Download or read book Modeling and Estimating Volatility of Options on Standard Poor s 500 Index written by Boleslaw Borkowski and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper explores the impact of volatility estimation methods on theoretical option values based upon the Black-Scholes-Merton (BSM) model. Volatility is the only input used in the BSM model that cannot be observed in the market or a priori determined in a contract. Thus, properly calculating volatility is crucial. Two approaches to estimate volatility are implied volatility and historical prices. Iterative techniques are applied, based on daily S&P index options. Additionally, using option data on S&P 500 Index listed on the Chicago Board of Options Exchange, historical volatility can be estimated.

Download or read book A Test of Efficiency for the S P 500 Index Option Market Using Variance Forecasts written by Jaesun Noh and published by . This book was released on 1993 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: To forecast future option prices, autoregressive models of implied volatility derived from observed option prices are commonly employed [see Day and Lewis (1990), and Harvey and Whaley (1992)]. In contrast, the ARCH model proposed by Engle (1982) models the dynamic behavior in volatility, forecasting future volatility using only the return series of an asset. We assess the performance of these two volatility prediction models from S&P 500 index options market data over the period from September 1986 to December 1991 by employing two agents who trade straddles, each using one of the two different methods of forecast. Straddle trading is employed since a straddle does not need to be hedged. Each agent prices options according to her chosen method of forecast, buying (selling) straddles when her forecast price for tomorrow is higher (lower) than today's market closing price, and at the end of each day the rates of return are computed. We find that the agent using the GARCH forecast method earns greater profit than the agent who uses the implied volatility regression (IVR) forecast model. In particular, the agent using the GARCH forecast method earns a profit in excess of a cost of $0.25 per straddle with the near-the-money straddle trading.

Download or read book Can Standard Preferences Explain the Prices of Out of the Money S P 500 Put Options written by Luca Benzoni and published by . This book was released on 2005 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prior to the stock market crash of 1987, Black-Scholes implied volatilities of S & P 500 index options were relatively constant across moneyness. Since the crash, however, deep out-of-the-money S & P 500 put options have become 'expensive' relative to the Black-Scholes benchmark. Many researchers (e.g., Liu, Pan and Wang (2005)) have argued that such prices cannot be justified in a general equilibrium setting if the representative agent has 'standard preferences' and the endowment is an i.i.d. process. Below, however, we use the insight of Bansal and Yaron (2004) to demonstrate that the 'volatility smirk' can be rationalized if the agent is endowed with Epstein-Zin preferences and if the aggregate dividend and consumption processes are driven by a persistent stochastic growth variable that can jump. We identify a realistic calibration of the model that simultaneously matches the empirical properties of dividends, the equity premium, the prices of both at-the-money and deep out-of-the-money puts, and the level of the risk-free rate. A more challenging question (that to our knowledge has not been previously investigated) is whether one can explain within a standard preference framework the stark regime change in the volatility smirk that has maintained since the 1987 market crash. To this end, we extend the model to a Bayesian setting in which the agent updates her beliefs about the average jump size in the event of a jump. Note that such beliefs only update at crash dates, and hence can explain why the volatility smirk has not diminished over the last eighteen years. We find that the model can capture the shape of the implied volatility curve both pre- and post-crash while maintaining reasonable estimates for expected returns, price-dividend ratios, and risk-free rates.

Download or read book The Information Content of Implied Volatilities and Model Free Volatility Expectations written by Stephen J. Taylor and published by . This book was released on 2008 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volatility information content of stock options for individual firms is measured using option prices for 149 U.S. firms during the period from January 1996 to December 1999. Volatility forecasts defined by historical stock returns, at-the-money (ATM) implied volatilities and model-free (MF) volatility expectations are compared for each firm. The recently developed model-free volatility expectation incorporates information across all strike prices, and it does not require the specification of an option pricing model.Our analysis of ARCH models shows that, for one-day-ahead estimation, historical estimates of conditional variances outperform both the ATM and the MF volatility estimates extracted from option prices for more than one-third of the firms. This result contrasts with the consensus about the informational efficiency of options written on stock indices; several recent studies find that option prices are more informative than daily stock returns when estimating and predicting index volatility. However, for the firms with the most actively traded options, we do find that the option forecasts are nearly always more informative than historical stock returns. When the prediction horizon extends until the expiry date of the options, our regression results show that the option forecasts are more informative than forecasts defined by historical returns for a substantial majority (86%) of the firms. Although the model-free (MF) volatility expectation is theoretically more appealing than alternative volatility estimates and has been demonstrated to be the most accurate predictor of realized volatility by Jiang and Tian (2005) for the Samp;P 500 index, the results for our firms show that the MF expectation only outperforms both the ATM implied volatility and the historical volatility for about one-third of the firms. The firms for which the MF expectation is best are not associated with a relatively high level of trading in away-from-the-money options.

Download or read book Predictable Dynamics in the S P 500 Index Options Implied Volatility Surface written by Sílvia Gonçalves and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of fitting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time. In this paper, we study whether the resulting predictability patterns in the IVS coefficients may be exploited in practice. We propose a two-stage approach to modeling and forecasting the Samp;P 500 index options IVS. In the first stage, we model the surface along the cross-sectional moneyness and time-to-maturity dimensions, similarly to Dumas, et. al., (1998). In the second-stage, we model the dynamics of the cross-sectional first-stage implied volatility surface coefficients by means of vector autoregression models. We find that not only the Samp;P 500 implied volatility surface can be successfully modeled, but also that its movements over time are highly predictable in a statistical sense. We then examine the economic significance of this statistical predictability with mixed findings. Whereas profitable delta-hedged positions can be set up that exploit the dynamics captured by the model under moderate transaction costs and when trading rules are selective in terms of expected gains from the trades, most of this profitability disappears when we increase the level of transaction costs and trade multiple contracts off wide segments of the IVS. This suggests that predictability of the time-varying Samp;P 500 implied volatility surface may be not inconsistent with market efficiency.

Download or read book Models for S P 500 Dynamics written by Peter Christoffersen and published by . This book was released on 2009 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the resulting biases. We investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on Samp;P 500 returns. Finally, we employ nonlinear least squares on a panel of option data. In comparison with earlier studies that explicitly solve the filtering problem, we analyze a more comprehensive option data set. The scope of our analysis is feasible because of our use of the particle filter. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of the alternative volatility specifications is a model with linear rather than square root diffusion for variance which we refer to as the VAR model. This model captures the stylized facts in realized volatilities, it performs well in fitting various samples of index returns, and it has the lowest option implied volatility mean squared errors in- and out-of-sample.

Download or read book Volatility Surface and Term Structure written by Kin Keung Lai and published by Routledge. This book was released on 2013-09-11 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides different financial models based on options to predict underlying asset price and design the risk hedging strategies. Authors of the book have made theoretical innovation to these models to enable the models to be applicable to real market. The book also introduces risk management and hedging strategies based on different criterions. These strategies provide practical guide for real option trading. This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market. This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.

Download or read book Forecasting Volatility and Option Prices of the S P 500 Index written by Jaesun Noh and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Pricing and Hedging Index Options Under Stochastic Volatility written by Saikat Nandi and published by . This book was released on 1996 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Jump and Volatility Risk and Risk Premia written by Pedro Santa-Clara and published by . This book was released on 2004 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: We use a novel pricing model to filter times series of diffusive volatility and jump intensity from S&P 500 index options. These two measures capture the ex-ante risk assessed by investors. We find that both components of risk vary substantially over time, are quite persistent, and correlate with each other and with the stock index. Using a simple general equilibrium model with a representative investor, we translate the filtered measures of ex-ante risk into an ex-ante risk premium. We find that the average premium that compensates the investor for the risks implicit in option prices, 10.1 percent, is about twice the premium required to compensate the same investor for the realized volatility, 5.8 percent. Moreover, the ex-ante equity premium that we uncover is highly volatile, with values between 2 and 32 percent. The component of the premium that corresponds to the jump risk varies between 0 and 12 percent.

Download or read book Proceedings of the 2nd International Conference Quantitative and Qualitative Methodologies in the Economic and Administrative Sciences written by Christos Frangos and published by Christos Frangos. This book was released on 2009 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Essays in Volatility Modeling and Option Pricing written by Mathieu Fournier and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Evaluating Volatility Forecasts in Option Pricing in the Context of a Simulated Options Market written by Evdokia Xekalaki and published by . This book was released on 2005 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: The performance of an ARCH model selection algorithm based on the standardized prediction error criterion (SPEC) is evaluated. The evaluation of the algorithm is performed by comparing different volatility forecasts in option pricing through the simulation of an options market. Traders employing the SPEC model selection algorithm use the model with the lowest sum of squared standardized one-step-ahead prediction errors for obtaining their volatility forecast. The cumulative profits of the participants in pricing one-day index straddle options always using variance forecasts obtained by GARCH, EGARCH and TARCH models are compared to those made by the participants using variance forecasts obtained by models suggested by the SPEC algorithm. The straddles are priced on the Standard and Poor 500 (Samp;P500) index. It is concluded that traders, who base their selection of an ARCH model on the SPEC algorithm, achieve higher profits than those, who use only a single ARCH model. Moreover, the SPEC algorithm is compared with other criteria of model selection that measure the ability of the ARCH models to forecast the realized intra-day volatility. In this case too, the SPEC algorithm users achieve the highest returns. Thus, the SPEC model selection method appears to be a useful tool in selecting the appropriate model for estimating future volatility in pricing derivatives.

Download or read book Inside Volatility Filtering written by Alireza Javaheri and published by John Wiley & Sons. This book was released on 2015-08-24 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new, more accurate take on the classical approach to volatility evaluation Inside Volatility Filtering presents a new approach to volatility estimation, using financial econometrics based on a more accurate estimation of the hidden state. Based on the idea of "filtering", this book lays out a two-step framework involving a Chapman-Kolmogorov prior distribution followed by Bayesian posterior distribution to develop a robust estimation based on all available information. This new second edition includes guidance toward basing estimations on historic option prices instead of stocks, as well as Wiener Chaos Expansions and other spectral approaches. The author's statistical trading strategy has been expanded with more in-depth discussion, and the companion website offers new topical insight, additional models, and extra charts that delve into the profitability of applied model calibration. You'll find a more precise approach to the classical time series and financial econometrics evaluation, with expert advice on turning data into profit. Financial markets do not always behave according to a normal bell curve. Skewness creates uncertainty and surprises, and tarnishes trading performance, but it's not going away. This book shows traders how to work with skewness: how to predict it, estimate its impact, and determine whether the data is presenting a warning to stay away or an opportunity for profit. Base volatility estimations on more accurate data Integrate past observation with Bayesian probability Exploit posterior distribution of the hidden state for optimal estimation Boost trade profitability by utilizing "skewness" opportunities Wall Street is constantly searching for volatility assessment methods that will make their models more accurate, but precise handling of skewness is the key to true accuracy. Inside Volatility Filtering shows you a better way to approach non-normal distributions for more accurate volatility estimation.

Download or read book Mathematical and Statistical Methods for Actuarial Sciences and Finance written by Marco Corazza and published by Springer Nature. This book was released on with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Option Pricing Models and Volatility Using Excel VBA written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2012-06-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive guide offers traders, quants, and students the tools and techniques for using advanced models for pricing options. The accompanying website includes data files, such as options prices, stock prices, or index prices, as well as all of the codes needed to use the option and volatility models described in the book. Praise for Option Pricing Models & Volatility Using Excel-VBA "Excel is already a great pedagogical tool for teaching option valuation and risk management. But the VBA routines in this book elevate Excel to an industrial-strength financial engineering toolbox. I have no doubt that it will become hugely successful as a reference for option traders and risk managers." —Peter Christoffersen, Associate Professor of Finance, Desautels Faculty of Management, McGill University "This book is filled with methodology and techniques on how to implement option pricing and volatility models in VBA. The book takes an in-depth look into how to implement the Heston and Heston and Nandi models and includes an entire chapter on parameter estimation, but this is just the tip of the iceberg. Everyone interested in derivatives should have this book in their personal library." —Espen Gaarder Haug, option trader, philosopher, and author of Derivatives Models on Models "I am impressed. This is an important book because it is the first book to cover the modern generation of option models, including stochastic volatility and GARCH." —Steven L. Heston, Assistant Professor of Finance, R.H. Smith School of Business, University of Maryland

Download or read book The Roles of Short Run and Long Run Volatility Factors in Options Market written by Yang-Ho Park and published by . This book was released on 2015 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines the option pricing implications of short-run and long-run volatility factors, which are assumed to be driven by short-run and long-run news events, respectively. Using a comprehensive dataset of S&P 500 index options over 1993-2008, I find that the proposed two-factor volatility models have two desirable properties that help capture the term structures of option-implied volatility and skewness. First, the options data show evidence of time-variation in the long-run expectation of volatility, which may be caused by long-run news events. While this feature is inconsistent with a single-factor volatility assumption, the two-factor volatility models do a good job of matching the entire term structure of implied volatility. Second, the options data reveal that the term structure of implied skewness is nearly flat on average. This feature is hard to reconcile with single-factor volatility models and jumps in returns. In contrast, I find that the two-factor volatility models can generate flat term structures much like those seen in the data. In particular, the short-run volatility factor is dominant in generating short-term skewness, while the long-run volatility factor plays a pivotal role in generating long-term skewness.