Academic literature on the topic 'Implied volatility skew'
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Journal articles on the topic "Implied volatility skew"
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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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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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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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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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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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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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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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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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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>
Dissertations / Theses on the topic "Implied volatility skew"
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Broodryk, Ryan. "The Lifted Heston Stochastic Volatility Model." Master's thesis, Faculty of Commerce, 2021. http://hdl.handle.net/11427/32614.
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Can we capture the explosive nature of volatility skew observed in the market, without resorting to non-Markovian models? We show that, in terms of skew, the Heston model cannot match the market at both long and short maturities simultaneously. We introduce Abi Jaber (2019)'s Lifted Heston model and explain how to price options with it using both the cosine method and standard Monte-Carlo techniques. This allows us to back out implied volatilities and compute skew for both models, confirming that the Lifted Heston nests the standard Heston model. We then produce and analyze the skew for Lifted Heston models with a varying number N of mean reverting terms, and give an empirical study into the time complexity of increasing N. We observe a weak increase in convergence speed in the cosine method for increased N, and comment on the number of factors to implement for practical use.
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ANSELMI, GIULIO. "ESSAYS ON OPTION IMPLIED VOLATILITY RISK MEASURES FOR BANKS." Doctoral thesis, Università Cattolica del Sacro Cuore, 2016. http://hdl.handle.net/10280/10402.
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La tesi comprende tre saggi sul ruolo della volatilità implicita per le banche. La tesi è organizzata in tre capitoli. Capitolo I - studia il ruolo di skew e spread della volatilità implicita nel determinare i rendimenti delle azioni bancarie. Capitolo II - analizza gli effetti degli skew della volatilità implicita e della realized volatility sulla leva finanziaria delle banche. Capitolo III - si focalizza sul rapporto tra il coefficiente di liquidità delle banche e le misure per il rischio estratte dalla volatilità (skew, spread, realized volatility).The thesis comprehends three essays on option implied volatility risk measures for banks. The thesis is organized in three chapters. Chapter I - studies the informational content for banks' stock returns in option's implied volatilities skews and spread. Chapter II - analyzes the effect of volatility risk measures (volatility skew and realized volatility) on banks' leverage. Chapter III - studies the relationship between banks' liquidity ratio and volatility risk measures.
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Piccirilli, Marco. "Additive models for energy markets." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3426712.
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This Dissertation explores the capability of additive models to describe prices in energy
markets, by focusing in particular on the specific case of electricity and natural gas. In
Chapter 1 we study a dynamic portfolio optimization problem designed for intraday electricity
trading. In Chapter 2 we introduce a no-arbitrage tractable framework based on the Heath-
Jarrow-Morton approach for a multicommodity energy forward market. Chapter 3 deals with
a thorough empirical study of a two-factor model derived by the framework of Chapter 2,
with an application to the German power futures market. Finally, in Chapter 4 we discuss
option pricing for additive factor models by Fourier transform methods. We introduce a
two-factor futures price model with jumps in order to capture the implied volatility smile
of European electricity options. An application to the European Energy Exchange Power
Derivatives market is presented.Questa Tesi esplora la capacità dei modelli additivi di descrivere i prezzi nei mercati energetici, concentrandosi in particolare sul caso specifico dell’elettricità e del gas naturale. Nel Capitolo 1 studiamo un problema di ottimizzazione dinamica di portafoglio per il trading di energia elettrica su mercati intraday. Nel Capitolo 2 introduciamo un framework trattabile e privo di arbitraggio basato sull’approccio di Heath-Jarrow-Morton per mercati a termine energetici multicommodity. Il Capitolo 3 si occupa di uno studio empirico approfondito di un modello a due fattori derivato dal framework del Capitolo 2, con un’applicazione al mercato a termine elettrico tedesco. Infine, nel Capitolo 4 discutiamo il prezzaggio di opzioni per modelli fattoriali additivi con metodi di trasformata di Fourier. Introduciamo un modello di prezzi futures a due fattori con salti al fine di catturare lo smile delle volatilità implicite di opzioni Europee sull’elettricità. Viene presentata un’applicazione al mercato European Energy Exchange Power Derivatives.
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ZHU, YI, and 朱易. "Implied Volatility Skew of ETF Option, Return and Volatility." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/b32auq.
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碩士逢甲大學
財務金融學系
107
This paper examines the relationship between the implied volatility skew of the China 50 ETF options and the returns and volatility of its underlying index ETF. We separately employ the methods of Yan (2010) and Mixon (2011) to abstract the implied volatility skew from the daily ETF option prices. Using the datasets of the China 50 ETF and ETF op-tions from February, 2015 to September, 2018, our empirical results show that the implied volatility skew contains the information concern-ing the future returns and volatility. Higher returns and volatility are fol-lowed by an increase in implied volatility skew. In addition, the predic-tive ability of implied volatility skew for the return and volatility is stronger when the ETF market is in a trend of downward prices.
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Chang, Ing-Jye, and 張英傑. "The Determinants of the Slope of implied Volatility Skew and Risk-Neutral Distribution Implied in Equity Options." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/eqhpw2.
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博士國立臺灣科技大學
企業管理系
95
The aim of this study is to investigate the structure and characteristics of the implied volatility smile, and the determinants of the slope of implied volatility skew, using prices of individual equity and FTSE 100 index options traded on LIFFE. Several interesting hypotheses were tested in fist issue and some important empirical results were obtained. First, the slope of implied volatility curve is significantly negative for both individual stocks and index options, and the slope is less negative for longer-term options. The implied volatility skew can be described by risk-neutral skewness and kurtosis with the former the first-order effect and the later second-order. Moreover, the implied volatility skew for individual stock options is less severe than that of the index options, and the idiosyncratic component dominates the market component in determining the individual stock risk-neutral skewness. Finally, the empirical estimation for the risk-aversion parameter is significantly positive and quite consistent across time-to-maturities, confirming the stable relationship between the real and the risk-neutral moments implied in option prices. The results indicate that for FTSE 100 index and stock options traded on LIFFE, the slope of implied volatility skew is flatter than that for S&P 100 index options and stock options traded on CBOE. In second issue we examine the firm-specific and market wide determinants of the slope of implied volatility skew. In the cross-sectional analysis the results indicate that the firm-specific variables such as leverage ratio, firm size, beta, and traded volume provide useful explain in the slope of smile. On average, the larger firms, and larger traded volume firms tend have more negative slope of the smile. There is no evidence that the slope of smile is related to put-to-call traded volume ratio. The relationships between the higher risk-neutral moments and volatility smile are consistent with the results of fist issue. In panel analysis the results indicate the consistent significantly negative coefficients for the variable leverage ratio, the more negative skewness of FTSE 100 index option the steeper of the slope of smile of individual stock options, and the greater kurtosis of FTSE 100 index option the flatter of the slope of smile of individual stock options. Additionally, we find the firm-specific variables provide more explanatory power than the market wide variables in determining the implied volatility skew.
Book chapters on the topic "Implied volatility skew"
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Alòs, Elisa, and Jorge A. León. "On the Short-Time Behaviour of the Implied Volatility Skew for Spread Options and Applications." In Trends in Mathematics, 97–99. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51753-7_16.
Full textConference papers on the topic "Implied volatility skew"
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Shaw, William T. "Instability of implied volatility, fictitious skews and smiles and the hazards of exotics: The importance of the inverse function theorem in mathematical finance." In Disordered and complex systems. AIP, 2001. http://dx.doi.org/10.1063/1.1358201.
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