Model-free Implied Volatility Research Articles

Exploring asymmetries in cryptocurrency intraday returns and implied volatility: New evidence for high-frequency traders

This paper aims to analyze the return-volatility relationship of Bitcoin and Ethereum across different return frequencies and all conditional quantiles of implied volatility, based on a unique 6.5 million observations. We employ the newly constructed Model-Free Implied Volatility (MFIV) of Bitcoin (BitVol) and Ethereum (EthVol) and use an asymmetric Quantile Regression Model (QRM) to capture the intraday asymmetric return-volatility relationship at different quantiles of the distribution of the dependent variable. Our findings show that the estimated coefficient using daily data is significant only at medium- to high-volatility regimes, while the estimated coefficients using high-frequency data are highly significant across all volatility regimes. Moreover, our results indicate that the asymmetry varies across frequencies and quantiles, with weak asymmetric effects at low quantiles and high frequencies, and strong asymmetric effects at high quantiles and low frequencies. This study provides new insight, especially for high-frequency traders.

Return-volatility relationships in cryptocurrency markets: Evidence from asymmetric quantiles and non-linear ARDL approach

Implied volatility has consistently demonstrated its reliability as a superior estimator of the expected short-term volatility of underlying assets. In this study, we employ the newly constructed robust model-free implied volatility (MFIV) indices for Bitcoin and Ethereum (BitVol and EthVol) to explore the asymmetric return-volatility relationship of these cryptocurrencies through the lens of behavioral finance theories. Utilizing the asymmetric quantile regression model (QRM) and the Non-linear ARDL (NARDL) approach, our results reveal a notable difference from equities. Both positive and negative return shocks in the cryptocurrency market lead to an increase in volatility. However, during high volatility regimes, positive (negative) return shocks exert a more substantial impact on positive innovations of volatility for Bitcoin (Ethereum) compared to negative (positive) return shocks. The degree of asymmetry steadily intensifies as we progress from medium to uppermost quantiles of the volatility distribution. These observed phenomena can be attributed to behavioral aspects among market participants, including noise trading, behavioral biases, and fear of missing out (FOMO). Our findings hold significant implications for various aspects of cryptocurrency trading, portfolio hedging strategies, volatility derivatives pricing, and risk management.

No Model No Cry? Intraday Model-Free Implied Volatility and the Leverage Effect for Individual Equities

We analyze intraday model-free implied volatility for a large sample of individual equities. For that purpose we adapt the CBOE VIX methodology and derive an intraday measure based on 1-minute option data. Within a review of the model-free IV theory and CBOE replication methodology we highlight the data requirements and caveats which influence the quality of the results. Since weekly option contracts exist for only a small fraction of underlying stocks, we propose a cubic spline interpolation approach which aims at achieving the quality of the weekly VIX results. In a benchmark comparison it proves to be more accurate than the 2003 VIX method. Relying on our newly developed volatility measures, we analyze the leverage effect and find evidence thereof within an intraday context.

High-Frequency Return-Implied Volatility Relationship: Empirical Evidence from Nifty and India VIX

The risk-return trade-off is a fundamental query in financial literature. Theories envisage the relationship to be positive in long run. However, empirical evidence suggests that the relationship is negative in short-run. This paper investigates the shortterm relationship of risk-return using model-free implied-volatility as a proxy for risk. The relationship is tested by employing high-frequency five-minute interval data of return and model-free implied volatility. Previous studies argue three competing hypotheses to elucidate the short-term relationship. Leverage hypothesis and volatilityfeedback hypothesis are founded on the causality of the relationship between return and volatility. Recent developments of the behavioural finance offer explanations based on existing biases of the market participants. This study examines the short-run relationship considering these three competing hypotheses. The Vector Auto regression (VAR) is employed to test the traditional leverage and volatility-feedback hypotheses. The VAR predicts unidirectional relationship in favour of leverage hypothesis, albeit inconclusive in case of extreme distributions of these two timeseries. The exploratory analysis of intra-day behaviour of return and implied-volatility in a short interval of reveal that VAR methodology is inadequate to elicit the extreme behaviour of the relationship. The quantile regression framework captures the relationship in the extreme movements of return and model-free implied-volatility. The relationship elicits that traditional hypotheses namely leverage and volatility-feedback are inadequate to capture the complete spectrum of the dynamic relationship between these two time-series. Rather, results from quantile regressions reveal that the explanation of the relationship is improved considering recently developed behavioural hypotheses. The study gathers support for the affect’s heuristics of behavioural theory in which traders react differently to positive and negative returns. The negative innovation in returns are the most significant factors for the sharp rise of India VIX, indicating the consistency of the behavioural explanation. The study reveals that the short-term relationship between risk-return is not only negative but also asymmetric. Among the three competitive hypotheses, the behavioural hypothesis best explicates the negative and asymmetric relationship between risk and return.

Who predicts dollar-rupee volatility better? A tale of two options markets

PurposeThe purpose of this paper is to examine whether volatility implied from dollar-rupee options is an unbiased and efficient predictor ofex postvolatility, 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.Design/methodology/approachThe 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.FindingsImplied volatility from both OTC and exchange-traded options is found to contain significant information for predictingex postvolatility, 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.Practical implicationsThis 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.Originality/valueThis 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.

Model-Based versus Model-Free Implied Volatility:Evidence from North American, European, and Asian Index Option Markets

The Black–Scholes (BS) implied volatility is well known to be a rather noisy forecast of future volatility. On the one hand, it has the advantage of potentially incorporating current information that cannot be captured by any statistical technique that relies on historical data. On the other hand, it is “risk neutral,” meaning that the market’s true volatility forecasts are distorted by risk preferences. But no other pricing model has taken the place of BS, so the forecasting performance “horse race” has been between BS IVs versus statistical models such as GARCH. In recent years, “model-free” implied volatility (MFIV) is becoming more common. MFIV is extracted from the entire set of current option prices without the need to assume any specific pricing model. That is certainly a desirable property, but there are a variety of methodological issues in calculating and using MFIV. In this article, Biktimirov and Wang conduct a serious horse race among these models, looking at how much each one contributes to forecast accuracy in predicting future volatility in 13 major international stock markets over a 10-year period. The winner, somewhat surprisingly, is BS IV, both in terms of in-sample “encompassing” models that include several forecasts in the same combined specification and also in out-of-sample forecasting.

Volatility Risk Premium in Indian Options Prices

The article examines the volatility forecasting and option pricing performance of model‐free implied volatility (MFIV) in comparison to that of the forecasts based on model‐free realized volatility (RV). There is evidence that the forecasts based on RV are significantly more efficient and less biased than those based on MFIV, whereas the option prices based on MFIV are significantly more efficient and less biased than those based on RV. These contrasting results can be reconciled by accounting for the volatility risk premium (VRP), which is found to follow an autoregressive process in this study. The significant daily returns, observed for various option strategies used to exploit the VRP, are substantially reduced, when the normal transaction costs are accounted for. Although the VRP is priced in the Indian options market, it can provide economic benefits only to those option writers, who have sufficiently low transaction costs. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:795–812, 2015

Model-Based versus Model-Free Implied Volatility: Evidence from US, European, and Asian Index Option Markets

This study compares the efficacy of Black–Scholes implied volatility (BSIV) with model-free implied volatility (MFIV) in providing volatility forecasts for 13 North American, European, and Asian stock market indexes: S&P 500 (United States), S&P/ASX 200 (Australia), S&P/TSX 60 (Canada), AEX (the Netherlands), EURO STOXX 50 (Eurozone) CAC 40 (France), DAX 30 (Germany), HSI (Hong Kong), NIFTY 50 (India), Nikkei 225 (Japan), KOSPI 200 (Korea), SMI (Switzerland), and FTSE 100 (United Kingdom). In-sample volatility forecasts show that both BSIV and MFIV significantly improve the fit of a GJR-GARCH(1,1) model. However, BSIV dominates MFIV for predicting future volatility. Out-of-sample one-month volatility forecasts also indicate that BSIV outperforms both MFIV and GJR-GARCH(1,1) volatility.

The Information Content of Model‐Free Implied Volatility

This study examines the information content of model‐free implied volatility (MFIV) estimates with respect to the options and futures markets in Hong Kong. In this study, the volatility forecasting performance of MFIV is compared, using different prediction horizons, to IV estimates based on Black's futures option pricing model (BIV) and time‐series forecasts based on historical volatility (TS‐HV). The results show that the BIV prediction is unbiased for different horizon forecasts. MFIV outperforms TS‐HV forecasts and, most importantly, BIV subsumes the information content of both MFIV and TS‐HV forecasts. The results are largely maintained for next‐day forecasts but the forecasting quality of the two IV measures declines as expiration day approaches. The information contents of MFIV and TS‐HV forecasts are complementary. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 32:792‐806, 2012

Empirical Comparison of Alternative Implied Volatility Measures of the Forecasting Performance of Future Volatility*

Implied volatility from the Black and Scholes (Journal of Political Economy 81, 1973, p. 637) model has been empirically analyzed for the forecasting performance of future volatility and is well known to be biased. Based on the belief that implied volatility from option prices can best estimate future volatility, this study identifies the best way to derive implied volatility to overcome the forecast bias associated with the Black–Scholes model. For this, the following three models are considered: Heston’s model, which best addresses the problems associated with the Black–Scholes model for pricing and hedging options; Britten-Jones and Neuberger’s model-free implied volatility (MFIV), which eliminates the model-oriented bias; and VKOSPI, the Korean version of the Chicago Board Options Exchange Market Volatility Index. This study conducts a comparative analysis of implied volatilities from the Black–Scholes model, Heston’s model, the MFIV, and VKOSPI for their abilities to forecast future volatility. The results of the empirical analysis of the KOSPI 200 options market indicate that Heston’s model can eliminate most of the bias associated with the Black–Scholes model, whereas the MFIV and VKOSPI do not show any improvement in terms of forecasting performance.

Study on Model-Free Implied Volatility of Hang Seng Index options

This paper carries out studies on the Model-Free Implied Volatility (MF-IV) and other two competing volatility measurements including Black-Scholes Implied Volatility (BS-IV) and GARCH (1,1) with respect to forecasting error and information content. It is known that MF-IV is a volatility measurement independent of any option pricing model and it provides a direct test on market efficiency. The study introduces data of Hang Seng Index Call Options over two different forecasting horizons to compare the forecasting performance. The empirical results indicate that MF-IV contains richer information content than BS-IV over both monthly and bi-monthly forecasting horizons. However, MF-IV has better predictive accuracy in monthly forecasting horizon, while BS-IV performs better over bi-monthly forecasting horizon.

Construction and Interpretation of Model-Free Implied Volatility

The notion of model-free implied volatility (MFIV), constituting the basis for the highly publicized VIX volatility index, can be hard to measure with accuracy due to the lack of precise prices for options with strikes in the tails of the return distribution. This is reflected in practice as the VIX index is computed through a tail-truncation which renders it more compatible with the related concept of corridor implied volatility (CIV). We provide a comprehensive derivation of the CIV measure and relate it to MFIV under general assumptions. In addition, we price the various volatility contracts, and hence estimate the corresponding volatility measures, under the standard Black-Scholes model. Finally, we undertake the first empirical exploration of the CIV measures in the literature. Our results indicate that the measure can help us refine and systematize the information embedded in the derivatives markets. As such, the CIV measure may serve as a tool to facilitate empirical analysis of both volatility forecasting and volatility risk pricing across distinct future states of the world for diverse asset categories and time horizons.

The Model-Free Implied Volatility and Its Information Content

Britten-Jones and Neuberger (2000) derived a model-free implied volatility under the diffusion assumption. In this article, we extend their model-free implied volatility to asset price processes with jumps and develop a simple method for implementing it using observed option prices. In addition, we perform a direct test of the informational efficiency of the option market using the model-free implied volatility. Our results from the Standard & Poor's 500 index (SPX) options suggest that the model-free implied volatility subsumes all information contained in the Black--Scholes (B--S) implied volatility and past realized volatility and is a more efficient forecast for future realized volatility. Copyright 2005, Oxford University Press.