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Journal articles on the topic 'Implied volatilitie'

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Published: 9 March 2023
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1

LEE, ROGER W. "IMPLIED AND LOCAL VOLATILITIES UNDER STOCHASTIC VOLATILITY." International Journal of Theoretical and Applied Finance 04, no. 01 (February 2001): 45–89. http://dx.doi.org/10.1142/s0219024901000870.

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For asset prices that follow stochastic-volatility diffusions, we use asymptotic methods to investigate the behavior of the local volatilities and Black–Scholes volatilities implied by option prices, and to relate this behavior to the parameters of the stochastic volatility process. We also give applications, including risk-premium-based explanations of the biases in some naïve pricing and hedging schemes. We begin by reviewing option pricing under stochastic volatility and representing option prices and local volatilities in terms of expectations. In the case that fluctuations in price and volatility have zero correlation, the expectations formula shows that local volatility (like implied volatility) as a function of log-moneyness has the shape of a symmetric smile. In the case of non-zero correlation, we extend Sircar and Papanicolaou's asymptotic expansion of implied volatilities under slowly-varying stochastic volatility. An asymptotic expansion of local volatilities then verifies the rule of thumb that local volatility has the shape of a skew with roughly twice the slope of the implied volatility skew. Also we compare the slow-variation asymptotics against what we call small-variation asymptotics, and against Fouque, Papanicolaou, and Sircar's rapid-variation asymptotics. We apply the slow-variation asymptotics to approximate the biases of two naïve pricing strategies. These approximations shed some light on the signs and the relative magnitudes of the biases empirically observed in out-of-sample pricing tests of implied-volatility and local-volatility schemes. Similarly, we examine the biases of three different strategies for hedging under stochastic volatility, and we propose ways to implement these strategies without having to specify or estimate any particular stochastic volatility model. Our approximations suggest that a number of the empirical pricing and hedging biases may be explained by a positive premium for the portion of volatility risk that is uncorrelated with asset risk.
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2

Kang, Byung Jin, Sohyun Kang, and Sun-Joong Yoon. "Information Content of Adjusted Implied Volatility in the KOSPI 200 Index Options Market." Journal of Derivatives and Quantitative Studies 17, no. 4 (November 30, 2009): 75–103. http://dx.doi.org/10.1108/jdqs-04-2009-b0003.

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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.
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STEFANICA, DAN, and RADOŠ RADOIČIĆ. "AN EXPLICIT IMPLIED VOLATILITY FORMULA." International Journal of Theoretical and Applied Finance 20, no. 07 (November 2017): 1750048. http://dx.doi.org/10.1142/s0219024917500480.

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We show that an explicit approximate implied volatility formula can be obtained from a Black–Scholes formula approximation that is 2% accurate. The relative error of the approximate implied volatility is uniformly bounded for options with any moneyness and with arbitrary large or small option maturities and volatilities, including for long dated options and options on highly volatile underlying assets. For options within a large trading range, such as options with maturity less than five years and implied volatility less than 150%, the error of the approximate implied volatility relative to the Black–Scholes implied volatility is less than 10% points.
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Matić, Ivan, Radoš Radoičić, and Dan Stefanica. "Pólya-based approximation for the ATM-forward implied volatility." International Journal of Financial Engineering 04, no. 02n03 (June 2017): 1750032. http://dx.doi.org/10.1142/s2424786317500323.

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We introduce a closed form approximation for the implied volatility of ATM-forward options. The relative error of this approximation is uniformly bounded for all option maturities and implied volatilities. The approximation is extremely precise, having relative error less than [Formula: see text] for all options with integrated volatility less than [Formula: see text], such as options with maturity less than three years and implied volatility less than 100%. Moreover, the approximate implied volatilities fall within the implied volatility bid–ask spread for all the liquid options, such as options with volatility less than 200% and maturity less than nine years.
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Dennis, Patrick, Stewart Mayhew, and Chris Stivers. "Stock Returns, Implied Volatility Innovations, and the Asymmetric Volatility Phenomenon." Journal of Financial and Quantitative Analysis 41, no. 2 (June 2006): 381–406. http://dx.doi.org/10.1017/s0022109000002118.

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AbstractWe study the dynamic relation between daily stock returns and daily innovations in optionderived implied volatilities. By simultaneously analyzing innovations in index- and firmlevel implied volatilities, we distinguish between innovations in systematic and idiosyncratic volatility in an effort to better understand the asymmetric volatility phenomenon. Our results indicate that the relation between stock returns and innovations in systematic volatility (idiosyncratic volatility) is substantially negative (near zero). These results suggest that asymmetric volatility is primarily attributed to systematic market-wide factors rather than aggregated firm-level effects. We also present evidence that supports our assumption that innovations in implied volatility are good proxies for innovations in expected stock volatility.
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6

SHEIKH, AAMIR M. "Stock Splits, Volatility Increases, and Implied Volatilities." Journal of Finance 44, no. 5 (December 1989): 1361–72. http://dx.doi.org/10.1111/j.1540-6261.1989.tb02658.x.

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7

Park, Yuen Jung. "The Information Content of the Implied Volatility in OTC Individual Stock Options Market." Journal of Derivatives and Quantitative Studies 20, no. 2 (May 31, 2012): 195–235. http://dx.doi.org/10.1108/jdqs-02-2012-b0003.

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This paper investigates the information content of implied volatilities inferred from individual stock options quoted over-the-counter (OTC). First, we examine whether the implied volatility has better explanatory power than historical volatility for forecasting future realized volatility of the underlying stock return. Next, we analyze the properties of volatility spreads, the difference between implied volatilities and realized volatilities. Using near-the-money options for 10 firms over the sample period from April 2005 to April 2010, we first demonstrate that the implied volatilities for most firms don’t have additional information beyond what are already contained in historical volatilities. However, the implied volatilities with some specific remaining maturities for two firms dominate historical volatilities in explaining the future realized volatilities. Second, we find that during the period before global financial crisis, the implied volatilities are systematically lower than the future realized volatilities whereas this reversal disappears after the year 2008. This finding suggests that there’s a possibility of the risk loving behavior of the investors in OTC individual stock options market during the pre-global crisis period. Finally, through the comparative analysis of the KOSPI200 index options quoted OTC over the same sample period, we conclude that the OTC individual stock options market has distinctive characteristics like the KRW/USD OTC currency options market.
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BRIGO, DAMIANO, and LAURENT COUSOT. "THE STOCHASTIC INTENSITY SSRD MODEL IMPLIED VOLATILITY PATTERNS FOR CREDIT DEFAULT SWAP OPTIONS AND THE IMPACT OF CORRELATION." International Journal of Theoretical and Applied Finance 09, no. 03 (May 2006): 315–39. http://dx.doi.org/10.1142/s0219024906003597.

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In this paper we investigate implied volatility patterns in the Shifted Square Root Diffusion (SSRD) model as functions of the model parameters. We begin by recalling the Credit Default Swap (CDS) options market model that is consistent with a market Black-like formula, thus introducing a notion of implied volatility for CDS options. We examine implied volatilities coming from SSRD prices and characterize the qualitative behavior of implied volatilities as functions of the SSRD model parameters. We introduce an analytical approximation for the SSRD implied volatility that follows the same patterns in the model parameters and that can be used to have a first rough estimate of the implied volatility following a calibration. We compute numerically the CDS-rate volatility smile for the adopted SSRD model. We find a decreasing pattern of SSRD implied volatilities in the interest-rate/intensity correlation. We check whether it is possible to assume zero correlation after the option maturity in computing the option price.
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9

Qabhobho, Thobekile, Emmanuel Asafo-Adjei, Peterson Owusu Junior, and Anokye M. Adam. "Quantifying information transfer between Commodities and Implied Volatilities in the Energy Markets: A Multi-frequency Approach." International Journal of Energy Economics and Policy 12, no. 5 (September 27, 2022): 472–81. http://dx.doi.org/10.32479/ijeep.13403.

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We investigate the multi-scale information transmission between two implied volatilities in the energy markets (crude oil volatility and volatility in the energy market) and energy commodities returns (global energy commodity, brent, heating oil, natural gas and petroleum). The Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) based Rényi transfer entropy approach is employed to accomplish the research objective. The study’s outcome underscores that information flow between implied volatilities and energy commodities is negative with significance being scale-dependent. Especially, significant negative information flow is found at specific intrinsic mode functions (IMFs) such as IMF1, and from IMFs 6-9 suggesting short-, upper medium and long-term energy markets dynamics. Comparatively, we find profound negative information flow with the crude oil implied volatility than the volatility in the entire energy market implying the former’s strong hedging benefits. Investors and policymakers should have knowledge about the dynamics of implied volatilities, particularly, the crude oil implied volatility when designing strategies for the energy commodities markets.
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10

Dash, Mihir. "Modeling of implied volatility surfaces of nifty index options." International Journal of Financial Engineering 06, no. 03 (September 2019): 1950028. http://dx.doi.org/10.1142/s2424786319500282.

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The implied volatility of an option contract is the value of the volatility of the underlying instrument which equates the theoretical option value from an option pricing model (typically, the Black–Scholes[Formula: see text]Merton model) to the current market price of the option. The concept of implied volatility has gained in importance over historical volatility as a forward-looking measure, reflecting expectations of volatility (Dumas et al., 1998). Several studies have shown that the volatilities implied by observed market prices exhibit a pattern very different from that assumed by the Black–Scholes[Formula: see text]Merton model, varying with strike price and time to expiration. This variation of implied volatilities across strike price and time to expiration is referred to as the volatility surface. Empirically, volatility surfaces for global indices have been characterized by the volatility skew. For a given expiration date, options far out-of-the-money are found to have higher implied volatility than those with an exercise price at-the-money. For short-dated expirations, the cross-section of implied volatilities as a function of strike is roughly V-shaped, but has a rounded vertex and is slightly tilted. Generally, this V-shape softens and becomes flatter for longer dated expirations, but the vertex itself may rise or fall depending on whether the term structure of at-the-money volatility is upward or downward sloping. The objective of this study is to model the implied volatility surfaces of index options on the National Stock Exchange (NSE), India. The study employs the parametric models presented in Dumas et al. (1998); Peña et al. (1999), and several subsequent studies to model the volatility surfaces across moneyness and time to expiration. The present study contributes to the literature by studying the nature of the stationary point of the implied volatility surface and by separating the in-the-money and out-of-the-money components of the implied volatility surface. The results of the study suggest that an important difference between the implied volatility surface of index call and put options: the implied volatility surface of index call options was found to have a minimum point, while that of index put options was found to have a saddlepoint. The results of the study also indicate the presence of a “volatility smile” across strike prices, with a minimum point in the range of 2.3–9.0% in-the-money for index call options and of 10.7–29.3% in-the-money for index put options; further, there was a jump in implied volatility in the transition from out-of-the-moneyness to in-the-moneyness, by 10.0% for index call options and about 1.9% for index put options.
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11

Yoon, Sun-Joong. "Structured Products Markets and Implied Volatility Distortion." Journal of Derivatives and Quantitative Studies 22, no. 3 (August 31, 2014): 433–64. http://dx.doi.org/10.1108/jdqs-03-2014-b0003.

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This study verifies the existence of implied volatility distortion by the rapid growth of structured products such as Equity Linked Securities (ELS) in Korean financial markets and provides the policy implications to overcome such a distortion. The most ELS products issued in Korea have a step-down auto-callable payoff structure consisting of short position in down-and-in barrier put options and long position in digital call options. Financial companies which have issued ELS are exposed to the volatility risk, i.e. long vega position, and tend to execute the volatility transactions of short vega. For instance, the financial companies issue Equity-Linked Warrants or sell listed/over-the-counter vanilla options, both of which have short position in volatility risk. Accordingly, the demand for selling volatility is stronger than for buying volatility in the Korean financial markets. According to the empirical results, we conform that the rapid growth of the ELS products induces the pressure for lowering volatility and furthermore, the volatility spreads, defined as the difference between implied volatility and realized volatility, also decrease with respect the amount of the newly issued ELS. Lastly, to mitigate the volatility distortion effect, we suggest to list VKOSPI-related derivatives securities such as VKOSPI futures and options, which in turn balance the trading demands for selling and buying volatilities.
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12

Ahn, Dohyun, Kyoung-Kuk Kim, and Younghoon Kim. "Small-Time smile for the multifactor volatility heston model." Journal of Applied Probability 57, no. 4 (June 2020): 1070–87. http://dx.doi.org/10.1017/jpr.2020.63.

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AbstractWe extend the existing small-time asymptotics for implied volatilities under the Heston stochastic volatility model to the multifactor volatility Heston model, which is also known as the Wishart multidimensional stochastic volatility model (WMSV). More explicitly, we show that the approaches taken in Forde and Jacquier (2009) and Forde, Jacqiuer and Lee (2012) are applicable to the WMSV model under mild conditions, and obtain explicit small-time expansions of implied volatilities.
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13

BONDARENKO, Maksym, and VICTOR BONDARENKO. "MODELING RELATION BETWEEN ATM LOCAL AND IMPLIED VOLATILITY FOR MICROSOFT STOCKS." Herald of Khmelnytskyi National University 292, no. 2 (May 2021): 21–29. http://dx.doi.org/10.31891/2307-5740-2021-292-2-4.

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In this work simple linear and polynomial regression to model the relation between at-the-money (ATM) implied and at-the-money local volatility of Microsoft stocks has been applied. Local volatility is extracted from the set of Vanilla option prices on Microsoft stocks by assuming that Microsoft stock price follows Dupire local volatility process. ATM Local volatility is then used in linear regression predictor while implied volatility is a resulting variable. The model is validated by predicting out-of-sample implied volatility with local volatility. The statistical significance and predictive ability of such model have been measured and autocorrelation tendencies have been studied. The conclusion that assumptions to use linear regression are held has been made. No autocorrelation tendencies were discovered in the time series. Finally, the conclusion that both the 1st and the 3rd order linear regression models demonstrate good predictive ability of local volatility over out-of-sample implied volatility has been made. None of the models proves statistical significance of local volatility as a predictor of the implied volatility but both can be actually used for practical purpose as they predict well out-of-the-sample implied volatilities. This is an important practical result as it means that complex non-linear relationship between implied and local volatilities formalized by Dupire can actually be reduced to simplier linear relationship that demonstrates reasonable discrepancies. Despite the 3rd order model fits the data better, but for the reasons of overfitting in general it’s safer to apply the 1st order model as it demonstrates more stable predictions over datasets with jumps.
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AMMANN, MANUEL, DAVID SKOVMAND, and MICHAEL VERHOFEN. "IMPLIED AND REALIZED VOLATILITY IN THE CROSS-SECTION OF EQUITY OPTIONS." International Journal of Theoretical and Applied Finance 12, no. 06 (September 2009): 745–65. http://dx.doi.org/10.1142/s0219024909005440.

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Using a complete sample of US equity options, we analyze patterns of implied volatility in the cross-section of equity options with respect to stock characteristics. We find that high-beta stocks, small stocks, stocks with a low-market-to-book ratio, and non-momentum stocks trade at higher implied volatilities after controlling for historical volatility. We find evidence that implied volatility overestimates realized volatility for low-beta stocks, small caps, low-market-to-book stocks, and stocks with no momentum and vice versa. However, we cannot reject the null hypothesis that implied volatility is an unbiased predictor of realized volatility in the cross section.
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15

Lorig, Matthew, Stefano Pagliarani, and Andrea Pascucci. "EXPLICIT IMPLIED VOLATILITIES FOR MULTIFACTOR LOCAL-STOCHASTIC VOLATILITY MODELS." Mathematical Finance 27, no. 3 (September 29, 2015): 926–60. http://dx.doi.org/10.1111/mafi.12105.

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16

Bielykh, Artem, Sergiy Pysarenko, Dong Meng Ren, and Oleksandr Kubatko. "Market expectation shifts in option-implied volatilities in the US and UK stock markets during the Brexit vote." Investment Management and Financial Innovations 18, no. 4 (December 24, 2021): 366–79. http://dx.doi.org/10.21511/imfi.18(4).2021.30.

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This paper investigates the effect of the Brexit vote on the connection between UK stock market expectations and US stock market returns. To gauge UK stock market expectations, the option-implied volatilities of the FTSE 100 index are calculated in the period starting five months before and ending four months after the Brexit referendum. To keep the analysis “clean”, it stops right before the 2016 US presidential elections. It uses an OLS regression to estimate the change in the relationship between US and UK stock market expectations.The main findings show that the US and UK stock markets became somewhat less integrated four months after the Brexit referendum compared to the five months before it. The S&P 500 Index returns have a statistically significant impact on implied volatilities of the FTSE 100 only before the Brexit referendum. However, the British risk-free rate (LIBOR) became a statistically significant factor affecting FTSE 100 implied volatilities only after Brexit. This analysis may be used by decision-makers in the money management industry to act appropriately during Black Swan events. When UK citizens unexpectedly voted in favor of Brexit, the risk-free rate dropped, making it cheaper to invest, increasing the Sharpe ratios of equity portfolios. Coupled with increased uncertainty, this caused portfolio reallocations. In turn, expected volatility measured by options-implied volatility increased. AcknowledgmentThe authors would like to thank Olesia Verchenko for critique, a KSE M.A., external defense reviewer for helpful comments.
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Kang, Byung Jin. "Information Content of Implied Volatilities in KRW/USD Currency Option Markets." Journal of Derivatives and Quantitative Studies 19, no. 2 (May 31, 2011): 207–32. http://dx.doi.org/10.1108/jdqs-02-2011-b0004.

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This paper investigate the information content of implied volatilities derived from KRW/USD OTC currency options. First, we examined the explanatory power of implied volatilities in forecasting future realized volatilities of the spot exchange rates. Next, we examined the dynamic properties of volatility spreads, the difference between implied volatilities and realized volatilities, observed in KRW/USD currency option markets. Using the sample data from January 2006 through March 2010, we first find that even though the implied volatilities have a little explanatory power in forecasting future realized volatilities, they don't improve the information content of simple historical volatilities at all. Second, this paper finds that during the period before global financial crisis in 2008, the implied volatilities are consistently lower than the realized volatilities. This suggests that we cannot exclude the possibility of risk seeking behavior of the investors in KRW/USD OTC currency option markets at that time. Finally, from the comparative analysis with KOSPI 200 index options for the same sample period, we confirmed that our empirical results are uniquely observed only in KRW/USD OTC currency option markets.
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CARDINALI, ALESSANDRO. "A GENERALIZED MULTISCALE ANALYSIS OF THE PREDICTIVE CONTENT OF EURODOLLAR IMPLIED VOLATILITIES." International Journal of Theoretical and Applied Finance 12, no. 01 (February 2009): 1–18. http://dx.doi.org/10.1142/s0219024909005130.

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It is widely believed that implied volatilities contains information that would enable prediction of spot volatility for a wide range of financial assets. Lead-lag analysis based on the Discrete Wavelet Transform has been proposed as one method for identifying and extracting that predictive information. Unfortunately this approach can fail to identify periodic components that are not proportional to an increasing dyadic scale. We propose a multiscale analysis of the Eurodollar realized volatility and at-the-money (ATM) implied volatilities. After filtering the long memory components we produce a decomposition of cross-correlation by using wavelet packet methods. A threshold cost functional based on asymptotic confidence intervals was used along with the best basis algorithm in order to select an adaptive frequency partition of the sample cross-correlation. We found substantial evidence that Eurodollar implied volatilities contain predictive information about realized volatilities. Moreover, in our analysis the new technique outperforms the lead-lag analysis based on the nondecimated Discrete Wavelet Transform. Therefore we contend that the proposed technique will improve detection of predictive information and recommend further testing in a range of applied contexts.
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Park, Hye Jin, Dae Won Lee, and Jae Wook Lee. "Implied Volatility Surface Estimation Using Transductive Gaussian Fields Regression." Key Engineering Materials 467-469 (February 2011): 1781–86. http://dx.doi.org/10.4028/www.scientific.net/kem.467-469.1781.

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Implied volatility estimation is one of the fundamental tasks for asset pricing and risk management. In this paper, we investigate the applicability of semi-supervised regression techniques to estimate an implied volatility surface from the real market option data. Specifically, we employ a transductive Gaussian field regression method since it is able to predict a distribution of the implied volatilities for unlabelled data using only partially labeled data. We've conducted simulation on S&P 500 index data before and after the global financial crisis with discussions of the observed empirical properties of the method.
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Rhee, Byung Kun, and Sang Won Hwang. "An Empirical Research on the Informational Efficiency of Model Free Implied Volatility." Journal of Derivatives and Quantitative Studies 16, no. 2 (November 30, 2008): 67–94. http://dx.doi.org/10.1108/jdqs-02-2008-b0003.

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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.
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21

Xi, Wenwen, Dermot Hayes, and Sergio Horacio Lence. "Variance risk premia for agricultural commodities." Agricultural Finance Review 79, no. 3 (June 3, 2019): 286–303. http://dx.doi.org/10.1108/afr-07-2018-0056.

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Purpose The purpose of this paper is to study the variance risk premium in corn and soybean markets, where the variance risk premium is defined as the difference between the historical realized variance and the corresponding risk-neutral expected variance. Design/methodology/approach The authors compute variance risk premiums using historical derivatives data. The authors use regression analysis and time series econometrics methods, including EGARCH and the Kalman filter, to analyze variance risk premiums. Findings There are moderate commonalities in variance within the agricultural sector, but fairly weak commonalities between the agricultural and the equity sectors. Corn and soybean variance risk premia in dollar terms are time-varying and correlated with the risk-neutral expected variance. In contrast, agricultural commodity variance risk premia in log return terms are more likely to be constant and less correlated with the log risk-neutral expected variance. Variance and price (return) risk premia in agricultural markets are weakly correlated, and the correlation depends on the sign of the returns in the underlying commodity. Practical implications Commodity variance (i.e. volatility) risk cannot be hedged using futures markets. The results have practical implications for US crop insurance programs because the implied volatilities from the relevant options markets are used to estimate the price volatility factors used to generate premia for revenue insurance products such as “Revenue Protection” and “Revenue Protection with Harvest Price Exclusion.” The variance risk premia found implies that revenue insurance premia are overpriced. Originality/value The empirical results suggest that the implied volatilities in corn and soybean futures market overestimate true expected volatility by approximately 15 percent. This has implications for derivative products, such as revenue insurance, that use these implied volatilities to calculate fair premia.
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Ap Gwilym, Owain, and Mike Buckle. "Forward/forward volatilities and the term structure of implied volatility." Applied Economics Letters 4, no. 5 (May 1997): 325–28. http://dx.doi.org/10.1080/758532602.

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23

Renault, Eric, and Nizar Touzi. "OPTION HEDGING AND IMPLIED VOLATILITIES IN A STOCHASTIC VOLATILITY MODEL." Mathematical Finance 6, no. 3 (July 1996): 279–302. http://dx.doi.org/10.1111/j.1467-9965.1996.tb00117.x.

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24

Härdle, Wolfgang Karl, and Elena Silyakova. "Implied basket correlation dynamics." Statistics & Risk Modeling 33, no. 1-2 (January 1, 2016): 1–20. http://dx.doi.org/10.1515/strm-2014-1176.

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AbstractEquity basket correlation can be estimated both using the physical measure from stock prices, and also using the risk neutral measure from option prices. The difference between the two estimates motivates a so-called “dispersion strategy”. We study the performance of this strategy on the German market and propose several profitability improvement schemes based on implied correlation (IC) forecasts. Modelling IC conceals several challenges. Firstly the number of correlation coefficients would grow with the size of the basket. Secondly, IC is not constant over maturities and strikes. Finally, IC changes over time. We reduce the dimensionality of the problem by assuming equicorrelation. The IC surface (ICS) is then approximated from the implied volatilities of stocks and the implied volatility of the basket. To analyze the dynamics of the ICS we employ a dynamic semiparametric factor model.
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Dutta, Anupam. "Modeling and forecasting oil price risk: the role of implied volatility index." Journal of Economic Studies 44, no. 6 (November 13, 2017): 1003–16. http://dx.doi.org/10.1108/jes-11-2016-0218.

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Purpose While numerous empirical studies have tried to model and forecast the oil price volatility over the years, such attempts using the crude oil volatility index (OVX) rarely exist. In order to conceal this void, the purpose of this paper is to investigate whether including OVX in the realized volatility (RV) models improve the accuracy of predictions. Design/methodology/approach At the empirical stage, the authors employ several measures to frame the RV of crude oil futures returns. In particular, the authors use three different range-based RV estimators recommended by Parkinson (1980), Rogers and Satchell (1991) and Alizadeh et al. (2002), respectively. Findings The findings reveal that the information content of crude OVX helps to provide more accurate volatility predictions in comparison to the base-line RV model which contains only historical oil volatilities. Besides, the forecast encompassing test further suggests that the modified RV model (when OVX is introduced in the base-line RV model) forecast encompasses the conventional RV forecast in majority of the cases. Practical implications Since forecasting oil price volatility plays a vital role in portfolio optimization, derivatives pricing, optimum asset allocation decisions and risk management, the findings of this study thus carry important implications for energy economists, investors and policymakers. Originality/value This paper adds to the existing literature, since it is one of the initial studies to explore whether OVX is informative about the realized variance of the US oil market returns. The findings recommend that the information content of oil implied volatilities should be taken into account when modeling the US oil market volatility. In addition, range-based measures should be utilized while estimating the RV.
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Liu, Shuaiqiang, Cornelis Oosterlee, and Sander Bohte. "Pricing Options and Computing Implied Volatilities using Neural Networks." Risks 7, no. 1 (February 9, 2019): 16. http://dx.doi.org/10.3390/risks7010016.

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This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent’s iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.
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Alsubaie, Shafi Madhkar, Khaled H. Mahmoud, Ahmed Bossman, and Emmanuel Asafo-Adjei. "Vulnerability of Sustainable Islamic Stock Returns to Implied Market Volatilities: An Asymmetric Approach." Discrete Dynamics in Nature and Society 2022 (July 19, 2022): 1–22. http://dx.doi.org/10.1155/2022/3804871.

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There has been increasing interests in the sustainable way of investing as enjoined by several sustainability initiatives. However, investors require effective portfolio diversification at various market conditions (stress, benign, and boom) and would consider sustainable equities to the extent that they aid in the minimisation of portfolio risks. As a result, a better way investors can mitigate portfolio risk is by forming portfolios with relevant volatility indices as enshrined in extant literature. It becomes necessary to investigate the susceptibility of Islamic stocks in a sustainable way to shocks from volatility indices to enhance effective portfolio decisions. In this regard, we investigate the asymmetric effect of implied volatility indices on sustainable Islamic stocks across different market conditions. Hence, the quantile regression and quantile-on-quantile regression techniques are employed. The study discovered an asymmetric influence of volatility on sustainable Islamic stock returns at various quantiles. Furthermore, most volatilities’ asymmetric effects were generally inversely associated to sustainable Islamic stock returns, implying diversification benefits across market outcomes. Also, with the exception of the extreme quantiles, there is a causal effect of volatilities on Islamic stock returns for most quantiles. It seems to reason that ordinary market outcomes, rather than market stress or boom, have a greater impact on causal estimates for our quantile regression model.
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Durrleman, Valdo. "Convergence of At-The-Money Implied Volatilities to the Spot Volatility." Journal of Applied Probability 45, no. 2 (June 2008): 542–50. http://dx.doi.org/10.1239/jap/1214950366.

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We study the convergence of at-the-money implied volatilities to the spot volatility in a general model with a Brownian component and a jump component of finite variation. This result is a consequence of the robustness of the Black-Scholes formula and of the central limit theorem for martingales.
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Durrleman, Valdo. "Convergence of At-The-Money Implied Volatilities to the Spot Volatility." Journal of Applied Probability 45, no. 02 (June 2008): 542–50. http://dx.doi.org/10.1017/s0021900200004411.

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We study the convergence of at-the-money implied volatilities to the spot volatility in a general model with a Brownian component and a jump component of finite variation. This result is a consequence of the robustness of the Black-Scholes formula and of the central limit theorem for martingales.
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Benavides, Guillermo. "PREDICTIVE ACCURACY OF FUTURES OPTIONS IMPLIED VOLATILITY: THE CASE OF THE EXCHANGE RATE FUTURES MEXICAN PESO-US DOLLAR." PANORAMA ECONÓMICO 5, no. 9 (April 26, 2017): 41. http://dx.doi.org/10.29201/pe-ipn.v5i9.83.

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There has been substantial research effort aimed to forecast futures price return volatilities of financial assets. A significant part of the literature shows that volatility forecast accuracy is not easy to estimate regardless of the forecasting model applied. This paper examines the volatility accuracy of several volatility forecast models for the case of the Mexican peso-USD exchange rate futures returns. The models applied here are a univariate GARCH, a multivariate ARCH (the BEKK model), two option implied volatility models and a composite forecast model. The composite model includes time-series (historical) and option implied volatility forecasts. Different to other works in the literature, in this paper there is a more rigorous analysis of the option implied volatilities calculations. The results show that the option implied models are superior to the historical models in terms of accuracy and that the composite forecast model was the most accurate one (compared to the alternative models) having the lowest mean-squared-errors. However, the results should be taken with caution given that the coefficient of determination in the regressions was relatively low. According to these findings it is recommended to use a composite forecast model if both types of data are available i.e. the time-series (historical) and the option implied.
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31

Mayhew, Stewart. "Implied Volatility." Financial Analysts Journal 51, no. 4 (July 1995): 8–20. http://dx.doi.org/10.2469/faj.v51.n4.1916.

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RAHAYUNI, IDA AYU EGA, KOMANG DHARMAWAN, and LUH PUTU IDA HARINI. "PERBANDINGAN KEEFISIENAN METODE NEWTON-RAPHSON, METODE SECANT, DAN METODE BISECTION DALAM MENGESTIMASI IMPLIED VOLATILITIES SAHAM." E-Jurnal Matematika 5, no. 1 (January 30, 2016): 1. http://dx.doi.org/10.24843/mtk.2016.v05.i01.p113.

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Black-Scholes model suggests that volatility is constant or fixed during the life time of the option certainly known. However, this does not fit with what happen in the real market. Therefore, the volatility has to be estimated. Implied Volatility is the etimated volatility from a market mechanism that is considered as a reasonable way to assess the volatility's value. This study was aimed to compare the Newton-Raphson, Secant, and Bisection method, in estimating the stock volatility value of PT Telkom Indonesia Tbk (TLK). It found that the three methods have the same Implied Volatilities, where Newton-Raphson method gained roots more rapidly than the two others, and it has the smallest relative error greater than Secant and Bisection methods.
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Stefanica, Dan, and Radoš Radoičić. "A sharp approximation for ATM-forward option prices and implied volatilites." International Journal of Financial Engineering 03, no. 01 (March 2016): 1650002. http://dx.doi.org/10.1142/s242478631650002x.

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In this paper, we provide an approximation formula for at-the-money forward options based on a Pólya approximation of the cumulative density function of the standard normal distribution, and prove that the relative error of this approximation is uniformly bounded for options with arbitrarily large (or small) maturities and implied volatilities. This approximation is viable in practice: for options with implied volatility less than 95% and maturity less than three years, which includes the large majority of traded options, the values given by the approximation formula fall within the tightest typical implied vol bid–ask spreads. The relative errors of the corresponding approximate option values are also uniformly bounded for all maturities and implied volatilities. The error bounds established here are the first results in the literature holding for all integrated volatilities, and are vastly superior to those of two other approximation formulas analyzed in this paper, including the Brenner–Subrahmanyam formula.
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Lee, Geon, Tae-Kyoung Kim, Hyun-Gyoon Kim, and Jeonggyu Huh. "Newton–Raphson Emulation Network for Highly Efficient Computation of Numerous Implied Volatilities." Journal of Risk and Financial Management 15, no. 12 (December 18, 2022): 616. http://dx.doi.org/10.3390/jrfm15120616.

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In finance, implied volatility is an important indicator that reflects the market situation immediately. Many practitioners estimate volatility by using iteration methods, such as the Newton–Raphson (NR) method. However, if numerous implied volatilities must be computed frequently, the iteration methods easily reach the processing speed limit. Therefore, we emulate the NR method as a network by using PyTorch, a well-known deep learning package, and optimize the network further by using TensorRT, a package for optimizing deep learning models. Comparing the optimized emulation method with the benchmarks, implemented in two popular Python packages, we demonstrate that the emulation network is up to 1000 times faster than the benchmark functions.
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35

Padhi, Puja, and Imlak Shaikh. "ON THE RELATIONSHIP OF IMPLIED, REALIZED AND HISTORICAL VOLATILITY: EVIDENCE FROM NSE EQUITY INDEX OPTIONS." Journal of Business Economics and Management 15, no. 5 (November 27, 2014): 915–34. http://dx.doi.org/10.3846/16111699.2013.793605.

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This study examines the information content of implied volatility, using the options of the underlying S&P CNX Nifty index. In this study, implied, historical and realized volatilities are calculated using non-overlapping monthly at-the-money samples. The study covers the period from introduction of options on the derivative segment of NSE, June 2001 to May 2011. The results reveal that call and put implied volatility of S&P CNX Nifty index option does contain information about future realized return volatility. This study accounts for the problem of error-in-variable and controls for it by using the instrumental variable technique. In the 2SLS estimation, the Hausman H-statistic shows that call implied volatility is measured with error. Hence, 2SLS coefficients are more consistent than the OLS estimates. Results of this study might prove to be helpful to the volatility traders in volatility forecasting and option pricing.
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Quaye, Enoch, and Radu Tunaru. "The stock implied volatility and the implied dividend volatility." Journal of Economic Dynamics and Control 134 (January 2022): 104276. http://dx.doi.org/10.1016/j.jedc.2021.104276.

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37

Derman, Emanuel, and Iraj Kani. "Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility." International Journal of Theoretical and Applied Finance 01, no. 01 (January 1998): 61–110. http://dx.doi.org/10.1142/s0219024998000059.

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In this paper we present an arbitrage pricing framework for valuing and hedging contingent equity index claims in the presence of a stochastic term and strike structure of volatility. Our approach to stochastic volatility is similar to the Heath-Jarrow-Morton (HJM) approach to stochastic interest rates. Starting from an initial set of index options prices and their associated local volatility surface, we show how to construct a family of continuous time stochastic processes which define the arbitrage-free evolution of this local volatility surface through time. The no-arbitrage conditions are similar to, but more involved than, the HJM conditions for arbitrage-free stochastic movements of the interest rate curve. They guarantee that even under a general stochastic volatility evolution the initial options prices, or their equivalent Black–Scholes implied volatilities, remain fair. We introduce stochastic implied trees as discrete implementations of our family of continuous time models. The nodes of a stochastic implied tree remain fixed as time passes. During each discrete time step the index moves randomly from its initial node to some node at the next time level, while the local transition probabilities between the nodes also vary. The change in transition probabilities corresponds to a general (multifactor) stochastic variation of the local volatility surface. Starting from any node, the future movements of the index and the local volatilities must be restricted so that the transition probabilities to all future nodes are simultaneously martingales. This guarantees that initial options prices remain fair. On the tree, these martingale conditions are effected through appropriate choices of the drift parameters for the transition probabilities at every future node, in such a way that the subsequent evolution of the index and of the local volatility surface do not lead to riskless arbitrage opportunities among different option and forward contracts or their underlying index. You can use stochastic implied trees to value complex index options, or other derivative securities with payoffs that depend on index volatility, even when the volatility surface is both skewed and stochastic. The resulting security prices are consistent with the current market prices of all standard index options and forwards, and with the absence of future arbitrage opportunities in the framework. The calculated options values are independent of investor preferences and the market price of index or volatility risk. Stochastic implied trees can also be used to calculate hedge ratios for any contingent index security in terms of its underlying index and all standard options defined on that index.
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38

Manfredo, Mark R., Raymond M. Leuthold, and Scott H. Irwin. "Forecasting Fed Cattle, Feeder Cattle, and Corn Cash Price Volatility: The Accuracy of Time Series, Implied Volatility, and Composite Approaches." Journal of Agricultural and Applied Economics 33, no. 3 (December 2001): 523–38. http://dx.doi.org/10.1017/s1074070800020988.

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AbstractEconomists and others need estimates of future cash price volatility to use in risk management evaluation and education programs. This paper evaluates the performance of alternative volatility forecasts for fed cattle, feeder cattle, and corn cash price returns. Forecasts include time series (e.g. GARCH), implied volatility from options on futures contracts, and composite specifications. The overriding finding from this research, consistent with the existing volatility forecasting literature, is that no single method of volatility forecasting provides superior accuracy across alternative data sets and horizons. However, evidence is provided suggesting that risk managers and extension educators use composite methods when both time series and implied volatilities are available.
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39

STROBL, KARL. "ON THE CONSISTENCY OF THE DETERMINISTIC LOCAL VOLATILITY FUNCTION MODEL ('IMPLIED TREE')." International Journal of Theoretical and Applied Finance 04, no. 03 (June 2001): 545–65. http://dx.doi.org/10.1142/s0219024901001036.

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We show that the frequent claim that the implied tree prices exotics consistently with an arbitrage-free market is untrue if the local volatilities are stochastic. This is a consequence of the market incompleteness under stochastic volatility. We also show that the problem cannot be mitigated by conveniently defining some 'weakly stochastic' local volatility, as this would violate the no-arbitrage condition. In the process of constructing the proof, we analyse — in the most general context — the impact of stochastic variables on the P&L of a hedged portfolio. We find that any stochastic tradeable either has quadratic variation — and therefore a Γ-like P&L on instruments with non-linear exposure to that asset — or it introduces arbitrage opportunities.
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40

Wang, Jying-Nan, Hung-Chun Liu, and Lu-Jui Chen. "On Forecasting Taiwanese Stock Index Option Prices: The Role of Implied Volatility Index." International Journal of Economics and Finance 9, no. 9 (August 20, 2017): 133. http://dx.doi.org/10.5539/ijef.v9n9p133.

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This paper aims to propose four volatility measures: The first is the GARCH model advocated by Bollerslev (1986); the second is the GARCHVIX model which extends the GARCH model by including the volatility index (VIX) as explanatory variable for volatility; the last two are HS20D and HS252D, which represent the historical volatilities generated by traditional rolling window technique with 20- and 252-day historical index returns data, respectively. We examine the price information on VIX to improve the predictive performance of GARCH model for valuing TAIEX stock index call options (TXO) over the period from January 2014 to May 2015. Empirical results firstly indicate that both the GARCH and GARCHVIX models consistently perform better than the historical volatility models for forecasting call value of TXO under different moneynesses. Secondly, the GARCHVIX model significantly outperforms the GARCH model for most cases, indicating that the GARCH-based option price forecasts can be effectively improved with the additional information contained in VIX. Finally, the use of GARCHVIX model can greatly reduce model mispricing especially for out-the-money TXO option case. Thus, volatility index is crucial for option traders to efficiently predict TXO option value with GARCH model.
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41

Campani, Carlos Heitor, and Assis Gustavo da Silva Durães. "Forecasting USD-BRL Currency Rate Volatility using Realized and Implied Volatilities Data." Estudos Econômicos (São Paulo) 48, no. 4 (December 2018): 687–719. http://dx.doi.org/10.1590/0101-41614845cca.

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Abstract This article assesses the impact of exogenous variables in GARCH models, when applied to volatility forecasts for the Brazilian USD-BRL currency market. As exogenous variables, we used the realized variance, based on high frequency data, and the FXVol index, based on market implied volatility data. This is the first study to use the FXVol index and to investigate its effects on Brazilian foreign exchange volatility. The results indicate statistical significance of the superiority of the extended models when predicting volatility. We conclude that high frequency data and market implied volatility contain relevant information with respect to USD-BRL currency volatility. These find ings are relevant for hedgers, speculators and practitioners in general.
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42

Ackert, Lucy F., Jonathan Hao, and William C. Hunter. "The effect of circuit breakers on expected volatility: Tests using implied volatilities." Atlantic Economic Journal 25, no. 2 (June 1997): 117–27. http://dx.doi.org/10.1007/bf02298379.

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43

Privault, Nicolas, and Qihao She. "Option pricing and implied volatilities in a 2-hypergeometric stochastic volatility model." Applied Mathematics Letters 53 (March 2016): 77–84. http://dx.doi.org/10.1016/j.aml.2015.09.008.

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44

Wirjanto, Tony S., and Anyi Zhu. "Implied volatility surfaces during the period of global financial crisis." International Journal of Financial Engineering 05, no. 01 (March 2018): 1850001. http://dx.doi.org/10.1142/s2424786318500019.

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This paper adopts a parametric regression approach to model and calibrate implied volatility surface during the period of the global financial crisis. Due to its relatively low computational cost, it facilitates comparison across a great number of different competing models. The proposed regression models are backtested against historical S&P 500 prices during both volatile and non-volatile periods as proxied by the VIX index around the same time period, and the fits of the models are assessed. Furthermore both an equally weighted scheme and an alternative scheme based on observed implied volatilities as the weight are deployed and the results produced by these two schemes are contrasted and compared. Finally the concept of promptness, instead of the more traditional concept of time to maturity, is introduced as a covariate in the regression models to better capture the shape of the volatility surface during the period characterized by a prolonged low interest-rate environment.
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45

LINARAS, CHARILAOS E., and GEORGE SKIADOPOULOS. "IMPLIED VOLATILITY TREES AND PRICING PERFORMANCE: EVIDENCE FROM THE S&P 100 OPTIONS." International Journal of Theoretical and Applied Finance 08, no. 08 (December 2005): 1085–106. http://dx.doi.org/10.1142/s0219024905003359.

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This paper examines the pricing performance of various discrete-time option models that accept the variation of implied volatilities with respect to the strike price and the time-to-maturity of the option (implied volatility tree models). To this end, data from the S&P 100 options are employed for the first time. The complex implied volatility trees are compared to the standard Cox–Ross–Rubinstein model and the ad-hoc traders model. Various criteria and interpolation methods are used to evaluate the performance of the models. The results have important implications for the pricing accuracy of the models under scrutiny and their implementation.
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46

Rosenberg, Joshua V. "Implied Volatility Functions." Journal of Derivatives 7, no. 3 (February 29, 2000): 51–64. http://dx.doi.org/10.3905/jod.2000.319124.

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47

Corcuera, José Manuel, Florence Guillaume, Peter Leoni, and Wim Schoutens. "Implied Lévy volatility." Quantitative Finance 9, no. 4 (June 2009): 383–93. http://dx.doi.org/10.1080/14697680902965548.

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48

Jäckel, Peter. "Implied Normal Volatility." Wilmott 2017, no. 88 (March 2017): 54–57. http://dx.doi.org/10.1002/wilm.10581.

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Jäckel, Peter. "Implied Normal Volatility." Wilmott 2017, no. 90 (July 2017): 54–57. http://dx.doi.org/10.1002/wilm.10608.

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50

Cho, Dam. "Implied Volatility of the KOSPI 200 Index Option Market." Journal of Derivatives and Quantitative Studies 23, no. 4 (November 30, 2015): 517–41. http://dx.doi.org/10.1108/jdqs-04-2015-b0002.

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This paper analyzes implied volatilities (IVs), which are computed from trading records of the KOSPI 200 index option market from January 2005 to December 2014, to examine major characteristics of the market pricing behavior. The data includes only daily closing prices of option transactions for which the daily trading volume is larger than 300 contracts. The IV is computed using the Black-Scholes option pricing model. The empirical findings are as follows; Firstly, daily averages of IVs have shown very similar behavior to historical volatilities computed from 60-day returns of the KOSPI 200 index. The correlation coefficient of IV of the ATM call options to historical volatility is 0.8679 and that of the ATM put options is 0.8479. Secondly, when moneyness, which is measured by the ratio of the strike price to the spot price, is very large or very small, IVs of call and put options decrease days to maturity gets longer. This is partial evidence of the jump risk inherent in the stochastic process of the spot price. Thirdly, the moneyness pattern showed heavily skewed shapes of volatility smiles, which was more apparent during the global financial crises period from 2007 to 2009. Behavioral reasons can explain the volatility smiles. When the moneyness is very small, the deep OTM puts are priced relatively higher due to investors’ crash phobia and the deep ITM calls are valued higher due to investors’ overconfidence and confirmation biases. When the moneyness is very large, the deep OTM calls are priced higher due to investors’ hike expectation and the deep ITM puts are valued higher due to overconfidence and confirmation biases. Fourthly, for almost all moneyness classes and for all sub-periods, the IVs of puts are larger than the IVs of calls. Also, the differences of IVs of deep OTM put ranges minus IVs of deep OTM calls, which is known to be a measure of crash phobia or hike expectation, shows consistent positive values for all sub-periods. The difference in the financial crisis period is much bigger than in other periods. This suggests that option traders had a stronger crash phobia in the financial crisis.
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