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The purpose of this paper is to examine whether the superiority of the implied volatility from a stochastic volatility model over the implied volatility from the Black and Scholes model on the forecasting performance of future realized volatility still holds when intraday data are analyzed.

Two implied volatilities and a realized volatility on KOSPI200 index options are estimated every hour. The grander causality tests between an implied volatility and a realized volatility is carried out for checking the forecasting performance. A dummy variable is added to the grander causality test to examine the change of the forecasting performance when a specific environment is chosen. A trading simulation is conducted to check the economic value of the forecasting performance.

Contrary to the previous studies, the implied volatility from a stochastic volatility model is not superior to that from the Black and Scholes model for the intraday volatility forecasting even if both implied volatilities are informative on one hour ahead future volatility. The forecasting performances of both implied volatilities are improved under high volatile market or low return market.

The trading strategy using the forecasting power of an implied volatility earns positively, in particular, more positively under high volatile market or low return market. However, it looks risky to follow the trading strategy because the performance is too volatile. Between two implied volatilities, it is hardly to say that one implied volatility beats another in terms of the economic value.

This is the first study which shows the forecasting performances of implied volatilities on the intraday future volatility.

In this paper we compare three types of forecasts of the volatility of equity returns series. The first is an historical estimate based on a simple sample standard deviation. A second is an estimate found by implying the volatility using the Black‐ Scholes formula. Finally, the third is an estimate obtained by forecasting with an estimated generalized autoregressive conditional heteroscedasticity (GARCH) model.

This chapter analyzes the empirical performance of alternative option pricing models using Black and Scholes (1973) as a benchmark. Specifically, we consider the Heston (1993) and Corrado and Su (1996) models and price call options on the S&P 500 index over the period from November 2010 to April 2011, evaluating each model by computing in- and out-of-sample pricing errors. We find that the two proposed models reduce both types of errors and mitigate the smile effect with respect to the benchmark. Moreover, in most of the cases, the model in Corrado and Su (1996) beats that in Heston (1993). Then, we conclude that skewness and kurtosis matter for option pricing purposes.

This study examines the forecasting ability of the adjusted implied volatility (AIV), which is suggested by Kang, Kim and Yoon (2009), using the horserace competition with historical volatility, model-free implied volatility, and BS implied volatility in the KOSPI 200 index options market. The adjusted implied volatility is applicable when investors are not risk averse or when underlying returns do not follow a normal distribution. This implies that AIV is consistent with the presence of risk premia for other risk such as volatility risk and jump risk. Using KOSPI 200 index options, it is shown that the AIV outperforms other volatility estimates in terms of the unbiasedness for future realized volatilities as well as the forecasting errors.

With the presence of pricing errors, the authors consider statistical inference on the variance risk premium (VRP) and the associated implied variance, constructed from the option prices and the historic returns.

The authors propose a nonparametric kernel smoothing approach that removes the adverse effects of pricing errors and leads to consistent estimation for both the implied variance and the VRP. The asymptotic distributions of the proposed VRP estimator are developed under three asymptotic regimes regarding the relative sample sizes between the option data and historic return data.

This study reveals that existing methods for estimating the implied variance are adversely affected by pricing errors in the option prices, which causes the estimators for VRP statistically inconsistent. By analyzing the S&P 500 option and return data, it demonstrates that, compared with other implied variance and VRP estimators, the proposed implied variance and VRP estimators are more significant variables in explaining variations in the excess S&P 500 returns, and the proposed VRP estimates have the smallest out-of-sample forecasting root mean squared error.

This study contributes to the estimation of the implied variance and the VRP and helps in the predictions of future realized variance and equity premium.

This study is the first to propose consistent estimations for the implied variance and the VRP with the presence of option pricing errors.

The authors examine the relation between noise trading in equity markets and stochastic volatility by estimating a two-factor jump diffusion model. Their analysis shows that contemporaneous price deviations in the derivatives market are statistically significant in explaining movements in index futures prices and option-market volatility measures.

To understand the impact noise may have in the S&P 500 derivatives market, the authors first measure and evaluate the influence noise exerts on futures prices and then investigate its influence on option volatility.

In the period from 1996 to 2003, this study finds significant changes in the volatility and mean reversion in the noise level and a significant increase in its relation to implied volatility in option prices. The results are consistent with a bubble in technology stocks that occurred with significant increases in noise trading.

This study provides estimates for this model during the periods preceding and during the technology bubble. The study analysis shows that the volatility and mean reversion in the noise level are much stronger during the bubble period. Furthermore, the relation between noise trading and implied volatility in the futures market was of a significantly larger magnitude during this period. The study results support the importance of noise trading in market bubbles.

Bloomfield, O'Hara and Saar (2009) find that noise traders lower bid–ask spreads and improve liquidity through increases in trading volume and market depth. Such improved market conditions could have positive effects on market quality, and this impact could be evidenced by lower implied volatility when noise traders are more active. Indeed, the results in this study indicate that the level and characteristics of noise trading are fundamentally different during the technology bubble, and this noise trading activity has a larger impact during this period on implied volatility in the options market.

This paper uniquely analyzes derivatives on the S&P 500 Index in order to detect the presence and influence of noise traders. The authors derive and implement a two-factor jump diffusion noise model. In their model, noise rectifies the difference of analysts' opinions, market information and beliefs among traders. By incorporating a reduced-form temporal expression of heterogeneities among traders, the model is rich enough to capture salient time-series characteristics of equity prices (i.e. stochastic volatility and jumps). A singular feature of the authors’ model is that stochastic volatility represents the random movements in asset prices that are attributed to nonmarket fundamentals.

The topic of volatility measurement and estimation is central to financial and more generally time-series econometrics. In this chapter, we begin by surveying models of volatility, both discrete and continuous, and then we summarize some selected empirical findings from the literature. In particular, in the first sections of this chapter, we discuss important developments in volatility models, with focus on time-varying and stochastic volatility as well as nonparametric volatility estimation. The models discussed share the common feature that volatilities are unobserved and belong to the class of missing variables. We then provide empirical evidence on “small” and “large” jumps from the perspective of their contribution to overall realized variation, using high-frequency price return data on 25 stocks in the DOW 30. Our “small” and “large” jump variations are constructed at three truncation levels, using extant methodology of Barndorff-Nielsen and Shephard (2006), Andersen, Bollerslev, and Diebold (2007), and Aït-Sahalia and Jacod (2009a, 2009b, 2009c). Evidence of jumps is found in around 22.8% of the days during the 1993–2000 period, much higher than the corresponding figure of 9.4% during the 2001–2008 period. Although the overall role of jumps is lessening, the role of large jumps has not decreased, and indeed, the relative role of large jumps, as a proportion of overall jumps, has actually increased in the 2000s.

The purpose of this paper is to investigate empirically the forecasting performance of jump-diffusion option pricing models of (Merton and Bates) with the benchmark Black–Scholes (BS) model relative to market, for pricing Nifty index options of India. The specific period chosen for this study canvasses the extreme up and down limits (jumps) of the Indian capital market. In addition, equity markets keep on facing high and low tides of financial flux amid new economic and financial considerations. With this backdrop, the paper focuses on finding an impeccable option-pricing model which can meet the requirements of option traders and practitioners during tumultuous periods in the future.

Envisioning the fact, the all option-pricing models normally does wrong valuation relative to market. For estimating the structural parameters that governs the underlying asset distribution purely from the underlying asset return data, we have used the nonlinear least-square method. As an approach, we analyzed model prices by dividing the option data into 15 moneyness-maturity groups – depending on the time to maturity and strike price. The prices are compared analytically by continuously updating the parameters of two models using cross-sectional option data on daily basis. Estimated parameters then used to figure out the forecasting performance of models with corresponding BS and market – for pricing day-ahead option prices and implied volatility.

The outcomes of the paper reveal that the jump-diffusion models are a better substitute of classical BS, thus improving the pricing bias significantly. But compared to jump-diffusion model of Merton’s, the model of Bates’ can be applied more uniquely to find out the pricing of three popularly traded categories: deep-out-of-the-money, out-of-the-money and at-the-money of Nifty index options.

The outcome of this research work reveals that the jumps are important components of pricing dynamics of Nifty index options. Incorporation of jump-diffusion process into option pricing of Nifty index options leads to a higher pricing effectiveness, reduces the pricing bias and gives values closer to the market. As the models have been tested in extreme conditions to determine the dominant effectuality, the outcome of this paper helps traders in keeping the investment protected under normal conditions.

The specific period chosen for this study is very unique; it canvasses the extreme up and down limits (jumps) of the Indian capital market and provides the most apt situation for testifying the pricing competitiveness of the models in question. To testify the robustness of models, they have been put into a practical implication of complete cycle of financial frame.

The implied volatility surface is the collection of volatilities implied by option contracts for different strike prices and time-to-maturity. We study factor models to capture the dynamics of this three-dimensional implied volatility surface. Three model types are considered to examine desirable features for representing the surface and its dynamics: a general dynamic factor model, restricted factor models designed to capture the key features of the surface along the moneyness and maturity dimensions, and in-between spline-based methods. Key findings are that: (i) the restricted and spline-based models are both rejected against the general dynamic factor model, (ii) the factors driving the surface are highly persistent, and (iii) for the restricted models option Δ is preferred over the more often used strike relative to spot price as measure for moneyness.

The purpose of this paper is to assess the informational efficiency of S&P CNX Nifty index options in Indian securities market. The S&P CNX Nifty index is a leading stock index of India, consists of 50 most frequently traded securities listed on NSE. For the purpose, the study covers a period of six years from 4 June 2001 (the starting date for index options in India) to 30 June 2007.

The informational efficiency of implied volatilities (IVs) has been tested vis‐à‐vis select conditional volatilities models, namely, GARCH(1,1) and EGARCH(1,1). The tests have been carried out for “in‐the‐sample” as well as “out‐of‐the‐sample” forecast efficiency of implied volatilities.

The results of the study reveal that implied volatilities do not impound all the information available in the past returns; therefore, these are indicative of the violation of efficient market hypothesis in the case of S&P CNX Nifty index options market in India.

The finance managers, in Indian context, should rely on conditional volatility models (especially the EGARCH(1,1) model) compared to IV‐based forecasts to predict volatility for the horizon of one week. The stock exchanges and market regulator (SEBI) need to take certain initiatives in terms of extending the short‐selling facility and start trading of volatility index (VIX) to enhance the accuracy of IV‐based forecasts.

The paper addresses an issue which is still unexplored in the context of Indian securities market and in that sense makes an important contribution to literature on microstructure studies.