Download or read book Implied Volatility and Risk Preference from Option Prices written by Kenneth S. Bartunek and published by . This book was released on 1991 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Option Implied Risk Neutral Distributions and Risk Aversion written by Jens Carsten Jackwerth and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Risk Adjusted Option Implied Moments written by Felix Brinkmann and published by . This book was released on 2016 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: Option-implied moments, like implied volatility, contain useful information about an underlying asset's return distribution but are derived under the risk-neutral probability measure. This paper provides a direct way of converting risk-neutral moments into the corresponding physical moments, which are required for many applications. The main result is a representation of physical moments in terms of observed option prices and a representative investor's preferences. As an empirical application of this result, we provide implied estimates of the representative stock market investor's disappointment aversion using S&P 500 index option prices. We find that disappointment aversion has a procyclical pattern. It is high in times of high index levels and declines when the index falls. We confirm the view that investors with high risk aversion and disappointment aversion leave the stock market during times of turbulence and reenter it after a period of high returns.

Download or read book Options and the Volatility Risk Premium written by Jared Woodard and published by Pearson Education. This book was released on 2011-02-17 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master the new edge in options trades: the hidden volatility risk premium that exists in options for every major asset class. One of the most exciting areas of recent financial research has been the study of how the volatility implied by option prices relates to the volatility exhibited by their underlying assets. Here, I’ll explain the concept of the volatility risk premium, present evidence for its presence in options on every major asset class, and show how to estimate, predict, and trade on it....

Download or read book General Equilibrium Option Pricing Method Theoretical and Empirical Study written by Jian Chen and published by Springer. This book was released on 2018-04-10 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book mainly addresses the general equilibrium asset pricing method in two aspects: option pricing and variance risk premium. First, volatility smile and smirk is the famous puzzle in option pricing. Different from no arbitrage method, this book applies the general equilibrium approach in explaining the puzzle. In the presence of jump, investors impose more weights on the jump risk than the volatility risk, and as a result, investors require more jump risk premium which generates a pronounced volatility smirk. Second, based on the general equilibrium framework, this book proposes variance risk premium and empirically tests its predictive power for international stock market returns.

Download or read book What Goes Into Risk Neutral Volatility Empirical Estimates of Risk and Subjective Risk Preferences written by Stephen Figlewski and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Under Black-Scholes (BS) assumptions, empirical volatility and risk neutral volatility are given by a single parameter, which captures all aspects of risk. Inverting the model to extract implied volatility from an option's market price gives the market's forecast of future empirical volatility. But real world returns are not lognormal, volatility is stochastic, and arbitrage is limited, so option prices embed both the market's estimate of the empirical returns distribution and also investors' risk attitudes, including possibly distinct preferences over different volatility-related aspects of the returns process, such as tail risk. All of these influences are reflected in the risk neutral density (RND), which can be extracted from option prices without requiring restrictive assumptions from a pricing model.We compute daily RNDs for the S&P 500 index over 15 years and find that risk neutral volatility is strongly influenced both by investors' projections of future realized volatility and also by the risk neutralization process. Several significant variables are connected in different ways to realized volatility, such as the daily trading range and tail risk; others reflect risk attitudes, such as the level of investor confidence and the size of recent volatility forecast errors.

Download or read book Option Prices with Uncertain Fundamentals written by Alexander David and published by . This book was released on 1999 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Option Volatility Pricing Advanced Trading Strategies and Techniques written by Sheldon Natenberg and published by McGraw Hill Professional. This book was released on 1994-08 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a thorough discussion of volatility, the most important aspect of options trading. Shows how to identify mispriced options and to construct volatility and "delta neutral" spreads.

Download or read book Three Essays in Theoretical and Empirical Derivative Pricing written by Hamed Ghanbari and published by . This book was released on 2017 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first essay investigates the option-implied investor preferences by comparing equilibrium option pricing models under jump-diffusion to option bounds extracted from discrete-time stochastic dominance (SD). We show that the bounds converge to two prices that define an interval comparable to the observed option bid-ask spreads for S&P 500 index options. Further, the bounds' implied distributions exhibit tail risk comparable to that of the return data and thus shed light on the dark matter of the divergence between option-implied and underlying tail risks. Moreover, the bounds can better accommodate reasonable values of the ex-dividend expected excess return than the equilibrium models' prices. We examine the relative risk aversion coefficients compatible with the boundary distributions extracted from index return data. We find that the SD-restricted range of admissible RRA values is consistent with the macro-finance studies of the equity premium puzzle and with several anomalous results that have appeared in earlier option market studies.The second essay examines theoretically and empirically a two-factor stochastic volatility model. We adopt an affine two-factor stochastic volatility model, where aggregate market volatility is decomposed into two independent factors; a persistent factor and a transient factor. We introduce a pricing kernel that links the physical and risk neutral distributions, where investor's equity risk preference is distinguished from her variance risk preference. Using simultaneous data from the S&P 500 index and options markets, we find a consistent set of parameters that characterizes the index dynamics under physical and risk-neutral distributions. We show that the proposed decomposition of variance factors can be characterized by a different persistence and different sensitivity of the variance factors to the volatility shocks. We obtain negative prices for both variance factors, implying that investors are willing to pay for insurance against increases in volatility risk, even if those increases have little persistence. We also obtain negative correlations between shocks to the market returns and each volatility factor, where correlation is less significant in transient factor and therefore has a less significant effect on the index skewness. Our empirical results indicate that unlike stochastic volatility model, join restrictions do not lead to the poor performance of two-factor SV model, measured by Vega-weighted root mean squared errors.In the third essay, we develop a closed-form equity option valuation model where equity returns are related to market returns with two distinct systematic components; one of which captures transient variations in returns and the other one captures persistent variations in returns. Our proposed factor structure and closed-form option pricing equations yield separate expressions for the exposure of equity options to both volatility components and overall market returns. These expressions allow a portfolio manager to hedge her portfolio's exposure to the underlying risk factors. In cross-sectional analysis our model predicts that firms with higher transient beta have a steeper term structure of implied volatility and a steeper implied volatility moneyness slope. Our model also predicts that variances risk premiums have more significant effect on the equity option skew when the transient beta is higher. On the empirical front, for the firms listed on the Dow Jones index, our model provides a good fit to the observed equity option prices.

Download or read book Risk adjusted Information Content in Option Prices written by Durga Prasad Panda and published by . This book was released on 2010 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many measures to price an option. This dissertation investigates a risk-adjusted measure to price the option with an alternative numeraire that retains the expected return of the underlying in the pricing equation. This model is consistent with the Black-Scholes model when their assumptions are imposed and is consistent with the standard capital asset pricing model. Unlike many asset pricing models that rely on historical data, we provide a forward-looking approach for extracting the ex ante return distribution parameters of the underlying from option prices. Using this framework and observing the market prices of options, we jointly extract implied return and implied volatility of the underlying assets for different days-to-maturity using a grid search method of global optima. Our approach does not use a preference structure or information about the market such as the market risk premium to estimate the expected return of the underlying asset. We find that when there are not many near-the-money traded options available our approach provides a better solution to forecast future volatility than the Black-Scholes implied volatility. Further, our results show that option prices reflect a higher expectation of stock return in the short-term, but a lower expectation of stock return in the long-term that is robust to many alternative tests. We further find that ex ante expected returns have a positive and significant cross-sectional relation with ex ante betas even in the presence of firm size, book-to-market, and momentum. The cross-sectional regression estimate of ex ante market risk premium has a statistical significance as well as an economic significance in that it contains significant forward-looking information on future macroeconomic conditions. Furthermore, in an ex ante world, firm size is still negatively significant, but book-to-market is also negatively significant, which is the opposite of the ex post results. Our risk-adjusted approach provides a framework for extraction of ex ante information from option prices with alternative assumptions of stochastic processes. In this vein, we provide a risk-adjusted stochastic volatility pricing model and discuss its estimation process.

Download or read book The volatility Smile of Canadian Index Options written by Dahai Sang and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Options Pricing and Hedging in a Regime Switching Volatility Model written by Melissa Anne Mielkie and published by . This book was released on 2014 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both deterministic and stochastic volatility models have been used to price and hedge options. Observation of real market data suggests that volatility, while stochastic, is well modelled as alternating between two states. Under this two-state regime-switching framework, we derive coupled pricing partial differential equations (PDEs) with the inclusion of a state-dependent market price of volatility risk (MPVR) term. Since there is no closed-form solution for this pricing problem, we apply and compare two approaches to solving the coupled PDEs, assuming constant Poisson intensities. First we solve the problem using numerical solution techniques, through the application of the Crank- Nicolson numerical scheme. We also obtain approximate solutions in terms of known Black- Scholes formulae by reformulating our problem and applying the Cauchy-Kowalevski PDE theorem. Both our pricing equations and our approximate solutions give way to the analysis of the impact of our state-dependent MPVR on theoretical option prices. Using financially intuitive constraints on our option prices and Deltas, we prove the necessity of a negative MPVR. An exploration of the regime-switching option prices and their implied volatilities is given, as well as numerical results and intuition supporting our mathematical proofs. Given our regime-switching framework, there are several different hedging strategies to investigate. We consider using an option to hedge against a potential regime shift. Some practical problems arise with this approach, which lead us to set up portfolios containing a basket of two hedging options. To be more precise, we consider the effects of an option going too far in- and out-of-the-money on our hedging strategy, and introduce limits on the magnitude of such hedging option positions. A complementary approach, where constant volatility is assumed and investor's risk preferences are taken into account, is also analysed. Analysis of empirical data supports the hypothesis that volatility levels are a effected by upcoming financial events. Finally, we present an extension of our regime-switching framework with deterministic Poisson intensities. In particular, we investigate the impact of time and stock varying Poisson intensities on option prices and their corresponding implied volatilities, using numerical solution techniques. A discussion of some event-driven hedging strategies is given.

Download or read book Risk Aversion Fanning Preference and Volatility Smirk on S P500 Index Options written by Jian Chen and published by . This book was released on 2016 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes a novel way of pricing S&P500 index options in the presence of jump risk. Our analysis is built upon an equilibrium option pricing rule for a representative agent economy. In particular, we use the weighted utility's certainty equivalent to specify agent's risk preference, which displays a fanning out characteristic. We find that the fanning effect captures a remarkably large portion of the total market risk premium implicit in options. As a result, the model with fanning effect generates pronounced volatility smirks.

Download or read book Option Volatility Pricing Advanced Trading Strategies and Techniques written by Sheldon Natenberg and published by McGraw Hill Professional. This book was released on 1994-08-22 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most widely read books among active option traders around the world, Option Volatility & Pricing has been completely updated to reflect the most current developments and trends in option products and trading strategies. Featuring: Pricing models Volatility considerations Basic and advanced trading strategies Risk management techniques And more! Written in a clear, easy-to-understand fashion, Option Volatility & Pricing points out the key concepts essential to successful trading. Drawing on his experience as a professional trader, author Sheldon Natenberg examines both the theory and reality of option trading. He presents the foundations of option theory explaining how this theory can be used to identify and exploit trading opportunities. Option Volatility & Pricing teaches you to use a wide variety of trading strategies and shows you how to select the strategy that best fits your view of market conditions and individual risk tolerance. New sections include: Expanded coverage of stock option Strategies for stock index futures and options A broader, more in-depth discussion volatility Analysis of volatility skews Intermarket spreading with options

Download or read book Preference free Option Pricing with Path dependent Volatility written by Steven L. Heston and published by . This book was released on 1998 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: