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Journal articles on the topic 'Implied volatility skew'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Kim, Jin Woo, and Joon H. Rhee. "An Empirical Study on Implied Volatility Skew Using PCA." Journal of Derivatives and Quantitative Studies 24, no. 3 (August 31, 2016): 365–97. http://dx.doi.org/10.1108/jdqs-03-2016-b0001.

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This paper extracts the factors determining the implied volatility skew movements of KOSPI200 index options by applying PCA (Principal Component Analysis). In particular, we analyze the movement of skew depending on the changes of the underlying asset price. As a result, it turned out that two factors can explain 94.6%~99.8% of the whole movement of implied volatility. The factor1 could be interpreted as ‘parallel shift’, and factor2 as the movement of ‘tilt or slope’. We also find some significant structural changes in the movement of skew after the Financial Crisis. The explanatory power of factor1 becomes more important on the movement of skew in both call and put options after the financial crisis. On the other hand, the influences of the factor2 is less. In general, after financial crisis, the volatility skew has the strong tendency to move in parallel. This implies that the changes in the option price or implied volatility due to the some shocks becomes more independent of the strike prices.

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2

Mixon, Scott. "What Does Implied Volatility Skew Measure?" Journal of Derivatives 18, no. 4 (May 31, 2011): 9–25. http://dx.doi.org/10.3905/jod.2011.18.4.009.

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3

DE OLIVERA, FEDERICO, JOSÉ FAJARDO, and ERNESTO MORDECKI. "SKEWED LÉVY MODELS AND IMPLIED VOLATILITY SKEW." International Journal of Theoretical and Applied Finance 21, no. 02 (March 2018): 1850003. http://dx.doi.org/10.1142/s0219024918500036.

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We introduce skewed Lévy models, characterized by a symmetric jump measure multiplied by a damping exponential factor. These models exhibit a clear implied volatility pattern, where the damping parameter controls the implied volatility curve’s skew, resulting in a measure of the model’s skewness. We show that the variation of this parameter produces the typical smirk observed in implied volatility curves. Some theoretical facts supporting these findings are proved.

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4

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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5

FOUQUE, JEAN-PIERRE, GEORGE PAPANICOLAOU, and K. RONNIE SIRCAR. "FROM THE IMPLIED VOLATILITY SKEW TO A ROBUST CORRECTION TO BLACK-SCHOLES AMERICAN OPTION PRICES." International Journal of Theoretical and Applied Finance 04, no. 04 (August 2001): 651–75. http://dx.doi.org/10.1142/s0219024901001139.

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We describe a robust correction to Black-Scholes American derivatives prices that accounts for uncertain and changing market volatility. It exploits the tendency of volatility to cluster, or fast mean-reversion, and is simply calibrated from the observed implied volatility skew. The two-dimensional free-boundary problem for the derivative pricing function under a stochastic volatility model is reduced to a one-dimensional free-boundary problem (the Black-Scholes price) plus the solution of a fixed boundary-value problem. The formal asymptotic calculation that achieves this is presented here. We discuss numerical implementation and analyze the effect of the volatility skew.

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VARGAS, VINCENT, TUNG-LAM DAO, and JEAN-PHILIPPE BOUCHAUD. "SKEW AND IMPLIED LEVERAGE EFFECT: SMILE DYNAMICS REVISITED." International Journal of Theoretical and Applied Finance 18, no. 04 (June 2015): 1550022. http://dx.doi.org/10.1142/s0219024915500223.

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We revisit the "Smile Dynamics" problem, which consists in relating the implied leverage (i.e. the correlation of the at-the-money volatility with the returns of the underlying) and the skew of the option smile. The ratio between these two quantities, called "Skew-Stickiness Ratio" (SSR) by Bergomi (2009), saturates to the value 2 for linear models in the limit of small maturities, and converges to 1 for long maturities. We show that for more general, non-linear models (such as the asymmetric GARCH model), Bergomi's result must be modified, and can be larger than 2 for small maturities. The discrepancy comes from the fact that the volatility skew is, in general, different from the skewness of the underlying. We compare our theory with empirical results, using data both from option markets and from the underlying price series, for the S&P 500 and the DAX. We find, among other things, that although both the implied leverage and the skew appear to be too strong on option markets, their ratio is well explained by the theory. We observe that the SSR indeed becomes larger than 2 for small maturities, signalling the presence of non-linear effects.

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7

NADTOCHIY, SERGEY, and JAN OBłÓJ. "ROBUST TRADING OF IMPLIED SKEW." International Journal of Theoretical and Applied Finance 20, no. 02 (March 2017): 1750008. http://dx.doi.org/10.1142/s021902491750008x.

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In this paper, we present a method for constructing a (static) portfolio of co-maturing European options whose price sign is determined by the skewness level of the associated implied volatility. This property holds regardless of the validity of a specific model — i.e. the method is robust. The strategy is given explicitly and depends only on one’s beliefs about the future values of implied skewness, which is an observable market indicator. As such, our method allows the use of existing statistical tools to formulate the beliefs, providing a practical interpretation of the more abstract mathematical setting, in which the beliefs are understood as a family of probability measures. One of the applications of the results established herein is a method for trading one’s views on the future changes in implied skew, largely independently of other market factors. Another application of our results provides a concrete improvement of the model-independent super-replication and sub-replication strategies for barrier options proposed in [H. Brown, D. Hobson & L. C. G. Rogers (2001) Robust hedging of barrier options, Mathematical Finance 11 (3), 285–314.], which exploits the given beliefs on the implied skew. Our theoretical results are tested empirically, using the historical prices of S&P 500 options.

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8

Doran, James S., and Kevin Krieger. "Implications for Asset Returns in the Implied Volatility Skew." Financial Analysts Journal 66, no. 1 (January 2010): 65–76. http://dx.doi.org/10.2469/faj.v66.n1.9.

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9

FUKASAWA, MASAAKI. "VOLATILITY DERIVATIVES AND MODEL-FREE IMPLIED LEVERAGE." International Journal of Theoretical and Applied Finance 17, no. 01 (February 2014): 1450002. http://dx.doi.org/10.1142/s0219024914500022.

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We revisit robust replication theory of volatility derivatives and introduce a broader class which may be considered as the second generation of volatility derivatives. One of them is a swap contract on the quadratic covariation between an asset price and the model-free implied variance (MFIV) of the asset. It can be replicated in a model-free manner and its fair strike may be interpreted as a model-free measure for the covariance of the asset price and the realized variance. The fair strike is given in a remarkably simple form, which enable to compute it from the Black–Scholes implied volatility surface. We call it the model-free implied leverage (MFIL) and give several characterizations. In particular, we show its simple relation to the Black–Scholes implied volatility skew by an asymptotic method. Further to get an intuition, we demonstrate some explicit calculations under the Heston model. We report some empirical evidence from the time series of the MFIV and MFIL of the Nikkei stock average.

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10

Siddiqi, Hammad. "Financial market disruption and investor awareness: the case of implied volatility skew." Quantitative Finance and Economics 6, no. 3 (2022): 505–17. http://dx.doi.org/10.3934/qfe.2022021.

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<abstract> <p>The crash of 1987 is considered one of the most significant events in the history of financial markets due to the severity and swiftness of market declines worldwide. In the aftermath of the crash, a permanent change in options market occurred; implied volatility skew started appearing in options markets worldwide. In this article, we argue that the emergence of the implied volatility skew can be understood as arising from increased investor awareness about the stock price process and its implications for delta hedging. Delta-hedging aims to eliminate the directional risk associated with price movements in the underlying asset. Before the crash, investors were unaware of the proposition that "a delta-hedged portfolio is risky". That is, they implicitly believed in the proposition that "a delta-hedged portfolio is risk-free". The crash caused "portfolio insurance delta-hedges" to fail spectacularly. The resulting visceral shock drove home the lesson that "a delta-hedged portfolio is risky", thus, increasing investor awareness. We show that this sudden realization that a delta-hedged portfolio is risky is sufficient to generate the implied volatility skew and is equivalent to replacing the risk-free rate with a higher rate in the European call option formula. It follows that investor awareness (beyond asymmetric information) is an important consideration that matters for financial market behavior.</p> </abstract>

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11

Jeng, Siow Woon, and Adem Kilicman. "Approximation Formula for Option Prices under Rough Heston Model and Short-Time Implied Volatility Behavior." Symmetry 12, no. 11 (November 14, 2020): 1878. http://dx.doi.org/10.3390/sym12111878.

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Rough Heston model possesses some stylized facts that can be used to describe the stock market, i.e., markets are highly endogenous, no statistical arbitrage mechanism, liquidity asymmetry for buy and sell order, and the presence of metaorders. This paper presents an efficient alternative to compute option prices under the rough Heston model. Through the decomposition formula of the option price under the rough Heston model, we manage to obtain an approximation formula for option prices that is simpler to compute and requires less computational effort than the Fourier inversion method. In addition, we establish finite error bounds of approximation formula of option prices under the rough Heston model for 0.1≤H<0.5 under a simple assumption. Then, the second part of the work focuses on the short-time implied volatility behavior where we use a second-order approximation on the implied volatility to match the terms of Taylor expansion of call option prices. One of the key results that we manage to obtain is that the second-order approximation for implied volatility (derived by matching coefficients of the Taylor expansion) possesses explosive behavior for the short-time term structure of at-the-money implied volatility skew, which is also present in the short-time option prices under rough Heston dynamics. Numerical experiments were conducted to verify the effectiveness of the approximation formula of option prices and the formulas for the short-time term structure of at-the-money implied volatility skew.

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12

Pellegrino, T. "Capturing implied correlation skew from options prices via multiscale stochastic volatility models." International Journal of Financial Engineering 07, no. 04 (November 28, 2020): 2050042. http://dx.doi.org/10.1142/s2424786320500425.

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The aim of this paper is to derive a second-order asymptotic expansion for the price of European options written on two underlying assets, whose dynamics are described by multiscale stochastic volatility models. In particular, the second-order expansion of option prices can be translated into a corresponding expansion in implied correlation units. The resulting approximation for the implied correlation curve turns out to be quadratic in the log-moneyness, capturing the convexity of the implied correlation skew. Finally, we describe a calibration procedure where the model parameters can be estimated using option prices on individual underlying assets.

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13

Fengler, M. R., H. Herwartz, and C. Werner. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew." Journal of Financial Econometrics 10, no. 3 (March 6, 2012): 457–93. http://dx.doi.org/10.1093/jjfinec/nbr016.

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14

ANSELMI, GIULIO. "VOLATILITY MEASURES, LIQUIDITY AND CREDIT LOSS PROVISIONS DURING PERIODS OF FINANCIAL DISTRESS." Journal of Financial Management, Markets and Institutions 06, no. 02 (December 2018): 1850006. http://dx.doi.org/10.1142/s2282717x18500068.

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In this paper, we investigate the role of liquidity in banks lending activity and how liquidity provision is related to bank’s credit risk and others market-based risk measures, such as bank’s implied volatility skew from options traded on the market and realized volatility from futures contract on LIBOR, during periods of global financial distress. Credit risk is given by the ratio between loan loss reserves and total assets and we find that losses from lending activity force banks to build up new liquidity provisions only during the period of financial distress. Liquidity ratio is given by the sum of cash and short-term assets over total assets and we discovered that credit risk reduces liquidity ratio only in bad times, as this demand for liquid asset is suddenly switched on and the more reserves from loan losses the bank has, the more it cleans its balance sheet from long-term commitments in order to replenish its cash and short-term securities. When we control for market-based risk measures, we evidence that both implied volatility skew and LIBOR’s realized volatility are negatively related with the liquidity ratio and are useful in predicting a distress in bank’s liquidity holdings.

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15

Alòs, Elisa, Jorge A. León, Monique Pontier, and Josep Vives. "A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility." Journal of Applied Mathematics and Stochastic Analysis 2008 (February 10, 2008): 1–17. http://dx.doi.org/10.1155/2008/359142.

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We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.

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16

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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De Spiegeleer, Jan, Monika B. Forys, Ine Marquet, and Wim Schoutens. "The impact of skew on the pricing of CoCo bonds." International Journal of Financial Engineering 04, no. 01 (March 2017): 1750012. http://dx.doi.org/10.1142/s2424786317500128.

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This paper presents a Heston-based pricing model for contingent convertible bonds (CoCos). The main finding is that skew in the implied volatility surface has a significant impact on the CoCo price. Hence stochastic volatility models, like the Heston model, which incorporate smile and skew are appropriate in the context of pricing CoCos. The financial crisis of 2007–2008 triggered an avalanche of financial worries for financial institutions around the globe. After the collapse of Lehman Brothers, governments intervened and bailed out banks using tax-payer’s money. Preventing such bail-outs in the future and designing a more stable banking sector in general, requires both higher capital levels and regulatory capital of a higher quality. Bank debt needed therefore to be made absorbing. This is where CoCos come in. The Lloyds Banking Group introduced the first CoCo bonds as early as December 2009. Since the first issuance of a CoCo bond more than five years ago, the market has continued to grow and has now reached a size over €120[Formula: see text]bn. CoCos are hybrid financial instruments that convert into equity or suffer a write-down of the face value upon the appearance of a trigger event, often in terms of the bank’s CET1 level in combination with a regulatory trigger. The valuation of CoCos boils down to the quantification of the trigger probability and the expected loss suffered by the investors if such a trigger event eventually takes place. There are at least two schools of thought regarding valuation of CoCos. Structural models can be put at work or investors can rely on market implied models. The latter category uses market data (share prices, CDS levels and implied volatility, etc.) in order to calculate the theoretical price of a CoCo bond. In De Spiegeleer and Schoutens The Journal of Derivatives, the pricing of CoCo notes has been worked out in a market implied Black–Scholes context. In this paper we move away from the assumption of a constant volatility which is the back-bone of Black–Scholes based valuation and put the Heston model at work and study CoCos in a stochastic volatility context. The existence of a semi closed-form formula for European options pricing under the Heston model allows for a fast calibration of the model. In our approach we combined market quotes of listed option prices with CDS data. As a case study, the procedure was applied on the Tier 2 10NC [Formula: see text] CoCo issued by Barclays in 2012.

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Clark, Iain J., and Saeed Amen. "Using FX Volatility Skew to Assess the Implied Probability of Hard Brexit." Wilmott 2018, no. 95 (May 2018): 64–69. http://dx.doi.org/10.1002/wilm.10677.

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Figueroa-López, José E., and Sveinn Ólafsson. "Short-term asymptotics for the implied volatility skew under a stochastic volatility model with Lévy jumps." Finance and Stochastics 20, no. 4 (September 13, 2016): 973–1020. http://dx.doi.org/10.1007/s00780-016-0313-3.

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Chan, Konan, Li Ge, and Tse-Chun Lin. "Informational Content of Options Trading on Acquirer Announcement Return." Journal of Financial and Quantitative Analysis 50, no. 5 (October 2015): 1057–82. http://dx.doi.org/10.1017/s0022109015000484.

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AbstractThis study examines the informational content of options trading on acquirer announcement returns. We show that implied volatility spread predicts positively on the cumulative abnormal return (CAR), and implied volatility skew predicts negatively on the CAR. The predictability is much stronger around actual merger and acquisition (M&A) announcement days, as compared with pseudo-event days. The prediction is weaker if pre-M&A stock price has incorporated part of the information, but stronger if the acquirer’s options trading is more liquid. Finally, we find that a higher relative trading volume of options to stock predicts higher absolute CARs. The relation also exists among the target firms.

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Seo, Sang Byung, and Jessica A. Wachter. "Option Prices in a Model with Stochastic Disaster Risk." Management Science 65, no. 8 (August 2019): 3449–69. http://dx.doi.org/10.1287/mnsc.2017.2978.

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Contrary to well-known asset pricing models, volatilities implied by equity index options exceed realized stock market volatility and exhibit a pattern known as the volatility skew. We explain both facts using a model that can also account for the mean and volatility of equity returns. Our model assumes a small risk of economic disaster that is calibrated based on international data on large consumption declines. We allow the disaster probability to be stochastic, which turns out to be crucial to the model’s ability both to match equity volatility and to reconcile option prices with macroeconomic data on disasters. This paper was accepted by Lauren Cohen, finance.

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Shaikh, Imlak, and Puja Padhi. "Stylized patterns of implied volatility in India: a case study of NSE Nifty options." Journal of Indian Business Research 6, no. 3 (August 12, 2014): 231–54. http://dx.doi.org/10.1108/jibr-12-2013-0103.

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Purpose – The aim of this study is to examine the “volatility smile” or/and “skew”, term structure and implied volatility surfaces based on those European options written in the standard and poor (S&P) Nifty equity index. The stochastic nature of implied volatility across strike price, time-to-expiration and moneyness violates the core assumption of the Black–Scholes option pricing model. Design/methodology/approach – The potential determinants of implied volatility are the degree of moneyness, time-to-expiration and the liquidity of the strikes. The empirical work has been expressed by means of a simple ordinary least squares (OLS) framework and presents the estimation results according to moneyness, time-to-expiration and liquidity of options. Findings – The options data give evidence of the existence of a classical U-shaped volatility smile for the Indian options market. Indeed, there is some evidence that the “volatility smirk” which pertains to 30-day options and also implied volatility remain higher for the shorter maturity options and decrease as the time-to-expiration increases. The results lead us to believe that in-the-money calls and out-of-the-money puts are of higher volatility than at-the-money options. Conclusion was drawn due to the persistence of the smile in the options market. Practical implications – The practical implication of studying stylized patterns of implied volatility is that it educates the volatility traders about how in-the-money and out-of-the-money options are priced in the options market, and provides an estimate of volatility for the pricing of future options. Originality/value – This study is an extension of previous work. The undertaking has been to examine the case of a more liquid and transparent options market, which is missing from the earlier work. The current study is more relevant because, since 2008, significant changes have been observed in the futures and options market in India.

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Ghosh, Bikramaditya, and Elie Bouri. "Long Memory and Fractality in the Universe of Volatility Indices." Complexity 2022 (January 20, 2022): 1–8. http://dx.doi.org/10.1155/2022/6728432.

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Unlike previous studies that consider the Chicago Board of Options Exchange (CBOE) implied volatility index (VIX), we examine long memory and fractality in the universe of nine CBOE volatility indices. Using daily data from October 5, 2007, to October 5, 2020, covering calm and crisis periods, we find evidence of long memory and fractality in all indices and a change in the degree of volatility persistence, which points to inefficiency. The long memory of the SKEW index is strong before the onset of three crisis periods, but eases afterwards. The findings provide new insights that matter to investment decisions and trading strategies.

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Liu, Shican, Yanli Zhou, Yonghong Wu, and Xiangyu Ge. "Option Pricing under the Jump Diffusion and Multifactor Stochastic Processes." Journal of Function Spaces 2019 (February 3, 2019): 1–12. http://dx.doi.org/10.1155/2019/9754679.

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In financial markets, there exists long-observed feature of the implied volatility surface such as volatility smile and skew. Stochastic volatility models are commonly used to model this financial phenomenon more accurately compared with the conventional Black-Scholes pricing models. However, one factor stochastic volatility model is not good enough to capture the term structure phenomenon of volatility smirk. In our paper, we extend the Heston model to be a hybrid option pricing model driven by multiscale stochastic volatility and jump diffusion process. In our model the correlation effects have been taken into consideration. For the reason that the combination of multiscale volatility processes and jump diffusion process results in a high dimensional differential equation (PIDE), an efficient finite element method is proposed and the integral term arising from the jump term is absorbed to simplify the problem. The numerical results show an efficient explanation for volatility smirks when we incorporate jumps into both the stock process and the volatility process.

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Alòs, Elisa, Antoine Jacquier, and Jorge A. León. "The implied volatility of Forward-Start options: ATM short-time level, skew and curvature." Stochastics 91, no. 1 (July 30, 2018): 37–51. http://dx.doi.org/10.1080/17442508.2018.1499105.

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Deng, Guohe. "Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model." Complexity 2020 (September 1, 2020): 1–15. http://dx.doi.org/10.1155/2020/1960121.

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Empirical evidence shows that single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew, and certain financial assets may exhibit jumps in returns and volatility. This paper introduces a two-factor stochastic volatility jump-diffusion model in which two variance processes with jumps drive the underlying stock price and then considers the valuation on European style option. We derive a semianalytical formula for European vanilla option and develop a fast and accurate numerical algorithm for the computation of the option prices using the fast Fourier transform (FFT) technique. We compare the volatility smile and probability density of the proposed model with those of alternative models, including the normal jump diffusion model and single-factor stochastic volatility model with jumps, respectively. Finally, we provide some sensitivity analysis of the model parameters to the options and several calibration tests using option market data. Numerical examples show that the proposed model has more flexibility to capture the implied volatility term structure and is suitable for empirical work in practice.

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Kim, Sol. "Ad Hoc Black and Scholes Procedures with the Time-to-Maturity." Journal of Derivatives and Quantitative Studies 22, no. 3 (August 31, 2014): 465–94. http://dx.doi.org/10.1108/jdqs-03-2014-b0004.

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There are two ad hoc approaches to Black and Scholes model. The “relative smile” approach treats the implied volatility skew as a fixed function of moneyness, whereas the “absolute smile” approach treats it as a function of the strike price. Previous studies reveal that the “absolute smile” approach is superior to the “relative smile” approach as well as to other sophisticated models for pricing options. We find that the time to maturity factors improve the pricing performance of the ad hoc procedures and the superiority of the “absolute smile” approach still holds even after the time to maturity is considered.

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Byun, Suk Joon, Sol Kim, and Dong Woo Rhee. "Ad Hoc Black and Scholes Procedures with the Time-to-Maturity." Review of Pacific Basin Financial Markets and Policies 21, no. 01 (January 18, 2018): 1850006. http://dx.doi.org/10.1142/s0219091518500066.

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There are two ad hoc approaches to Black and Scholes model. The “relative smile” approach treats the implied volatility skew as a fixed function of moneyness, whereas the “absolute smile” approach treats it as a function of the strike price. Previous studies reveal that the “absolute smile” approach is superior to the “relative smile” approach as well as to other sophisticated models for pricing options. We find that the time-to-maturity factors improve the pricing and hedging performance of the ad hoc procedures and the superiority of the “absolute smile” approach still holds even after the time-to-maturity is considered.

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Kwark, Noe-Keol, Hyoung-Goo Kang, and Sang-Gyung Jun. "Can Derivative Information Predict Stock Price Jumps?" Journal of Applied Business Research (JABR) 31, no. 3 (May 1, 2015): 845. http://dx.doi.org/10.19030/jabr.v31i3.9222.

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<p>This study examines the predictability of jumps in stock prices using options-trading information, the futures basis spread, the cross-sectional standard deviation of returns on components in the stock index, and exchange rates. A stock price jump was defined as a large fluctuation in the stock price that deviated from the distribution thresholds of the past rates of return. This empirical analysis shows that the implied volatility spread between ATM call and put options was a significant predictor for both upward and downward jumps, whereas the volatility skew was less significant. In addition, the futures basis spread was moderately significant for downward stock price jumps. Both the cross-sectional standard deviation of the rates of return on component stocks in the KOSPI 200 and the won-dollar exchange rates were significant predictors for both upward and downward jumps.</p>

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WANG, SHINN-WEN. "APPLYING THE GENETIC-BASED NEURAL NETWORKS TO VOLATILITY TRADING." New Mathematics and Natural Computation 01, no. 02 (July 2005): 285–93. http://dx.doi.org/10.1142/s1793005705000159.

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The Black-Scholes options pricing model is widely applied in various options contracts, including contract design, trading, assets evaluation, and enterprise value estimation, etc. Unfortunately, this theoretical model limited by the influences of many unexpected real world phenomena due to six unreasonable assumptions. If we were to soundly take these phenomena into account, the opportunity to gain an excess return would be created. This research therefore combines both the remarkable effects caused by the implied volatility smile (or skew) and the tick-jump discrepancy between the underlying and derivative prices to establish a two-phase options arbitrage model using a genetic-based neural network (GNN). Using evidence from the warrant market in Taiwan, it is shown that the GNN model with arbitrage operations is superior in terms of performance to the original Black-Scholes-based arbitrage model. The GNN model is found to be suitable for application to various options markets as the valuation factors are modified. This paper helps to integrate the theoretical model with important practical considerations.

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De Giuli, Maria Elena, Dennis Montagna, Federica Naldi, and Alessandra Tanda. "Enhance and Protect Portfolio Returns: A Dynamic Put Spread Optimization." International Journal of Economics and Finance 11, no. 12 (November 25, 2019): 66. http://dx.doi.org/10.5539/ijef.v11n12p66.

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The aim of this paper is to structure and optimize a dynamic put spread strategy to build an enhancement and protection portfolio. To implement the investment strategy a short put option acting as enhancement and a long put option providing protection are combined: the resulting put spread is modeled, thus assuming a dynamic configuration, depending on market conditions. The investment parameters and objectives are then translated into a proper optimization algorithm. The optimization procedure is implemented and backtested on S&P500 Index as the underlying asset, and it shows that the algorithm actually results in an optimal configuration of the final put spread. The backtest additionally exhibits that the optimized strategy provides an overall over-performance with respect to the underlying asset. The paper presents a novel approach when implementing put spread strategy to enhance and protect portfolio by explicitly modeling the implied volatility and volatility skew, and dynamically adjusting the portfolio depending on market conditions.

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Alòs, Elisa, and Jorge A. León. "On the short-maturity behaviour of the implied volatility skew for random strike options and applications to option pricing approximation." Quantitative Finance 16, no. 1 (March 20, 2015): 31–42. http://dx.doi.org/10.1080/14697688.2015.1013499.

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Li, M., and S. Yen. "Re-examining covariance risk dynamics in international stock markets using quantile regression analysis." Acta Oeconomica 61, no. 1 (March 1, 2011): 33–59. http://dx.doi.org/10.1556/aoecon.61.2011.1.3.

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This investigation is one of the first to adopt quantile regression (QR) technique to examine covariance risk dynamics in international stock markets. Feasibility of the proposed model is demonstrated in G7 stock markets. Additionally, two conventional random-coefficient frameworks, including time-varying betas derived from GARCH models and state-varying betas implied by Markov-switching models, are employed and subjected to comparative analysis. The empirical findings of this work are consistent with the following notions. First, the beta smile (beta skew) curve for the Italian, U.S. and U.K. (Canadian, French and German) markets. That is, covariance risk among global stock markets in extremely bull and/or bear market states is significantly higher than in stable periods. Additionally, the Japanese market provides a special case, and its beta estimate at extremely bust state is significantly lower, not higher than that at the middle region. Second, the quantile-varying betas are identified as possessing two key advantages. Specifically, the comparison of the system with quantile-varying betas against that with time-varying betas implied by GARCH models provides meaningful implications for correlation-volatility relationship among international stock markets. Furthermore, the quantile-varying beta design in this study relaxes a simple dual beta setting implied by Markov-switching models of Ramchand — Susmel (1998) and can identify dynamics of asymmetry in betas.

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Dokuchaev, Nikolai. "Two unconditionally implied parameters and volatility smiles and skews." Applied Financial Economics Letters 2, no. 3 (May 2006): 199–204. http://dx.doi.org/10.1080/17446540500426771.

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Corrado, C. J., and Tie Su. "Implied volatility skews and stock return skewness and kurtosis implied by stock option prices." European Journal of Finance 3, no. 1 (March 1, 1997): 73–85. http://dx.doi.org/10.1080/135184797337543.

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Corrado, Charles J., and Tie Su. "Implied Volatility Skews and Stock Index Skewness and Kurtosis Implied by S&P 500 Index Option Prices." Journal of Derivatives 4, no. 4 (May 31, 1997): 8–19. http://dx.doi.org/10.3905/jod.1997.407978.

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JOSHI, MARK, and CHAO YANG. "FAST AND ACCURATE PRICING AND HEDGING OF LONG-DATED CMS SPREAD OPTIONS." International Journal of Theoretical and Applied Finance 13, no. 06 (September 2010): 839–65. http://dx.doi.org/10.1142/s0219024910006029.

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We present a fast method to price and hedge CMS spread options in the displaced-diffusion co-initial swap market model. Numerical tests demonstrate that we are able to obtain sufficiently accurate prices and Greeks with computational times measured in milliseconds. Further, we find that CMS spread options are weakly dependent on the at-the-money Black implied volatility skews.

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SOBEHART, JORGE R. "A FORWARD LOOKING, SINGULAR PERTURBATION APPROACH TO PRICING OPTIONS UNDER MARKET UNCERTAINTY AND TRADING NOISE." International Journal of Theoretical and Applied Finance 08, no. 05 (August 2005): 635–58. http://dx.doi.org/10.1142/s0219024905003165.

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In this article we examine the pricing of options when trading noise and uncertainty in the options markets invalidates the assumption that the price of the option depends solely on the price of the underlying security (or any set of underlying state variables). We show that the introduction of trading noise in the options market affects the call-put parity relationship, and can also contribute to generate implied volatility skews.

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Tashpulatov, Sherzod N. "Modeling Electricity Price Dynamics Using Flexible Distributions." Mathematics 10, no. 10 (May 21, 2022): 1757. http://dx.doi.org/10.3390/math10101757.

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We consider the wholesale electricity market prices in England and Wales during its complete history, where price-cap regulation and divestment series were introduced at different points in time. We compare the impact of these regulatory reforms on the dynamics of electricity prices. For this purpose, we apply flexible distributions that account for asymmetry, heavy tails, and excess kurtosis usually observed in data or model residuals. The application of skew generalized error distribution is appropriate for our case study. We find that after the second series of divestments, price level and volatility are lower than during price-cap regulation and after the first series of divestments. This finding implies that a sufficient horizontal restructuring through divestment series may be superior to price-cap regulation. The conclusion could be interesting to other countries because the England and Wales electricity market served as the benchmark model for liberalizing energy markets worldwide.

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KIJIMA, MASAAKI, and CHI CHUNG SIU. "CREDIT-EQUITY MODELING UNDER A LATENT LÉVY FIRM PROCESS." International Journal of Theoretical and Applied Finance 17, no. 03 (May 2014): 1450021. http://dx.doi.org/10.1142/s0219024914500216.

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Recent empirical studies have demonstrated the informative nature of the equity returns in explaining the variation of the underlying firm's credit default swap (CDS) spreads. Motivated by these findings, we propose a unified credit-equity model by extending the latent structural model in Kijima et al. (2009). As in the original latent model, we treat the actual status of the firm to be unobservable and one can extract information from the marker process that is observable to the investors. Default occurs when the actual firm value drops below a default threshold for the first time. Different from the model in Kijima et al. (2009), however, we define the marker process to be the firm's equity process. Choosing firm's equity process to be a marker process subsequently relaxes the restrictions imposed in Kijima et al. (2009), enabling us to price firm-related securities. Additionally, we enrich the original latent structural model with jump and regime-switching dynamics. The purpose of the extensions is to capture more realistic credit spreads and implied volatility skews under different economic environments. The proposed model maintains analytical tractability even under such complex dynamics, for the prices of CDSs and equity options admit semi-closed-form solutions. In sum, our model can evaluate corporate securities and their derivatives in a unified framework.

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41

Mixon, Scott. "What Does Implied Volatility Skew Measure?" SSRN Electronic Journal, 2010. http://dx.doi.org/10.2139/ssrn.1618602.

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Doshi, Hitesh, Jan Ericsson, Stephen Szaura, and Fan Yu. "Accounting Transparency and the Implied Volatility Skew." SSRN Electronic Journal, 2022. http://dx.doi.org/10.2139/ssrn.4225996.

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Dewi, Kania Evita. "PERBANDINGAN METODE NEWTON-RAPHSON DAN ALGORITMA GENETIK PADA PENENTUAN IMPLIED VOLATILITY SAHAM." Komputa : Jurnal Ilmiah Komputer dan Informatika 1, no. 2 (October 26, 2012). http://dx.doi.org/10.34010/komputa.v1i2.56.

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Penelitian ini bertujuan untuk menentukan implied volatility dari suatu saham dengan menggunakan algoritma genetika dan metode Newton-Raphson. Algoritma genetika yang merupakan suatu cara untuk mencari solusi masalah optimasi, tidak memerlukan sifat dari fungsi yang akan dicari solusinya, dapat menyelesaikan semua fungsi dengan syarat fungsi tersebut dapat diubah kedalam masalah optimasi. Dalam penelitian ini hasil perhitungan yang menggunakan algoritma genetika dibandingkan dengan hasil perhitungan dengan metode Newton-Raphson yang sudah biasa digunakan. Hasil penelitian menunjukan implied volatility yang dihasilkan metode Newton-Raphson lebih mendekati volatilitas bursa dibanding yang dihasilkan algoritma genetika. Ini dapat dilihat dari selisih antara harga opsi teoritis dengan harga opsi dibursa yang dihasilkan metode Newton-Raphson lebih kecil dibanding yang dihasilkan algoritma genetika. Penelitian ini juga memperlihatkan bahwa volatilitas opsi put terhadap strike price berbentuk volatility smile dan untuk volatilitas opsi call terhadap strike price berbentuk volatility skew untuk opsi yang memiliki maturity time 1 bulan dan 2 bulan dan untuk maturity time yang lain volatilitasnya berbentuk volatility smile.

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Tian, Meng, and Liuren Wu. "Cross-sectional Variation of Option Implied Volatility Skew." SSRN Electronic Journal, 2020. http://dx.doi.org/10.2139/ssrn.3707006.

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Hasler, Michael, and Alexandre Jeanneret. "A Macrofinance Model for Option Prices: A Story of Rare Economic Events." Management Science, October 19, 2022. http://dx.doi.org/10.1287/mnsc.2022.4587.

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We propose a macrofinance model that rationalizes robust features in equity index option markets. When rare disasters are followed by economic recoveries, the slope of the implied volatility term structure is positive in good times but turns negative in bad times. Additionally, implied volatility decreases with moneyness in bad times (volatility skew), whereas the shape becomes a smile in good times in the presence of rare economic booms. Our theory contributes to understanding the dynamics of the implied volatility surface yet keeping standard asset-pricing moments realistic. This paper was accepted by Gustavo Manso, finance.

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46

Siddiqi, Hammad. "Analogy Making and the Structure of Implied Volatility Skew." SSRN Electronic Journal, 2014. http://dx.doi.org/10.2139/ssrn.2465738.

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Siddiqi, Hammad. "Analogy Making and the Structure of Implied Volatility Skew." SSRN Electronic Journal, 2013. http://dx.doi.org/10.2139/ssrn.2305314.

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Collin-Dufresne, Pierre, Vyacheslav Fos, and Dmitry Muravyev. "Informed Trading in the Stock Market and Option-Price Discovery." Journal of Financial and Quantitative Analysis, August 4, 2020, 1–40. http://dx.doi.org/10.1017/s0022109020000629.

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Abstract When activist shareholders file Schedule 13D filings, the average stock-price volatility drops by approximately 10%. Prior to filing days, volatility information is reflected in option prices. Using a comprehensive sample of trades by Schedule 13D filers that reveals on what days and in what markets they trade, we show that on days when activists accumulate shares, option-implied volatility decreases, implied volatility skew increases, and implied volatility time slope increases. The evidence is consistent with a theoretical model where it is common knowledge that informed trading occurs only in the stock market and market makers update option prices based on stock-price and order-flow dynamics.

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Zulfiqar, Noshaba, and Saqib Gulzar. "Implied volatility estimation of bitcoin options and the stylized facts of option pricing." Financial Innovation 7, no. 1 (September 6, 2021). http://dx.doi.org/10.1186/s40854-021-00280-y.

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AbstractThe recently developed Bitcoin futures and options contracts in cryptocurrency derivatives exchanges mark the beginning of a new era in Bitcoin price risk hedging. The need for these tools dates back to the market crash of 1987, when investors needed better ways to protect their portfolios through option insurance. These tools provide greater flexibility to trade and hedge volatile swings in Bitcoin prices effectively. The violation of constant volatility and the log-normality assumption of the Black–Scholes option pricing model led to the discovery of the volatility smile, smirk, or skew in options markets. These stylized facts; that is, the volatility smile and implied volatilities implied by the option prices, are well documented in the option literature for almost all financial markets. These are expected to be true for Bitcoin options as well. The data sets for the study are based on short-dated Bitcoin options (14-day maturity) of two time periods traded on Deribit Bitcoin Futures and Options Exchange, a Netherlands-based cryptocurrency derivative exchange. The estimated results are compared with benchmark Black–Scholes implied volatility values for accuracy and efficiency analysis. This study has two aims: (1) to provide insights into the volatility smile in Bitcoin options and (2) to estimate the implied volatility of Bitcoin options through numerical approximation techniques, specifically the Newton Raphson and Bisection methods. The experimental results show that Bitcoin options belong to the commodity class of assets based on the presence of a volatility forward skew in Bitcoin option data. Moreover, the Newton Raphson and Bisection methods are effective in estimating the implied volatility of Bitcoin options. However, the Newton Raphson forecasting technique converges faster than does the Bisection method.

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Azzone, Michele, and Roberto Baviera. "Short-time implied volatility of additive normal tempered stable processes." Annals of Operations Research, September 5, 2022. http://dx.doi.org/10.1007/s10479-022-04894-y.

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AbstractEmpirical studies have emphasized that the equity implied volatility is characterized by a negative skew inversely proportional to the square root of the time-to-maturity. We examine the short-time-to-maturity behavior of the implied volatility smile for pure jump exponential additive processes. An excellent calibration of the equity volatility surfaces has been achieved by a class of these additive processes with power-law scaling. The two power-law scaling parameters are $$\beta $$ β , related to the variance of jumps, and $$\delta $$ δ , related to the smile asymmetry. It has been observed, in option market data, that $$\beta =1$$ β = 1 and $$\delta =-1/2$$ δ = - 1 / 2 . In this paper, we prove that the implied volatility of these additive processes is consistent, in the short-time, with the equity market empirical characteristics if and only if $$\beta =1$$ β = 1 and $$\delta =-1/2$$ δ = - 1 / 2 .

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