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

Model-Free Implied Volatility under Jump-Diffusion Models

The model-free implied volatility (MFIVol) is intended to measure the variability of underlying asset price on which options are written. Analytically, however, it does not measure exactly the variability under jump diffusion. Our extensive empirical study suggests that the approximation error can be as much as about 3%--5% although most samples over the data period exhibit less than 1% errors. Even with the non-negligible errors, the MFIVol may be still considered a valid volatility measure from the perspective of risk-neutral return density, in the sense that it is bounded by the two variability measures as well as reflecting the shape of the risk-neutral density via its higher central moments

Volatility and stock market direction: a study on emerging markets.

Volatility indices, such VIX, can be used for determining stock market direction. In this paper, we analyze the relationship between changes in the VIX direction and changes in the turning point of S&P 500 and the MSCI Latin-America Emerging Market index, in order to see whether they anticipate the changes. Also, the volatility of emerging markets measured by standard deviation and their relationship with the stock market movements within this market are calculated, since the greater the value of the volatility, the greater the likelihood of a rise or fall. In order to locate the turning point and the upward and downward phases of the cycles, empirical methods are applied and are characterized by using a set of decision rules that reflect the practical experience gained by analysts. Our conclusions include: Turning points, or peaks and troughs, in the VIX are coincident with peaks and troughs in the opposite direction for the S&P 500 index and in emerging markets

Do CDS spreads reflect default risks? Evidence from UK bank bailouts

CDS spreads are generally considered to reflect the credit risks of their reference entities. However, CDS spreads of the major UK banks remained relatively stable in response to the recent credit crisis. We suggest that this can be explained by changes in loss given default (LGD). To obtain the result we first derive the probabilities of default from stock option prices and then determine the LGD consistent with actual CDS spreads. Our results reveal a significant decrease in the LGD of bailed out banks over the observed period in contrast to banks which were not bailed out and non-financial companies

Modelling FX smile : from stochastic volatility to skewness

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Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results

Exponential L\'evy processes can be used to model the evolution of various financial variables such as FX rates, stock prices, etc. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes, and the corresponding implied volatility surfaces have been analyzed in some detail. In the non-asymptotic regimes, option prices are described by the Lewis-Lipton formula which allows one to represent them as Fourier integrals; the prices can be trivially expressed in terms of their implied volatility. Recently, attempts at calculating the asymptotic limits of the implied volatility have yielded several expressions for the short-time, long-time, and wing asymptotics. In order to study the volatility surface in required detail, in this paper we use the FX conventions and describe the implied volatility as a function of the Black-Scholes delta. Surprisingly, this convention is closely related to the resolution of singularities frequently used in algebraic geometry. In this framework, we survey the literature, reformulate some known facts regarding the asymptotic behavior of the implied volatility, and present several new results. We emphasize the role of fractional differentiation in studying the tempered stable exponential Levy processes and derive novel numerical methods based on judicial finite-difference approximations for fractional derivatives. We also briefly demonstrate how to extend our results in order to study important cases of local and stochastic volatility models, whose close relation to the L\'evy process based models is particularly clear when the Lewis-Lipton formula is used. Our main conclusion is that studying asymptotic properties of the implied volatility, while theoretically exciting, is not always practically useful because the domain of validity of many asymptotic expressions is small.Comment: 92 pages, 15 figure