On the volatility of volatility

The Chicago Board Options Exchange (CBOE) Volatility Index, VIX, is calculated based on prices of out-of-the-money put and call options on the S&P 500 index (SPX). Sometimes called the "investor fear gauge," the VIX is a measure of the implied volatility of the SPX, and is observed to be correlated with the 30-day realized volatility of the SPX. Changes in the VIX are observed to be negatively correlated with changes in the SPX. However, no significant correlation between changes in the VIX and changes in the 30-day realized volatility of the SPX are observed. We investigate whether this indicates a mispricing of options following large VIX moves, and examine the relation to excess returns from variance swaps.Comment: 15 pages, 12 figures, LaTe

Maximum likelihood approach for several stochastic volatility models

Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility follow a two-dimensional diffusion process where volatility is the stochastic diffusion coefficient of the log-price dynamics. We apply this method to the simplest versions of the expOU, the OU and the Heston stochastic volatility models and we study their performance in terms of the log-price probability, the volatility probability, and its Mean First-Passage Time. The approach has some predictive power on the future returns amplitude by only knowing current volatility. The assumed models do not consider long-range volatility auto-correlation and the asymmetric return-volatility cross-correlation but the method still arises very naturally these two important stylized facts. We apply the method to different market indexes and with a good performance in all cases.Comment: 26 pages, 15 figure

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

Exchange Rate Volatility and Export Trade in Nigeria: An Empirical Investigation

The paper seeks to quantitatively assess the impact of exchange rate volatility on non oil export flows in Nigeria. Theoretically, volatility-trade link is ambiguous, although a strand of studies reported inverse link between export flow and volatility. The paper employed fundamental analysis where the flow of non oil exports from the Nigerian economy is assumed to be predicated on fundamental variables: the naira exchange rate volatility, the US dollar volatility, Nigeria’s terms of trade (TOT) and index of openness (OPN). Empirical results showed presence of unit root at level, however, the null hypothesis of nonstationarity was rejected at first difference. Cointegration results revealed that a stable long run equilibrium relationship exists between non oil exports and the fundamental variables. Using quarterly observations for twenty years, vector cointegration estimate revealed that the naira exchange rate volatility decreased non oil exports by 3.65% while the same estimate for the US dollar volatility increased export of non oil in Nigeria by 5.2% in the year 2003. The paper recommends measures that would promote greater openness of the economy and exchange rate stability in the economy