148 research outputs found
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
The optimal corridor for implied volatility: from calm to turmoil periods
Corridor 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
Option based forecasts of volatility: An empirical study in the DAX index options market
Option 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
Call and put implied volatilities and the derivation of option implied trees
Standard 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 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
The relation between implied and realised volatility: are call options more informative than put options? Evidence from the DAX index options market
The 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
The no arbitrage condition in option implied trees: evidence from the Italian index options market
A major issue in the construction of implied trees is the no arbitrage property preservation. Within the literature on deterministic smile-consistent trees using forward induction, two major contributions are: Derman and Kani (1994) and Barle and Cakici (1998). The former proposes a methodology to override the nodes that violate the no arbitrage condition. The latter extends the Derman and Kani’s algorithm, in order to increase its stability in the presence of high interest rates. The aim of the present paper is to modify the Derman and Kani’s methodology in order to improve the fit of the implied tree to option prices. The proposed methodology is compared with Barle and Cakici both in the sample and out of sample with Italian index options data. Overall findings support a better performance of the modified Derman and Kani’s methodology.Binomial tree; implied volatility; calibration.
Option implied trees and implied moments
Implied trees are simple non-parametric discretizations of one- or two-dimension diffusions, aimed at introducing non-constant volatility in an option pricing model. The aim of the paper is twofold. First we investigate the ability of different option implied trees in pricing European options. Second, we compare the implied moments obtained with the use of option implied trees with the risk–neutral moments obtained with the use of Bakshi et al. (2003) formula and with realised physical moments. The comparison is pursued in the Italian market by analysing a data set which covers the years 2005-2009 and span both a relatively tranquil and a turmoil period. Keywords
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