Download or read book Are Classical Option Pricing Models Consistent with Observed Option Second Order Moments Evidence from High Frequency Data written by Francesco Audrino and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: As a means of validating an option pricing model, we compare the ex-post intra-day realized variance of options with the realized variance of the associated underlying asset that would be implied using assumptions as in the Black and Scholes (BS) model, the Heston and the Bates model. Based on data for the S&P 500 index, we find that the BS model is strongly directionally biased due to the presence of stochastic volatility. The Heston model reduces the mismatch in realized variance between the two markets, but deviations are still significant. With the exception of short-dated options, we achieve best approximations after controlling for the presence of jumps in the underlying dynamics. Finally, we provide evidence that, although heavily biased, the realized variance based on the BS model contains relevant predictive information that can be exploited when option high-frequency data is not available.

Download or read book A General Theory of Option Pricing written by David Gershon and published by . This book was released on 2019 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a new formalism for option pricing that does not require an assumption on the stochastic process of the underlying asset price and yet produces remarkably accurate results versus the market. The new formalism applies for general Markovian stochastic behavior including continuous and discontinuous (jump) processes and in its broadest scheme contains all known models for Markovian option pricing and some new ones. The method is based on obtaining the risk neutral density function that satisfies a consistency condition, guaranteeing no arbitrage. For example, we show that when the underlying asset undergoes a continuous stochastic process with deterministic time dependent standard deviation the formalism produces the Black-Scholes-Merton formula without using a Wiener process. We show that in the general case the price of European options depends only on all the moments of the price return of the underlying asset. We offer a method to calculate the prices of European options when the volatility smile at maturity is independent of the term structure prior to the maturity, as observed in options markets. In the continuous case where only moments up to second order contribute to the price then any set of three option prices with the same maturity contains the information to determine the whole volatility smile for this maturity. In all the many examples we examined our method generates option prices that match the option markets prices very accurately in all asset classes. This confirms that the options market exhibits no-arbitrage. Moreover, using bootstrapping we demonstrate how to determine the conditional density function from inception to maturity, thus allowing the calculation of path dependent options. The new formalism also allows for the replication of 'W-shape' volatility smile that infrequently appears in some equity markets.

Download or read book A Time Series Approach to Option Pricing written by Christophe Chorro and published by Springer. This book was released on 2014-12-04 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current world financial scene indicates at an intertwined and interdependent relationship between financial market activity and economic health. This book explains how the economic messages delivered by the dynamic evolution of financial asset returns are strongly related to option prices. The Black Scholes framework is introduced and by underlining its shortcomings, an alternative approach is presented that has emerged over the past ten years of academic research, an approach that is much more grounded on a realistic statistical analysis of data rather than on ad hoc tractable continuous time option pricing models. The reader then learns what it takes to understand and implement these option pricing models based on time series analysis in a self-contained way. The discussion covers modeling choices available to the quantitative analyst, as well as the tools to decide upon a particular model based on the historical datasets of financial returns. The reader is then guided into numerical deduction of option prices from these models and illustrations with real examples are used to reflect the accuracy of the approach using datasets of options on equity indices.

Download or read book Option Pricing Using Realized Volatility written by Lars Stentoft and published by . This book was released on 2008 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present paper we suggest to model Realized Volatility, an estimate of daily volatility based on high frequency data, as an Inverse Gaussian distributed variable with time varying mean, and we examine the joint properties of Realized Volatility and asset returns. We derive the appropriate dynamics to be used for option pricing purposes in this framework, and we show that our model explains some of the mispricings found when using traditional option pricing models based on interdaily data. We then show explicitly that a Generalized autoregressive Conditional Heteroskedastic model with Normal Inverse Gaussian distributed innovations is the corresponding benchmark model when only daily data is used. Finally, we perform an empirical analysis using stock options for three large American companies, and we show that in all cases our model performs significantly better than the corresponding benchmark model estimated on return data alone. Hence the paper provides evidence on the value of using high frequency data for option pricing purposes.

Download or read book Co jumps in Options Evidence from High frequency Data written by Maximilian Lunzer and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The following thesis analyzes jumps in high-frequency data of the S\&P500 index and options written on the index. With the non-parametric jump test of Lee and Mykland both assets are investigated separately without imposing any option pricing model. In a second step jump patterns of different frequencies and option types are analyzed. This includes the point of time when jumps and co-jumps occur. I found that jumps tend to happen in the morning and as frequency is decreased co-jumps are detected more often. This is due to the fact that only extreme returns are classified as jumps for longer observation times and it is more likely to find them in option prices too. Furthermore I analyzed the jump behavior after the release of the FOMC announcements on the federal reserve fund target rate and the construction spending release. I found that both types of news induce jumps at the time of the release. For the FOMC releases a higher jump activity in the following 30 minute period was detected. Macroeconomic news can induce co-jumps for all types of options considered in this study. Finally, I tested if the option sensitivities computed with the Bates model can explain the empirical jump patterns of the S\&P500 together with the call options. I found that based on a delta-approximation there should be more co-jumps as there are in reality.

Download or read book A Markup Approach to Option Pricing written by Dao Xiong Teng and published by . This book was released on 2010 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the heart of the classical Black-Scholes option pricing model lies the no arbitrage pricing principal with the assumption of a complete market which renders options as redundant assets. It is widely accepted that the market prices of options are generally inconsistent with the pricing model. In the existing literature, most papers have attributed the inconsistencies to the unrealistic assumptions of the classical Black-Scholes model. This paper proposes that even if option prices do follow the Black-Scholes model perfectly, we should not expect the market prices to coincide with prices calculated from the model. We propose two simple alternative approaches to the model on market prices of options, keeping most of the major assumptions under the classical model. We also examine their efficacies in estimating future volatilities and their efficacies in providing a perfect hedge to a long position in various options. Empirical results show some evidence that supports the alternative approaches. Results also show that for certain classifications of options, the alternative models provide a better delta-neutral portfolio.

Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.

Download or read book Introduction to Option Pricing Theory written by Gopinath Kallianpur and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the appearance of seminal works by R. Merton, and F. Black and M. Scholes, stochastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This work examines, in some detail, that part of stochastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of stochastic finance that are relevant to the theory, omitting such topics as futures and term-structure. This self-contained work begins with five introductory chapters on stochastic analysis, making it accessible to readers with little or no prior knowledge of stochastic processes or stochastic analysis. These chapters cover the essentials of Ito's theory of stochastic integration, integration with respect to semimartingales, Girsanov's Theorem, and a brief introduction to stochastic differential equations. Subsequent chapters treat more specialized topics, including option pricing in discrete time, continuous time trading, arbitrage, complete markets, European options (Black and Scholes Theory), American options, Russian options, discrete approximations, and asset pricing with stochastic volatility. In several chapters, new results are presented. A unique feature of the book is its emphasis on arbitrage, in particular, the relationship between arbitrage and equivalent martingale measures (EMM), and the derivation of necessary and sufficient conditions for no arbitrage (NA). {\it Introduction to Option Pricing Theory} is intended for students and researchers in statistics, applied mathematics, business, or economics, who have a background in measure theory and have completed probability theory at the intermediate level. The work lends itself to self-study, as well as to a one-semester course at the graduate level.

Download or read book Black Scholes and Beyond Option Pricing Models written by Neil Chriss and published by McGraw-Hill. This book was released on 1997 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: An unprecedented book on option pricing! For the first time, the basics on modern option pricing are explained ``from scratch'' using only minimal mathematics. Market practitioners and students alike will learn how and why the Black-Scholes equation works, and what other new methods have been developed that build on the success of Black-Shcoles. The Cox-Ross-Rubinstein binomial trees are discussed, as well as two recent theories of option pricing: the Derman-Kani theory on implied volatility trees and Mark Rubinstein's implied binomial trees. Black-Scholes and Beyond will not only help the reader gain a solid understanding of the Balck-Scholes formula, but will also bring the reader up to date by detailing current theoretical developments from Wall Street. Furthermore, the author expands upon existing research and adds his own new approaches to modern option pricing theory. Among the topics covered in Black-Scholes and Beyond: detailed discussions of pricing and hedging options; volatility smiles and how to price options ``in the presence of the smile''; complete explanation on pricing barrier options.

Download or read book Empirical Studies of Alternative Option Pricing Models written by Constant Eduard Beckers and published by . This book was released on 1979 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Option Pricing with Maximum Entropy Densities written by Omid M. Ardakani and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entropy pricing applies notions of information theory to derive the theoretical value of options. This paper employs the maximum entropy formulation of option pricing, given risk-neutral moment constraints computed directly from the observed prices. First, higher-order moments are used to generate option prices. Then a generalization of Shannon entropy, known as Renyi entropy, is studied to account for extreme events. This maximum entropy problem provides a class of heavy-tailed distributions. Examples and Monte Carlo simulations are provided to examine the effects of moment constraints on option prices. The call option values are then constructed using daily S&P 500 index options. The findings suggest that entropy pricing with higher-order moment constraints provides higher forecasting accuracy.

Download or read book Option Pricing written by Menachem Brenner and published by Free Press. This book was released on 1983 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Building a Consistent Pricing Model from Observed Option Prices written by Jean-Paul Laurent and published by . This book was released on 1998 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility Models written by Bertram Düring and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth order accurate in space and second order accurate in time. Under some restrictions, theoretical results like unconditional stability in the sense of von Neumann are presented. Where the analysis becomes too involved we validate our findings by a numerical study. Numerical experiments for the European option pricing problem are presented. We observe fourth order convergence for non-smooth payoff.

Download or read book Option Pricing in Incomplete Markets written by Yoshio Miyahara and published by World Scientific. This book was released on 2012 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers the reader practical methods to compute the option prices in the incomplete asset markets. The [GLP & MEMM] pricing models are clearly introduced, and the properties of these models are discussed in great detail. It is shown that the geometric L(r)vy process (GLP) is a typical example of the incomplete market, and that the MEMM (minimal entropy martingale measure) is an extremely powerful pricing measure. This volume also presents the calibration procedure of the [GLP \& MEMM] model that has been widely used in the application of practical problem

Download or read book Option Data Missing Tails and the Intraday Variation of Implied Moments written by Anselm Ivanovas and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The risk-neutral distribution of returns, implied by S & P 500 option prices, has been a popular topic of research for many years. Because of its forward-looking nature, it gives valuable insights into the expectation and risk attitude of investors. The moments of this distribution condense important characteristics of these expectations into just a few key figures. This thesis provides an approach to not only compute the first four moments (or more specifically the mean, standard deviation, skewness and kurtosis) under realistic data situations, but to observe how the moments (and therefore investor's expectations) evolve over time. It covers three parts. An analysis of the data, an analysis of a correction method if insufficient data is available, and finally the application of computing moment time series from high-frequency option data.

Download or read book Vinzenz Bronzin s Option Pricing Models written by Wolfgang Hafner and published by Springer. This book was released on 2009-07-13 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1908, Vinzenz Bronzin, a professor of mathematics at the Accademia di Commercio e Nautica in Trieste, published a booklet in German entitled Theorie der Prämiengeschäfte (Theory of Premium Contracts) which is an old type of option contract. Almost like Bachelier’s now famous dissertation (1900), the work seems to have been forgotten shortly after it was published. However, almost every element of modern option pricing can be found in Bronzin’s book. He derives option prices for an illustrative set of distributions, including the Normal. - This volume includes a reprint of the original German text, a translation, as well as an appreciation of Bronzin's work from various perspectives (economics, history of finance, sociology, economic history) including some details about the professional life and circumstances of the author. The book brings Bronzin's early work to light again and adds an almost forgotten piece of research to the theory of option pricing.