et al. (2021) by incorpo- ́
rating a penalty component into investors’ utility functions when they invest in firms
with lower ESG compliance (brown firms). Our model highlights the dual behavior of
investors who gain utility from investing in green firms (fully ESG-compliant) while
incurring disutility from holding brown firms. We introduce a formulation where
firms’ green characteristics are represented by a vector of ESG scores, with 1 for full
compliance and 0 for non-compliance. The penalty is defined as a function of the deviation from full ESG compliance, adjusted for each investor’s ESG preferences. This
leads to a modified CAPM equation that reflects both the non-pecuniary benefits of
green investments and the penalties for brown investments
Fundamentalists heterogeneity and the role of the sentiment indicator
No full textThis paper is a contribution to the literature on the role of the sentiment indices in heterogeneous asset pricing models. We propose a new sentiment index in a financial market where we assume that transactions take place between two groups of fundamentalists that differentiate on the perception of the fundamental value. We assume that the fraction of fundamentalists in the two groups depends on the sentiment index. After studying the analytical properties of the deterministic discrete dynamical system we compare the new index with a previous index introduced in financial literature. For this purpose, by adding stochastic components to the fundamentalist' demands, we measure the performance of our model under different sentiment indices and we test its explanatory power to reproduce the stylized facts of financial data relying on the S&P500 index
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