FTSE 100 index level and FTSE-100 volatility index, VFTSE (January 2000-June 2009) Right hand side axis the VFTSE levels and the Left Hand side Axis the FTSE-100 levels 

Context in source publication

Context 1

... recent financial crisis which started in 2007 has resulted in periods of extreme volatility in financial markets. This has prompted new studies on the behaviour of stock market volatility (see, Schwert, 2011, Mencía and Sentana, 2011, Andersen et. al. 2011 and Bollerslev and Todorov, 2011), especially in conjunction with option price implied volatility indexes such as the VIX. Since the introduction in 1993 by the Chicago Board 2 of Trade (CBOE) of the equity market volatility index based on the seminal work of Whaley (1993) on the implied volatility obtained from both call and put equity index options, the information content of the volatility index in forecasting future realized volatility has become an area of intense investigation. Whaley (2000) coined the term “investor fear gauge ” to highlight the fact that the volatility index peaks when the underlying market index is at the lowest level and hence reflects investors ‟ fear about market crashes. The volatility index also features in the pricing of volatility derivatives for hedging non-diversifiable market risk and is also cited in the management of systemic risk conditions. In September 2003, the CBOE adopted the so called model-free method, for the construction of the VIX. Technically, VIX is the square root of the risk neutral expectation under a Q-measure of the integrated variance of the SP-500 over the next 30 calendar days reported on an annualized basis. The replication of this is independent of any model and involves only directly observed prices for out-of-the-money calls and out-of-the-money puts with the same maturity (see, Britten-Jones and Neuberger, 2000 3 and Carr and Madan,1998). The relationship between the implied volatility and historically realized volatility has particular significance as the measure of volatility risk premium. As risk averse investors buy index options to hedge their underlying equity positions, Carr and Wu (2009), Bollerslev, Tauchen and Zhou (2009) and others have found that typically the spot VIX computed from option prices embeds volatility risk premium and exceeds expected realized volatility obtained under the P-measure. During turbulent market conditions, the value of traded option based volatility index goes up. However, the lack of robustness in the MFIV method for the VIX first identified by Jiang and Tian (2007), expecially under extreme market conditions, has implications for mispricing volatility derivatives such as VIX futures, options and variance swaps. Mencía and Sentana (2011) investigate the mispricing of volatility derivatives during the recent crisis. There is a large and growing literature on information from traded option implied distribution volatility indexes for their capacity (see, Giamouridis and Skiadopoulos, 2010, for a recent survey) to forecast future realized volatility and other statistics on the underlying asset. In recent conditions of severe market distress, Andersen et. al. (2011) have noted discrepancies in the intraday VIX in not showing a consistent inverse relationship with the underlying stock index, a condition that the „fear guage‟ should satisfy especially during turbulent market conditions. The objective of this paper is to use the extreme market volatility of about 30%-80% recorded in all the major stock index (daily) returns during the recent subprime financial crisis from mid 2007 to mid 2009 to test out the efficacy of differently constructed IV indexes to forecast realized volatility both in so called normal market conditions when volatility is no more than about 20% and during extreme market conditions. For this we analyse data on the FTSE-100 and its model free VFTSE volatility index from January 2000 to June 2009. The paper aims to test the MFIV using the VFTSE and to propose alternative IV models that can specifically deal with the interspersed nature of relatively calm periods with periods of extreme volatility of stock index returns. In particular, we aim to show how the implied volatility analytically derived from a closed form option pricing result of Markose and Alentorn (2011) using the Generalized Extreme Value risk neutral density (GEV-RND) can overcome the well known problems of MFIV and other extant methods of dealing with time varying tail shape of RND and resulting normal and extreme implied volatilities. The issues involved here are briefly reviewed below. Figure 1 plots the FTSE 100 index level (blue) and its volatility index, VFTSE (green), from 4th January 2000 to 1st June 2009. It shows that in relatively calm periods, the VFTSE volatility index ranges between 10% to about 20%. However, there are also some spikes in the VFTSE series. On 11th September 2001 (9/11), VFTSE spiked at around 50%, and during the American invasion of Iraq in March 2003, VFTSE peaked at over 40%. The spike points of VFTSE during the crisis of autumn 2008 have been much higher than any recent market down turn. The recent crisis has manifested in extreme spikes in VFTSE at about 55% on the 15th September 2008 corresponding to Lehman Brother Bankruptcy and near 80% on the 28th October 2008. At about the latter spike of the VFTSE, the FTSE-100 records the first of its extreme minima followed by its all time low of this period in early March ...