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The purpose of this paper is to examine whether volatility implied from dollar-rupee options is an unbiased and efficient predictor of ex post volatility, and to determine which options market is a better predictor of future realized volatility and to ascertain whether the model-free measure of implied volatility outperforms the traditional measure derived from the Black–Scholes–Merton model.

The information content of exchange-traded implied volatility and that of quoted implied volatility for OTC options is compared with that of historical volatility and a GARCH(1, 1)-based volatility. Ordinary least squares regression is used to examine the unbiasedness and informational efficiency of implied volatility. Robustness of the results is tested by using two specifications of implied volatility and realized volatility and comparison across two markets.

Implied volatility from both OTC and exchange-traded options is found to contain significant information for predicting ex post volatility, but is neither unbiased nor informationally efficient. The implied volatility of at-the-money options derived using the Black–Scholes–Merton model is found to outperform the model-free implied volatility (MFIV) across both markets. MFIV from OTC options is found to be a better predictor of realized volatility than MFIV from exchange-traded options.

This study throws light on the predictive power of currency options in India and has strong practical implications for market practitioners. Efficient currency option markets can serve as effective vehicles both for hedging and speculation and can convey useful information to the regulators regarding the market participants’ expectations of future volatility.

This study is a comprehensive study of the informational efficiency of options on an emerging currency such as the Indian rupee. To the author’s knowledge, this is one of the first studies to compare the predictive ability of the exchange-traded and OTC markets and also to compare traditional model-dependent volatility with MFIV.

This paper aims to propose the implied volatility index for the US dollar–Indian rupee pair (INRVIX). The study seeks to examine whether INRVIX truly reflects future USDINR (US Dollar-Indian rupee) volatility and signals profitable currency trading strategies.

Two measures of INRVIX are constructed and compared: a model-free version based on the methodology adopted by the Chicago Board of Options Exchange (CBOE) and a model-dependent version constructed from Black–Scholes–Merton-implied volatility. The proposed INRVIX is computed by tweaking some parameters of the CBOE methodology to ensure compatibility with the microstructure of the Indian currency derivatives market. The volatility forecasting ability of INRVIX is compared to that of a generalized autoregressive conditional heteroscedasticity (1,1) model. Ordinary least squares regression is used to examine the relationship between n-day-ahead USDINR returns and different quantiles of INRVIX.

Results indicate that INRVIX based on the model-free approach reflects ex post volatility in a better manner than its model-dependent counterpart, although neither measure is found to be an unbiased and efficient forecast. Subsample analysis across tranquil and turbulent periods corroborates the results. The volatility forecasting performance of INRVIX is found to be better than that of forecasts based on historical time-series. These results are consistent with similar studies of developed market currencies. The study does not find any significant relationship between extreme levels of INRVIX and the profitability of trading strategies based on such levels, which is contrary to results from the equity options market.

Foreign exchange volatility affects the costs of international trade and the external sector competitiveness of Indian multinationals. It is a significant risk factor for financial institutions and traders in the financial markets. An implied VIX for the USDINR could serve as an indicator of expected foreign exchange risk. It could thus provide a signal for a possible intervention in the forex market by the regulator. Regulators could introduce volatility derivative contracts based on the INRVIX. Such contracts would enable hedging of the pure volatility risk of dollar–rupee exposure. Thus, the study has practical implications for investors, hedgers, regulators and academicians alike.

To the author’s knowledge, this is one of a few studies to construct an implied VIX for an emerging currency like the rupee. The study is based on up-to-date sample data that includes the recent COVID-19 market crash. A novel contribution of this paper is that in addition to examining whether INRVIX contains information about future USDINR volatility, and it also examines the signalling power of INRVIX for currency trading strategies.

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.

Black-Scholes Imolied volatility (8SIV) has a few drawbacks. One is that the model Is not much successful in fitting the option prices. and It Is n야 guaranteed the model is correct one. Second. the usual tradition in using the BSIV is that only at-the-money Options are used. It is well-known that IV's of In-the-money or Qut-of-the-money ootions are much different from those estimated from near-the-money options.

In this regard, a new model is confronted with Korean market data. Brittenxmes and Neuberger (2000) derive a formula for volatility which is a function of option prices‘ Since the formula is derived without using any option pricing model. volatility estimated from the formula is called model-tree implied volatillty (MFIV). MFIV overcomes the two drawbacks of BSIV. Jiang and Tian (2005) show that. with the S&P index Options (SPX), MFIV is suoerlor to historical volatility (HV) or BSIV in forecasting the future volatllity.

In KOSPI 200 index options, when the forecasting performances are compared, MFIV is better than any other estimated volatilities. The hypothesis that MFIV contains all informations for realized volatility and the other volatilities are redundant is oot rejected in any cases.

More studies have investigated the relation between option measures and stock returns during scheduled corporate events. This study adds to the literature and investigates the informational role of options concerning stock returns following unscheduled corporate news events. The authors focus on individual analysts' recommendation changes rather than consensus revisions, as the recommendation consensus might discard a large amount of potentially valuable information in the aggregation process.

Based on the econometric model, the authors follow Bakshi et al. (2003) to construct the model-free option implied measures. The authors further decompose the implied option variance into upside and downside components. In such a way, the different informational roles of call and put options can be distinguished. A variety of regression analyses are conducted to examine the predictive power of option implied measures, and the ordered probit model is used to test the tipping hypothesis of analyst recommendations.

This study’s results show that the option market impounds the “valuable” firm-specific news; thus, the pre-event option market is strongly related to stock returns around recommendations even though recommendation changes are largely “unscheduled”. At the same time, these results suggest that upside (good) and downside (bad) implied volatilities contain distinctive information on subsequent stock returns.

This study provides new evidence that an increase in upside (downside) volatility around analyst recommendation changes would increase the probability that analysts upgrade (downgrade) the stock. The findings provide implications for investors and risk managers in making investment decisions.

The purpose of this paper is to propose a new method for estimating continuous‐time stochastic volatility (SV) models for the S&P 500 stock index process using intraday high‐frequency observations of both the S&P 500 index and the Chicago Board Options Exchange (CBOE) implied (or expected) volatility index (VIX).

A primary purpose of the paper is to provide a framework for using intraday high‐frequency data of both the indices' estimates, in particular, for improving the estimation accuracy of the leverage parameter, that is, the correlation between the two Brownian motions driving the diffusive components of the price process and its spot variance process, respectively.

Finite sample simulation results show that the proposed estimator delivers more accurate estimates of the leverage parameter than do existing methods.

The focus of the paper is on the Heston and non‐Heston leverage parameters.

Finite sample simulation results show that the proposed estimator delivers more accurate estimates of the leverage parameter than do existing methods.

The research findings are important for the analysis of ultra high‐frequency financial data.

The paper provides a framework for using intraday high‐frequency data of both indices' estimates, in particular, for improving the estimation accuracy of the leverage parameter, that is, the correlation between the two Brownian motions driving the diffusive components of the price process and its spot variance process, respectively.

This study investigates the impact of uncertainty on the mean-variance relationship. We find that the stock market's expected excess return is positively related to the market's conditional variances and implied variance during low uncertainty periods but unrelated or negatively related to conditional variances and implied variance during high uncertainty periods. Our empirical evidence is consistent with investors' attitudes toward uncertainty and risk, firms' fundamentals and leverage effects varying with uncertainty. Additionally, we discover that the negative relationship between returns and contemporaneous innovations of conditional variance and the positive relationship between returns and contemporaneous innovations of implied variance are significant during low uncertainty periods. Furthermore, our results are robust to changing the base assets to mimic the uncertainty factor and removing the effect of investor sentiment.

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.

In asset management, what if clients want to purchase protection from risk factors, under the form of variance risk premia. This paper aims to address this topic by developing a portfolio optimization framework based on the criterion of the minimum variance risk premium (VRP) for any investor selecting stocks with an expected target return while minimizing the risk aversion associated to the portfolio according to “good” and “bad” times.

To accomplish this portfolio selection problem, the authors compute variance risk-premium as the difference from high-frequencies' realized volatility and options' implied volatility stemming from 19 stock markets, estimate a 2-state Markov-switching model on the variance risk-premia and optimize variance risk-premia portfolios across non-overlapping regions. The period goes from March 16, 2011, to March 28, 2018.

The authors find that optimized portfolios based on variance-covariance matrices stemming from VRP do not consistently outperform the benchmark based on daily returns. Several robustness checks are investigated by minimizing historical, realized or implicit variances, with/without regime switching. In a boundary case, accounting for the realized variance risk factor in portfolio decisions can be seen as a promising alternative from a portfolio performance perspective.

As a new management “style”, the realized volatility approach can, therefore, bring incremental value to construct the conditional covariance matrix estimates.

The authors assess the portfolio performance determined by the variance-covariance matrices that are derived by four models: “naive” (Markowitz returns benchmark), non-switching VRP, maximum likelihood regime-switching VRP and Bayesian regime switching VRP. The authors examine the best return-risk combination through the calculation of the Sharpe ratio. They also assess another different portfolio strategy: the risk parity approach.

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.