Gramática

The VSTOXX index is based on implied volatility of EURO STOXX 50. To be more specific, it is based on real-time options prices across all options of a given time to expiration. The main index VSTOXX is designed as a rolling index at a fixed 30 days to expiry. The sub- indexes represent the eight expiry months with a maximum of 2 years. To tackle the imperfections of B-S model (or other similar models), model-free methods of recovering implied volatilities directly from option price quotes, have emerged in recent years. Thus, encouraged by the VIX of Chicago Board of Exchange that has been calculated with a model- free methodology since September of 2003, the VSTOXX also switched to similar methodology. The greatest distinction between the model-free method and the volatility derived from the option pricing models is that the first mentioned relies on much less restrictive assumptions. Although, assumptions of frictionless markets with no arbitrage opportunities and continuous return distribution of the underlying asset are still present in the model-free measures, the assumptions of the return generation process are not made.

The VSTOXX is calculated by using the two nearest expiration months of EURO STOXX 50 options. A rollover to the next expiration occurs eight calendar days prior to the expiry of the nearby option. The value of the index is derived from the prices of out-of-the-money and at- the-money puts and calls. The closer the option's strike price to the at-the-money value, the higher the weight its price receives in the calculation. VSTOXX is calculated directly from option prices, rather than solving it out of an option-pricing formula, which considerably relieves the problems of measurement errors and model misspecification that arise when option-pricing models are employed.

During the calculation hours for the VSTOXX (8:50 to 17:30 CET), the following data is used via snapshots every five seconds:

- EURO STOXX 50 Index

- OESX – Best bid and best ask of all EURO STOXX 50 options - EONIA (Euro Over-Night Index Average) – overnight interest rate

- EURIBOR (Euro Interbank Offered Rates) – money market reference rates for 1 to 12 months (calculated once a day, 11:00 CET, by the European Banking Federation)

- REX – Yield of the 2-year REX, indicator for German government bonds, as the longer-term interest rate (also calculated once a day using exchange-traded prices from the Frankfurt stock exchange by Deutsche Börse Group)

The index is calculated with following formula:

√ [∑ _{( )} ( ) ( )] [ ] (4)

,where F is the forward index level derived from option prices; is time to expiry of the ith

OESX; Xi is the strike price of the ith out-of-money OESX; is the interval between strike

prices; X0 is the first strike below F and ( ) is the midpoint of the bid-ask spread for each

option with strike Xi. Thus, the VSTOXX does not measure implied volatilities of ATM

options, but the implied variance across all options of given time to expiry. Besides, to avoid the shortcomings of the option pricing models, the calculation method aims at making pure volatility tradable. Hence, the index should be trackable by a portfolio which is delta-neutral, and only reacts to changes in volatility.

The value of VSTOXX has historically been somewhat higher than the most followed IV index the VIX, which has S&P 500 index as underlying (Figure 2). The average value of VSTOXX, from the beginning at January of 1999 to October of 2012, has been 26.35 %. At the same period the average value of VIX has been 22.22%. As mentioned, European banks have a very large weighting in the EURO STOXX 50, which have caused turmoil for the index during the latest financial crises.

Figure 2 – Values of VSTOXX and EURO STOXX 50

The chart clearly shows how the VSTOXX and its underlying EURO STROXX 50 index generally tends to move to opposite directions and that stable VIX (around 15-25%) usually means bull market.

The VIX Index, which is the most followed IV index in the world, is often called as the “investor fear gauge”. Since the VIX is constructed from the implied volatilities of S&P 500 options – the most followed stock market index in the world – it is fair to define it as a measure of expected stock market risk. The definition has been very incisive: the VIX has acted reliably as a fear gauge since the beginning of the index calculation. High levels of VIX are coincident with high degrees of market turmoil (Whaley, 1993B). Panerjee et al. (2007) found that VIX variables significantly affect returns for most portfolios, with the relationship stronger for high-beta portfolios. In similar way, VSTOXX has obtained the same nick name, which is not that commonly used though as with VIX. However, VSTOXX can be used to value stock market risk in EURO STOXX 50 and thus the risk in the whole Eurozone. Simon (2003) suggested that demand for put options increases after a drop because investors are more willing to buy insurance for their portfolios. The increased demand naturally raises the prices of options and thus implied volatility rises. He also added that when market rises, options with higher strike prices become eventually at-the-money options. Since as well- documented volatility smile suggests, options with higher strike have smaller IV. Thus, IV decreases, even though the IV of the certain option, that is then an ITM option, has not changed.

Figure 3 – Historical values of VSTOXX and VIX

This table describes the historical values of VIX and VSTOXX. On average, VSTOXX has had a higher value indicating that volatility, or risk, in EURO STOXX 50 is higher than volatility in S&P 500.

In 2005, Eurex introduced volatility index futures as a new asset class. In 2008, driven by customer demand, Eurex changed its VSTOXX futures into VSTOXX Mini Futures. The only difference between the Mini Futures and former normal futures is the contract size, which was changed from EUR 1000 to EUR 100. CBOE Futures Exchange has been offering VIX futures since 2004. Prior to that, volatility was traded only with over-the-counter derivatives and by constructing straddle positions with options. The contract value of VSTOXX futures, currently called VSTOXX mini futures, is EUR 100 per index point of the underlying. Hence, if VSTOXX is at 25.00, value of one contract is EUR 2500. Price quotation is in points with two decimal places, while minimum price change is 0.05 points, equivalent to a value of EUR 5. The futures are settled with cash on the final settlement day, which is also the last trading day. This is usually the Wednesday prior to the second last Friday of the respective maturity month, if this is an exchange day. Otherwise, the final settlement day is the exchange day immediately preceding that day.

Volume of traded contracts of VSTOXX futures has lately picked up significantly. In September 2012, the trading volume recorded a new high. Almost 400,000 contracts were traded during September and the same development has continued in October as well. The daily volume is nowadays about 20,000 contracts, while the daily average during 2010 was only 1686 traded contracts. Majority of the volume is actual screen volume and only on average some 20% of the trades are executed over-the-counter. Open interest has also been

high: during the whole October of 2012 number of open positions has remained at over 200,000 contracts. Additionally, volume of VSTOXX options has increased significantly. The average daily trading volume has more than doubled from 2154 contracts in 2011, as it has been 4407 contracts from January to September 2012. Figure 3 shows the monthly trading volumes and open interest of VSTOXX mini futures:

Figure 4 – Trading volume and open interest from September 2011 to September 2012

The figure demonstrates the increased trading volume and open interest in VSTOXX mini futures. Volume has increased significantly which in other words means that the liquidity has improved in the VSTOXX futures market. SOURCE: Eurex Monthly Statistics September 2012.