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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.

This chapter proposes a nonparametric estimator of the risk neutral density (RND) based on cross-sectional European option prices. The authors recast the arbitrage-free equation for option pricing as a functional linear regression model where the regressor is a curve and the independent variable is a scalar corresponding to the option price. Then, the authors show that the RND can be viewed as the solution of an ill-posed integral equation. To estimate the RND, the authors use an iterative method called Landweber-Fridman (LF). Then, the authors establish the consistency and asymptotic normality of the estimated RND. These results can be used to construct a confidence interval around the curve. Finally, some Monte Carlo simulations and application to the S&P 500 options show that this method performs well compared to alternative methods.

How do stock prices evolve over time? The standard assumption of geometric Brownian motion, questionable as it has been right along, is even more doubtful in light of the recent stock market crash and the subsequent prices of U.S. index options. With the development of rich and deep markets in these options, it is now possible to use options prices to make inferences about the risk-neutral stochastic process governing the underlying index. We compare the ability of models including Black–Scholes, naïve volatility smile predictions of traders, constant elasticity of variance, displaced diffusion, jump diffusion, stochastic volatility, and implied binomial trees to explain otherwise identical observed option prices that differ by strike prices, times-to-expiration, or times. The latter amounts to examining predictions of future implied volatilities.

Certain naïve predictive models used by traders seem to perform best, although some academic models are not far behind. We find that the better-performing models all incorporate the negative correlation between index level and volatility. Further improvements to the models seem to require predicting the future at-the-money implied volatility. However, an “efficient markets result” makes these forecasts difficult, and improvements to the option-pricing models might then be limited.

This paper compares the out-of-sample forecasting performance of three long-memory volatility models (i.e., fractionally integrated (FI), break and regime switching) against three short-memory models (i.e., GARCH, GJR and volatility component). Using S&P 500 returns, we find that structural break models produced the best out-of-sample forecasts, if future volatility breaks are known. Without knowing the future breaks, GJR models produced the best short-horizon forecasts and FI models dominated for volatility forecasts of 10 days and beyond. The results suggest that S&P 500 volatility is non-stationary at least in some time periods. Controlling for extreme events (e.g., the 1987 crash) significantly improved forecasting performance.

We examine the relation between investor sentiment proxies and the risk neutral skewness of S&P 500 index option. The risk neutral skewness is estimated by the method of Bakshi, Kapadia and Madan (2003), which is non-parametric method, and the interpolation-extrapolation method and trapezoidal rule is used. We use four sentiment proxies: Michigan Consumer Sentiment Index, non-commercial trader's net position of S&P 500 futures market, Baker and Wurgler (2006)'s sentiment index, and bull-bear survey of American Association of Individual Investors. We firstly conduct the regression to find the general relations of two variables, and then examine the lead-lag relation between investor sentiment proxies and risk neutral skewness through VAR analysis. Contrary to the previous studies, we observe that sentiment proxies show different signs by the economic conditions. Overall, the sentiment proxies explain the three-dimension moment better in the crisis in U.S, and especially non-commercial trader's net position of S&P 500 futures market explains bet among the proxies.

In this paper we make an analysis of KOSPI 200 index options listed in Korea Stock and Futures Exchange whose trading volume is world best these days. We adopt the stochastic volatility model suggested by Heston (1993) for the dynamics of the underlying asset and use EMM to estimate the parameters of option pricing kernel. The SNP distribution of the implied volatility contains AR (2) and ARCH effects, and the skewness of the distribution is much higher than normal distribution. The distribution has thinner left tail and fatter right tail than normal distribution, which is opposite to the case of S&P 500 options market. The result of estimation shows that Implied volatility series of KOSPI 200 options have weak mean reverting property and are almost nonstationary. The correlation coefficient between the implied volatility and returns is estimated to have negligible negative number. These features are also opposite to the case of S&P 500 options market where implied volatility is reported to have strong mean reversion, and the correlation between the implied VIatilIty and retturns is reported to have large negative number.

The payoffs of exotic options (e.g., up‐and‐out call options) are dependent on the time‐path of asset prices rather than the price of the asset at a fixed point in time. The authors of this article compare various models for calibrating volatility surfaces in order to price up‐and‐out call options.

Recently, there has been much progress in developing Markov switching stochastic volatility (MSSV) models for financial time series. Several studies consider various MSSV specifications and document superior forecasting power for volatility compared to the popular generalized autoregressive heteroscedasticity (GARCH) models. However, their application to option pricing remains limited, partially due to the lack of convenient closed-form option pricing formulas which integrate MSSV volatility estimates. We develop such a closed-form option pricing formula and the corresponding hedging strategy for a broad class of MSSV models. We then present an example of application to two of the most popular MSSV models: Markov switching multifractal (MSM) and component-driven regime switching (CDRS) models. Our results establish that these models perform well in one-day-ahead forecasts of option prices.

In this paper, we examine whether the risk neutral skewness and kurtosis from S&P 500 options have information for predicting the higher moments of the stock returns called skewness and kurtosis, which contain the important information for forecasting potential crash, spike upward and the fluctuations of stock index. We find that the implied risk neutral skewness and kurtosis does not provide the information contents for predicting the higher moments of S&P 500 index return, after eliminating the overlapping data. All the results are robust to the alternative measures of risk neutral moments from options prices, the sub-periods and forecasting periods.