Are Classical Option Pricing Models Consistent with Observed Option Second-Order Moments? Evidence from High-Frequency Data PDF Download
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Author: Francesco Audrino
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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.
Author: Francesco Audrino
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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.
Author: David Gershon
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
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.
Author: Christophe Chorro
Publisher: Springer
ISBN: 3662450372
Category : Business & Economics
Languages : en
Pages : 202
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Book Description
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.
Author: Lars Stentoft
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Book Description
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.
Author: Maximilian Lunzer
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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.
Author: Dao Xiong Teng
Publisher:
ISBN:
Category : Options (Finance)
Languages : en
Pages : 49
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Book Description
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.
Author: Lishang Jiang
Publisher: World Scientific
ISBN: 9812563695
Category : Science
Languages : en
Pages : 344
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Book Description
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.
Author: Gopinath Kallianpur
Publisher: Springer Science & Business Media
ISBN: 1461205115
Category : Mathematics
Languages : en
Pages : 266
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Book Description
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.
Author: Neil Chriss
Publisher: McGraw-Hill
ISBN:
Category : Business & Economics
Languages : en
Pages : 512
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Book Description
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.
Author: Constant Eduard Beckers
Publisher:
ISBN:
Category : Stocks
Languages : en
Pages : 264
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Book Description
