As Christine Lagarde perfectly coined it, “Markets love **volatility**.” Until automation is perfected and capable of making sound investment decisions, the free **market** is dominated by humans and their intuition for a financial advantage. Emotions and common sentiments across a population play a critical role in the **market** movement. Analyzing the common thinking or sentiment of a population towards a certain trend or idea would be the logical concept to look out for in a **market** where buying and selling, determines the outcome. In this paper, we will be largely focusing on the role of human emotions namely fear, which is the primary unit for emotion in the **market**. A lack of fear indicates a strong confidence in a position, on the contrary, an abundance of fear results in instability in a position. We can use levels of fear to gauge how investors think, make decisions, and react to events in the economy. In our study, we will be **using** the Chicago Board Options Exchange **Volatility** Index (VIX) which is termed the “investor fear gauge,” to determine and gauge future **market**, sector, **stock**, and equity performance. And how these common practices can be applied to predict trends, automate trends, and hopefully educate the public on the use of **volatility** as a **trading** strategy. In the next couple of pages, we will be introducing financial and business terms which are necessary to understand further technical details and strategies.

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This study compares parametric and non-parametric techniques in terms of their forecasting power on **implied** **volatility** indices. We extend our comparisons **using** combined and model-averaging models. The forecasting models are applied on eight **implied** **volatility** indices of the most important **stock** **market** indices. We provide evidence that the non-parametric models of Singular Spectrum Analysis combined with Holt-Winters (SSA-HW) exhibit statistically superior predictive ability for the one and ten **trading** days ahead forecasting horizon. By contrast, the model-averaged forecasts based on both parametric (Autoregressive Integrated model) and non-parametric models (SSA-HW) are able to provide improved forecasts, particularly for the ten **trading** days ahead forecasting horizon. For robustness purposes, we build two **trading** strategies based on the aforementioned forecasts, which further confirm that the SSA-HW and the ARI-SSA-HW are able to generate significantly higher net daily returns in the out-of-sample period.

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This paper describes the **implied** **volatility** function computed from options on the Italian **stock** **market** index between 1995 and 1998 and tries to find out potential explanatory variables. We find that the typical smirk observed for S&P500 **stock** index characterizes also Mib30 **stock** index. When potential determinants are investigated by a linear Granger Causality test, the important role played by option’s time to expiration, transacted volumes and historical **volatility** is detected. A possible proxy of portfolio insurance activity does poorly in explaining the observed pattern. Further analysis shows that the dynamic interrelation between the **implied** **volatility** function and some determinants could be, to a certain extent, non-linear.

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Other researchers to have studied S&P 500 options include Ederington and Guan (2002a), who examined how well the **implied** **volatility** forecasted future **stock** **market** **volatility** in an **active** **market** that was a subject to less measurement error. It is a result where the **implied** **volatility** deviate from the true **market** **volatility** due to the bid-ask spread, non-synchronous price and minimum price increment. The S&P 500 options **market** trades side-by-side with its underlying future, hence minimise the condition that can give rise to the measurement error.They found that the **implied** **volatility** had strong predictive power and subsumed the information in the historical **volatility**. Furthermore, the forecasting results were quite sensitive to the forecasting horizon. In a different paper, Ederington and Guan (2002b) compared the averages of **implied** volatilities used in Latane and Rendleman (1976), Beckers (1981), and Whaley (1982) papers, with the one used by the commercial vendors such as Bloomberg in the S&P 500 option **market**. The found that most of the **implied** **volatility** averages provided better forecasts than the time-series and naïve models, but the differences between the averages were small. The study also indicated that the **implied** **volatility** was upward biased in its measurement of expected **volatility**; however, the bias became stable over time. Furthermore, Ederington and Guan (2002c) examined the **volatility** smile caused by **using** the wrong pricing model to calculate the **implied** **volatility**. All the options, however, shared similar **implied** volatilities. They computed the **implied** **volatility** **using** Black’s (1976) model and the evidence indicated that high-**implied**-**volatility** options were significantly overpriced in relation to low-**implied**-**volatility** options. This reflected the demand for out-of-the-money puts to hedge against the **market** that failed to push up the **implied** **volatility** on the low-strike options.

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The early proposals which used VI as an underlying asset for **trading** **volatility** goes back to Gastineau (1977), Galai (1979), and Brenner and Gali (1993). Whaley (1993) showed how **volatility** derivative can be used by option **market** makers, portfolio managers and covered call writers for hedging the **market** **volatility** risk. Thus, in 1993, Chicago Board Options Exchange (CBOE) officially introduced its first **implied** VI, ticker symbol VIX, which has become the benchmark for risk measurement of the US Equity markets. Flemming et al (1995) investigated a strong contemporaneous negative correlation between the index returns and VIX changes. Whaley (2000) found that VIX as an indicator of expected future **stock** **market** **volatility** and hence termed it as “The Investors Fear gauge”.

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This paper provides a comparative evaluation of the ability of a wide range of GARCH, IV and RV models to forecast **stock** index return **volatility** for a number of US and European indices. Recent literature has shown that IV follows a predictable pattern. Therefore, this paper analyzes whether the IV forecasts are good predictors for the **stock** **market** **volatility**. A total of ten GARCH models are considered, GARCH, GJR, EGARCH, CGARCH and ACGARCH model and the encompassing variants of these models including IV as a regressor in the variance equation. Additionally, six ARMA models have been taken into consideration for forecasting IV indices and realized **volatility**. The results show that both the IV and RV forecasts contain significant information regarding the future **volatility**. With regard to the forecasting ability of IV itself, we find that IV forecasts are statistically significant. When the IV model accounts for the contemporaneous asymmetric effect its forecast strictly outperforms the random walk. As for the GARCH models, the inclusion of IV in the GARCH variance equations improves both the in-sample and out-of-sample performance of the GARCH models with an asymmetric GARCH to perform best. Encompassing regressions indicate that a linear combination of GARCH, IV and RV improves the forecasts. Finally, with regard to VaR forecasts, the ACGARCH combined with the realized **volatility** when the latter is forecasted by the ARFIMAX model is preferred followed by a combination of ACGARCH with ARFIMA for both IV and RV.

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Second set of regressions in both panels test weekly predictability **using** non-overlapping weekly observations. For the value-weighted returns in Panel A, the coe¢ cients of the **volatility** spread measures are still signi…cantly negative ranging from -0.0311 to -0.0826. In other words, when **volatility** spread measures increase by 1%, one-week ahead aggregate **stock** returns decrease by 3.11 to 8.26 basis points. However, two of the four **volatility** spread measures are not signi…cant at conventional levels. When we focus on equal-weighted **market** returns in Panel B, we …nd that all **volatility** spread measures have a signi…cantly negative relation with expected weekly **market** returns. The coe¢ cient estimates are between -0.0418 and -0.1156 and the corresponding t-statistics are between -1.92 and -2.64. Extending the measurement window for expected **market** returns to non-overlapping two weeks or one month takes away signi…cance of the slope coe¢ cients on **volatility** spread measures. For the value-weighted returns, at the two-week horizon, the coe¢ cient of HOVS (HVVS) has the lowest (highest) statistical signi…cance with a t-statistic of -0.09 (-1.31), whereas for the one-month horizon, the coe¢ cients of the **volatility** spread measures become positive but they are still insigni…cant. For the equal-weighted returns reported in Panel B, although we observe some signi…cantly negative coe¢ cients at the two-week horizon, the results are qualitatively similar to those reported for the value-weighted returns in Panel A. Collectively, these results suggest that there is an economically and statistically signi…cant relation between **volatility** spreads and **market** returns and this predictability extends to a weekly horizon. We believe that the weekly predictability that the results indicate is consistent with our information-based explanation as option and equity markets typically assimilate information quickly and it is not likely that it would take more than one week for any information revealed in the option **market** to be re‡ected in the **stock** **market**.

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In the way of Whaley [6], the relation between the VIX and SPX is asymmetric, so the VIX is an investors’ fear gauge in a **market** fall rather than an investors’ excitement gauge in a **market** rally. As a contrarian indicator, VIX is more relevant at **market** bottom 5 . Ralf Becker, Adam E. Clements and Andrew McClelland [7] consi- dered two issues relating to the information content of the VIX 6 . Silmai [8] investigated the information spillov- er between VIX changes and SPX returns. N. Bada and Y. Sakurai [9] investigated whether macroeconomic va- riables can predict the regime switches in the VIX index 7 . Jianhua Gang and Xiang Li [10] used the bivariate semi-nonparametric (SNP) model by Gallant and Tauchen [11] to study the contemporaneous relationship be- tween the innovation of VIX and the expected SPX returns 8 . Ghulam Sarwar [12] have examined whether the relation between **stock** **market** returns and VIX has changed over time 9 . Kozyra and Lento [13] provided an in- sight into the relation between the VIX and technical analysis 10 .

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Butterworth [23] studied the impact of futures **trading** on underlying **stock** index **volatility** in the FTSE, UK **market** and argued that introduction of the futures **market** leads to more complete **market** enhancing the information flow. Ryoo and Smith [24] argued that introduction of index futures **trading** have destabilized the spot **market**. They captured time varying nature of **volatility** phenomena in the data. The results implies futures **trading** increases the speed at which information is impounded into the spot **market** prices, otherwise reduces the persistence of information and increase the spot **market** **volatility**. The information **implied** from derivative prices are about the risk-neutral distribution of the underlying asset. Bhuyan and Chaudhury [25] asserts that apart from the derivative prices, non-price measures of activity in the derivatives **market** such as the open interest contain information about the future level of the underlying asset. The results suggest that the open-interest based **trading** strategies have the potential to generate enhanced **trading** returns or lower **trading** losses. Thereby, open interest based **active** **trading** strategies generate better returns compared to the passive benchmarks. Kim [26] examined the relationship between **trading** activities of the Korea **Stock** Price Index 200 derivative contracts and their underlying **stock** **market** **volatility**. He found positive relationship between **stock** **market** **volatility** and derivative volume while the relationship is negative between **volatility** and open interests. Robbani and Bhuyan [27] examined the effect of introduction of future & option on the DJIA on the **volatility** & **trading** volume of its underlying stocks. The result shows that level of **volatility** and **trading** volume increased after the introduction of futures& options on the index. Sabri [28] examined the impact of change in trade volume on **volatility** of **stock** prices as expressed by unified Arab Monetary fund **stock**

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In order to see whether option-**implied** **volatility** measures can predict **stock** returns after controlling for known firm-specific effects, we also include several firm-level control variables. To control for the size effect documented by Banz (1981), we use the natural logarithm of a company’s **market** capitalization (in thousands of USD) on the last **trading** day of each month. Following Fama and French (1992), we use the book-to-**market** ratio as another firm-level control variable. Jegadeesh and Titman (1993) document the existence of a momentum effect (i.e., past winners, on average, outperform past losers in short future periods). We use past one-month returns to capture the momentum effect. **Stock** **trading** volumes are included as another variable (measured in hundred millions of shares traded in the previous month). The **market** beta reflects the historical systematic risk and is calculated by **using** daily returns available in the previous month **using** the standard CAPM

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The main conclusions of this study are as follows. First, the KSM index exhibits strong **volatility** persistence and asymmetry. Second, the inclusion of contemporaneous trad- ing volume in the GJR-GARCH and EGARCH models results in a positive relationship between **trading** volume and **volatility**. Third, when contemporaneous and lagged **trading** volumes are included in the conditional variance equation, the former is positively correlated with volatil- ity but the latter is not. Thus, **trading** volume affects the flow of information, supporting the validity of MDH. Finally, the asymmetric effect of bad news on **volatility** is higher when contemporaneous **trading** volume is included, although **market** shocks, whether positive or negative, have similar effects on conditional **volatility**. Thus, we conclude that **trading** volume is a useful tool for predicting the **volatility** dynamics of the KSM.

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Several studies on other index options have been carried out **using** the same sampling procedure as Christensen and Prabhala (1998). Hansen (2001) analyses the information content of options on the Danish KFX share index. This option **market** is very illiquid compared to the OEX options **market**. It is shown that when error-in- variable problem is controlled by instrumental variable techniques, call **implied** **volatility** still contains more information about future realized **volatility** than historical **volatility** in such an illiquid option **market**. More recently, Shu and Zhang (2003) examine the options on S&P 500 index, and also report that **implied** **volatility** outperforms the subsequently historical index return **volatility**. Szakmary et al (2003) examine 35 futures options markets across eight separate exchanges and find that for a large majority of the commodities studied, **implied** **volatility** is a better predictor of future realized **volatility** than historical **volatility**.

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The efficient **market** hypothesis (EMH) assumes that investors are rational and value securities rationally. A rational investor would value a security by its net present value; the price of a **stock** in this framework is based on the discounted cash flow or the present value model. Although the EMH-based model is partially successful in computing fundamental **stock** prices, other anomalies such as high **trading** volume, high **volatility**, and **stock** **market** bubbles remain unexplained. These models assume rational investors who are utility maximizers. But some investors behave irrationally or against the predictions, and in the aggregate they become irrelevant. In this paper, we relax the assumption of investor rationality, and attempt to explain high **volatility**, high **trading** volume, and **stock** **market** bubbles by incorporating investor sentiment into the already existing asset pricing model.

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Our sample represents the US equity option **market** by comprising the **stock** options traded at the American **Stock** Exchange and the Chicago Board Options Exchange (CBOE) for the period from January 2001 to De- cember 2010. The data to undertake the research was collected from different sources. 1) The daily **implied** vo- latility for each individual company and the option open interest were collected from Tick Data and Option Me- trics; 2) **Stock** returns, share prices, and the number of shares outstanding are from Tick Data and CRSP and eq- uity book value are from Tick Data and Compustat; 3) daily returns for the the Carhart (1997) momentum factor (UMD) and three Fama and French (1993) factors (MKT, SMB, HML) were collected from Kenneth French’s website.

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The sample period extends from December 8, 1999 to July 28, 2002, representing a total of 138 weeks. All variables are calculated weekly. Return data are in percent. RETSPX is the weekly return to the S&P 500 index. RETNASD is the weekly return to the NASDAQ composite index. VOLS is the total **trading** volume of small-sized trades in billions of shares. NTS is the total number of small-sized trades. OIS is the total order imbalance of small-sized trades in billions of shares. OINUMS is the total order imbalance of small- sized trades measured by the number of trades. RETSPX is the weekly return to the S&P 500 index. RETNASD is the weekly return of the NASDAQ composite index. OL is the average daily number of unique visitors (thousands) to six leading online brokers’ websites. These six online brokers are Ameritrade, Datek, E*trade, Fidelity, Schwab, and TD Waterhouse. OL is our proxy for online **trading**. Transactions data are obtained from the NYSE Trade and Quote (TAQ) database. Small trades are defined as trades of 500 shares or less. Web traffic data are drawn from Media Metrix. In each regression, the first row gives the OLS coefficient estimates. The second row (in parentheses) contains the Newey-West standard errors. *, ** and *** represent statistical significance at the 10 percent, 5 percent, and 1 percent levels respectively.

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The …rst decomposition allows us to analyze the e¤ect order ‡ow has on prices when, for instance, no party has a speed advantage, i.e. both parties are humans or both parties are computers, and when either the maker has a speed advantage, CH, or the taker has a speed advantage, HC. This distinction may be particularly useful when analyzing the cross-rates, where computers likely have a clear advantage over humans in detecting short-lived triangular arbitrage opportunities. This decomposition may also allow us to study whether the liquidity supplier, who is traditionally assumed to be “uninformed”, is posting quotes strategically. This situation is more likely to arise in our database, a pure limit order book **market**, than in a hybrid **market** like the NYSE, because, as Parlour and Seppi (2008) point out, the distinction between liquidity supply and liquidity demand in limit order books is blurry. 7 Still, in our exchange rate data as in other …nancial data, the net of trades signed by who the taker is (the standard de…nition of order ‡ow) is clearly highly positively correlated with exchange rate returns, so that the taker is considered to be more "informed" than the maker. Thus we also consider prominently the more traditional second decomposition, human-taker and computer-taker order ‡ow, in our analysis of whose trades impact prices more. The third decomposition, human-maker and computer-maker order ‡ow, allows us, for instance, to determine whether computers or humans are more likely to provide liquidity when it is needed the most, e.g. during periods of high exchange rate **volatility**. Lastly, the fourth decomposition, computer-participation and human-human order ‡ow, allows us to determine whether any type of participation by computers, passive or **active**, is linked to excess **volatility** in the **market**.

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Having defined in Section (5.2) a consistent model with a global fit to prices under constraints, prices can now be generated such that the No-Dominance principle is preserved, and one can safely assess relative value between them. Bloch [2010] showed that the dynamics **implied** by the single parametric model for the entire **volatility** surface in Equation (9) were those of a mixture diffusion process associated to an uncertain-**volatility** model. That is, similarly to the SABR models, our model already assumes some dynamics of the **volatility** and the underlying asset expressed by a system of stochastic differential equations. In that model, the instantaneous **volatility** being a deterministic function of the spot price and time, we can simulate the underlying process with a local **volatility** model. However, the **implied** **volatility** surface being neither stationary nor Markovian but stochastic, we are going to com- bine the two different approaches to model the dynamics of the IV surfaces described in Section (6.1) by providing memory to the parameters of our model. Hence, we now consider the **implied** **volatility** surface to be a stochastic process driving the option prices and choose to model its dynamics in its full term and strike structure. Option prices deriving their values from an underlying security, it is natural to use mathematical tools to infer their dynamics from that of the underlying **stock** process. One approach is to model the **implied** **volatility** with dynamics based on a statistical analysis of its behaviour through time. It naturally leads us to model the **stock** price process discreetly with Markov chains. We impose that future smile surfaces should be compatible with today’s prices of calls and puts. Formalising the Kolmogorov- Compatibility condition, we impose that the future density is actually a conditional density. Knowing that when the number of fixing dates in a model is finite there is an infinity of conditional densities, we choose to satisfy this infinity of solution by giving the forward smile a shape consistent with its historical evolution. Following

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Prices of scrip’s in the **stock** **market** oscillate daily on the account of continuous **trading** (Buying and Selling). Technical analysis applied to the scrip’s to identify the current trends and risks associated with the scrip at par with the **market**. “Technical analyses believe that the historical performance of scripts & markets are indicators of future performance.” Mainly the movement of technical analysis examines the four dimensions, namely price, volume, time and breadth. Changes in price reflect changes in investor attitude. And price, the first dimension, indicates the attitude level of investors. It is helpful to observe price indicators such as price advances versus declines and price pattern of shares compared to the **market** index. Volume, the second dimension, reflects the intensity of changes in investor attitudes. The level of enthusiasm is **implied** by a price rise on low volumes and vice versa. Time, the third dimension, measures the length of cycles in investor psychology. Change in confidence goes through distinct cycles, some long and some short, as investors’ swing from excessive optimism towards deep pessimism.

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We examine whether the dynamic relationship between lagged returns and **trading** activity is symmetric in the sense of being driven equally by positive and negative return shocks. The linear VAR structure we have used thus far rules out any asymmetric dynamics, and non- linear specifications have to be used to examine asymmetries. Unless a well-specified theoretical structure is developed, one has to choose among a large collection of non-linear multivariate time series (see Granger and Terasvirta (1993)). In this study we use a Threshold Vector Autoregression (TVAR) model for turnover, **volatility**, and returns. This model can also be seen as a piecewise linear autoregression in the threshold variable (but non-linear in time). 18 The TVAR specification allows, for instance, the dynamic behavior of turnover to be different depending on the sign and/or the magnitude of lagged returns. We choose the lagged return as the threshold variable, assume two regimes, and then estimate the system through the two-step conditional least-squares procedure suggested by Tsai (1998). As we did for the linear VAR, we then proceed to compute Generalized Impulse Response Functions (GIRF). The details for our computation of GIRFs are reported in the Appendix.

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