An analysis between implied and realised volatility in the Greek Derivatives Market

In this article, we examine the relationship between implied and realised volatility in the Greek derivative market. We examine the differences between realised volatility and implied volatility of call and put options for at-the-money index options with a two-month expiration period. The findings provide evidence that implied volatility is not an efficient estimate of realised volatility. Implied volatility creates overpricing, for both call and put options, in the Greek market. This is an indication of inefficiency for the market. In addition, we find evidence that realised volatility ‘Granger causes’ implied volatility for call options, and implied volatility of call options ‘Granger causes’, the implied volatility of put option

Principal Component Analysis of Volatility Smiles and Skews

Several principal component models of volatility smiles and skews have been based on daily changes in implied volatilities, by strike and/or by moneyness. Derman and Kamal (1997) analyze S&P500 and Nikkei 225 index options where the daily change in the volatility surface is specified by delta and maturity. Skiadopoulos, Hodges and Clewlow (1998) apply PCA to first differences of implied volatilities for fixed maturity buckets, across both strike and moneyness metrics. And Fengler et. al. (2000) employ a common PCA that allows options on equities in the DAX of different maturities to be analyzed simultaneously.

Implied volatility of foreign exchange options: is it worth tracking?

Market analysts and central banks often use the implied volatility of FX options as an indicator of expected exchange rate uncertainty. The aim of our study is to investigate the limits of this statistic. We present some key factors that may deviate the value of implied volatility from the exchange rate variability expected by the market. These biasing factors are linked to the simplifying assumptions of the Black-Scholes option pricing model. Our empirical results show that forint/euro implied volatilities carry useful information about future exchange rate uncertainty when the forecast horizon is shorter than one month. However, implied volatility provides a biased estimate, and does not encompass the information included in other (GARCH, ARMA) predictors of volatility calculated from historical exchange rate data. These results are in line with the findings of similar analyses of other currency pairs.option, volatility, exchange rate.

Non-Parametric Extraction of Implied Asset Price Distributions

Extracting the risk neutral density (RND) function from option prices is well defined in principle, but is very sensitive to errors in practice. For risk management, knowledge of the entire RND provides more information for Value-at-Risk (VaR) calculations than implied volatility alone [1]. Typically, RNDs are deduced from option prices by making a distributional assumption, or relying on implied volatility [2]. We present a fully non-parametric method for extracting RNDs from observed option prices. The aim is to obtain a continuous, smooth, monotonic, and convex pricing function that is twice differentiable. Thus, irregularities such as negative probabilities that afflict many existing RND estimation techniques are reduced. Our method employs neural networks to obtain a smoothed pricing function, and a central finite difference approximation to the second derivative to extract the required gradients. This novel technique was successfully applied to a large set of FTSE 100 daily European exercise (ESX) put options data and as an Ansatz to the corresponding set of American exercise (SEI) put options. The results of paired t-tests showed significant differences between RNDs extracted from ESX and SEI option data, reflecting the distorting impact of early exercise possibility for the latter. In particular, the results for skewness and kurtosis suggested different shapes for the RNDs implied by the two types of put options. However, both ESX and SEI data gave an unbiased estimate of the realised FTSE 100 closing prices on the options' expiration date. We confirmed that estimates of volatility from the RNDs of both types of option were biased estimates of the realised volatility at expiration, but less so than the LIFFE tabulated at-the-money implied volatility.Comment: Paper based on Application of Physics in Financial Analysis,APFA5, Conference Presentation, Torino, Italy. 11.5 Page

Option pricing using EGARCH models

Various empirical studies have shown that the time-varying volatility of asset returns can be described by GARCH (generalised autoregressive conditional heteroskedasticity) models. The corresponding GARCH option pricing model of Duan (1995) is capable of depicting the smile-effect which often can be found in option prices. In some derivative markets, however, the slope of the smile is not symmetrical. In this paper an option pricing model in the context of the EGARCH (Exponential GARCH) process will be developed. Extensive numerical analyses suggest that the EGARCH option pricing model is able to explain the different slopes of the smile curve. --

Joint Modeling of Call and Put Implied Volatility

This paper exploits the fact that implied volatilities calculated from identical call and put options have often been empirically found to differ, although they should be equal in theory. We propose a new bivariate mixture multiplicative error model and show that it is a good fit to Nikkei 225 index call and put option implied volatility (IV). A good model fit requires two mixture components in the model, allowing for different mean equations and error distributions for calmer and more volatile days. Forecast evaluation indicates that in addition to jointly modeling the time series of call and put IV, cross effects should be added to the model: putside implied volatility helps forecast callside IV, and vice versa. Impulse response functions show that the IV derived from put options recovers faster from shocks, and the effect of shocks lasts for up to six weeks.Implied Volatility, Option Markets, Multiplicative Error Models, Forecasting

Modelling the MIB30 implied volatility surface. Does market efficiency matter?

We analyze the volatility surface vs. moneyness and time to expiration implied by MIBO options written on the MIB30, the most important Italian stock index. We specify and fit a number of models of the implied volatility surface and find that it has a rich and interesting structure that strongly departs from a constant volatility, Black-Scholes benchmark. This result is robust to alternative econometric approaches, including generalized least squares approaches that take into account both the panel structure of the data and the likely presence of heteroskedasticity and serial correlation in the random disturbances. Finally we show that the degree of pricing efficiency of this options market can strongly condition the results of the econometric analysis and therefore our understanding of the pricing mechanism underlying observed MIBO option prices. Applications to value-at-risk and portfolio choice calculations illustrate the importance of using arbitrage-free data only.Assets (Accounting) ; Prices

THE TERM STRUCTURE OF IMPLIED FORWARD VOLATILITY: RECOVERY AND INFORMATIONAL CONTENT IN THE CORN OPTIONS MARKET

Options with different maturities can be used to generate volatility estimates for non-overlapping future time intervals. This paper develops the term structure of volatility implied by corn futures options, and evaluates the informational content of the implied forward volatility as a predictor of subsequent realized volatility. Using data from 1987-2001 and employing a flexible method to obtain the implied forward volatilities, two types of information are examined: 1) the market's estimate of future realized volatility for the nearby interval of the term structure and, 2) the market's expectation of the direction and magnitude of change of future realized volatility over time. In contrast to previous research, the results indicate that the implied forward volatilities anticipate the realized volatilities provide unbiased forecasts and capture a larger portion of the systematic variability in the realized volatilities than forecasts based on historical volatilities. Using information on the direction and magnitude of change in volatility over time, we find that the early-year options forecast volatility about as well as the three-year moving average and better than the naive forecast, while later-year options and alternative forecasts are less able to predict the direction and magnitude of changing volatility. During this later-year period, the implied forward volatilities tend to over-predict the magnitude of actual volatility. Overall, we find that the term structure of volatility implied by corn futures options contains information on future realized volatility.corn options, implied forward volatility, informational content, term structure, Marketing,