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Option Pricing And Higher Order Moments Of The Risk Neutral Probability Density Function
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Book Synopsis Option Pricing and Higher Order Moments of the Risk-neutral Probability Density Function by : Lawrence Edward Kochard
Download or read book Option Pricing and Higher Order Moments of the Risk-neutral Probability Density Function written by Lawrence Edward Kochard and published by . This book was released on 1999 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Risk Neutral Probabilities and Option Bounds by : James Huang
Download or read book Risk Neutral Probabilities and Option Bounds written by James Huang and published by . This book was released on 2005 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we first present a geometric approach to option bounds. We show that if two risk neutral probability density functions intersect for certain number of times, then comparing the fatness of their tails we can tell which of them gives higher option prices. Thus we can derive option bounds by identifying the risk neutral probability density function which intersects all admissible ones for certain number of times. Applying this approach we tighten the first order stochastic dominance option bounds when the maximum value of the risk neutral density is known. The method present in this paper has wide applications in option pricing problems.
Book Synopsis Option-Implied Risk-Neutral Distributions and Risk Aversion by : Jens Carsten Jackwerth
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:
Book Synopsis Option-Implied Probability Distributions and Currency Excess Returns by : Allan M. Malz
Download or read book Option-Implied Probability Distributions and Currency Excess Returns written by Allan M. Malz and published by . This book was released on 2006 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper describes a method of extracting the risk-neutral probability distribution of future exchange rates from option prices. In foreign exchange markets interbank option pricing conventions make possible reliable inferences about risk-neutral probability distributions with relatively little data. Moments drawn from risk-neutral exchange rate distribution are used to explore several issues related to the puzzle of excess returns in currency markets. Tests of the international capital asset pricing model using risk-neutral moments as explanatory variables indicate that option-based moments have considerably greater explanatory power for excess returns in currency markets than has been found in earlier work. Tests of several hypotheses generated by the peso problem approach indicate that jump risk measured by the risk-neutral coefficient of skewness can explain only a small part of the forward bias. These tests take into account not only the second, but the third and fourth moments of the exchange rate implied by option prices, and avoid testing a joint hypothesis including a distributional assumption.
Book Synopsis Market Expectations and Option Prices by : Martin Mandler
Download or read book Market Expectations and Option Prices written by Martin Mandler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a slightly revised version of my doctoral dissertation which has been accepted by the Department of Economics and Business Administration of the Justus-Liebig-Universitat Giessen in July 2002. I am indebted to my advisor Prof. Dr. Volbert Alexander for encouraging and supporting my research. I am also grateful to the second member of the doctoral committee, Prof. Dr. Horst Rinne. Special thanks go to Dr. Ralf Ahrens for providing part of the data and to my colleague Carsten Lang, who spent much time reading the complete first draft. Wetzlar, January 2003 Martin Mandler Contents 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part I Theoretical Foundations 2 Arbitrage Pricing and Risk-Neutral Probabilities........ .. 7 2.1 Arbitrage Pricing in the Black/Scholes-Merton Model... . . .. . 7 2.2 The Equivalent Martingale Measure and Risk-Neutral Valuation ............................................... 11 2.3 Extracting Risk-Neutral Probabilities from Option Prices. . . .. 13 2.4 Summary............................................... 15 Appendix 2A: The Valuation Function in the Black/Scholes-Merton Model .................................................. 16 Appendix 2B: Some Further Details on the Replication Strategy ... 21 3 Survey of the Related Literature .......................... 23 3.1 The Information Content of Forward and Futures Prices. . . .. . 24 3.2 The Information Content of Implied Volatilities ............. 25 3.2.1 Implied Volatilities and the Risk-Neutral Probability Density .......................................... 27 3.2.2 The Term Structure of Implied Volatilities. . . . . . . .. . . 29 . 3.2.3 The Forecasting Information in Implied Volatilities. . .. 30 3.2.4 Implied Correlations as Forecasts of Future Correlations 43 VIII Contents 3.3 The Skewness Premium ..... . . . . . . . . . . . . . . . . . . .. . . 45 . . . . . . .
Book Synopsis Implied Risk-neutral Probability Density Functions from Option Prices by : Bhupinder Bahra
Download or read book Implied Risk-neutral Probability Density Functions from Option Prices written by Bhupinder Bahra and published by . This book was released on 1997 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Prices, Exchange Market Intervention, and the Higher Moment Expectations Channel by : Gabriele Galati
Download or read book Option Prices, Exchange Market Intervention, and the Higher Moment Expectations Channel written by Gabriele Galati and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A vast literature on the effects of sterilized intervention by the monetary authorities in the foreign exchange markets concludes that intervention systematically moves the spot exchange rate only if it is publicly announced, coordinated across countries, and consistent with the underlying stance of fiscal and monetary policy. Over the past fifteen years, researchers have also attempted to determine if intervention has any effects on the dispersion and directionality of market views concerning the future exchange rate. These studies usually focus on the variance around the expected future exchange rate - the second moment. In this paper we demonstrate how to use over-the-counter option prices to recover the risk-neutral probability density function (PDF) for the future exchange rate. Using the yen/dollar exchange rate as an example, we calculate measures of dispersion and directionality, such as variance and skewness, from estimated PDFs to test whether intervention by the Japanese Ministry of Finance had any impact on the higher moments of the exchange rate. We find little or no systematic effect, consistent with the findings of the literature on the spot rate as Japanese intervention during the period 1996-2004 was not publicly announced, rarely coordinated across countries and, in hindsight, probably inconsistent with the underlying stance of monetary policy.
Book Synopsis Option Pricing with Maximum Entropy Densities by : Omid M. Ardakani
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.
Book Synopsis Extracting Market Expectations from Options Prices by : Áron Gereben
Download or read book Extracting Market Expectations from Options Prices written by Áron Gereben and published by . This book was released on 2002 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pricing Derivative Securities by : T. W. Epps
Download or read book Pricing Derivative Securities written by T. W. Epps and published by World Scientific. This book was released on 2007 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents techniques for valuing derivative securities at a level suitable for practitioners, students in doctoral programs in economics and finance, and those in masters-level programs in financial mathematics and computational finance. It provides the necessary mathematical tools from analysis, probability theory, the theory of stochastic processes, and stochastic calculus, making extensive use of examples. It also covers pricing theory, with emphasis on martingale methods. The chapters are organized around the assumptions made about the dynamics of underlying price processes. Readers begin with simple, discrete-time models that require little mathematical sophistication, proceed to the basic Black-Scholes theory, and then advance to continuous-time models with multiple risk sources. The second edition takes account of the major developments in the field since 2000. New topics include the use of simulation to price American-style derivatives, a new one-step approach to pricing options by inverting characteristic functions, and models that allow jumps in volatility and Markov-driven changes in regime. The new chapter on interest-rate derivatives includes extensive coverage of the LIBOR market model and an introduction to the modeling of credit risk. As a supplement to the text, the book contains an accompanying CD-ROM with user-friendly FORTRAN, C++, and VBA program components.
Book Synopsis Mathematical Properties of Option Pricing Under Gamma Distribution Process by : Andrey Bogomolov
Download or read book Mathematical Properties of Option Pricing Under Gamma Distribution Process written by Andrey Bogomolov and published by . This book was released on 2014 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: A problem of risk neutral probability density function estimation for prices of risky assets is discussed when the asset pricing model uses exponential random process with independent increments. The structure of increments consists of two components: systematic drift and a random gamma distributed component. To determine the risk neutral probability density Escher transform is used. Obtained results help to define a formula for European call option pricing. Also we compare the found risk neutral density with the density, when the random component is defined by a Wiener process, driven by gamma process.
Book Synopsis Extracting Risk-neutral Probability Distributions from Option Prices Using Trading Volume as a Filter by : Dominique Y. Dupont
Download or read book Extracting Risk-neutral Probability Distributions from Option Prices Using Trading Volume as a Filter written by Dominique Y. Dupont and published by . This book was released on 2001 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Options and Market Expectations by : Piotr Banbula
Download or read book Options and Market Expectations written by Piotr Banbula and published by . This book was released on 2008 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of methods used for estimation of option-implied risk-neutral probability density functions (PDFs) is presented in the study, and one of such methods, double lognormal approach, is used for the analysis of the information content of the EUR/PLN currency options on the Polish market. Estimated PDFs have proven to provide superior information concerning future volatility than historical volatility, yet their forecasting power is comparable to that of the Black-Scholes model. There are no strong grounds for using PDFs as a predictor of the future EUR/PLN exchange rate. Low informative content does not directly follow, as PDFs can be used as an indicator of markets conditions. The issues that could be addressed more thoroughly in the future studies concern the assumption of risk neutrality and the impact of the estimation method on the higher moments of the distribution.
Book Synopsis Extracting Risk-Neutral Density and Its Moments from American Option Prices by : Yisong S. Tian
Download or read book Extracting Risk-Neutral Density and Its Moments from American Option Prices written by Yisong S. Tian and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been a surge in the use of option-implied moments (e.g., volatility, skewness and kurtosis) in various empirical applications such as volatility forecasting, variance risk premium, empirical asset pricing, and portfolio selection. One potential obstacle in such applications is the requirement of European option prices in the estimation of these moments. In this paper, we develop a simple, accurate method for extracting risk-neutral density and its moments from American option prices. A key advantage of our approach is that a single implied binomial tree is constructed to fit all American option prices, utilizing the full information set in the entire options market. Since American options are more commonly traded than European options, our methodology expands the scope of research on option-implied density and moments to a much wider class of underlying assets (e.g., equity and futures options).
Book Synopsis Recovering the Probability Density Function of Asset Prices Using GARCH as Diffusion Approximations by : Fabio Fornari
Download or read book Recovering the Probability Density Function of Asset Prices Using GARCH as Diffusion Approximations written by Fabio Fornari and published by . This book was released on 2001 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multi-Moment Approximate Option Pricing Models by : Emmanuel Jurczenko
Download or read book Multi-Moment Approximate Option Pricing Models written by Emmanuel Jurczenko and published by . This book was released on 2002 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: After the seminal paper of Jarrow and Rudd (1982), several authors have proposed to use different statistical series expansion to price options when the risk-neutral density is asymmetric and leptokurtic. Amongst them, one can distinguish the Gram-Charlier Type A series expansion (Corrado and Su, 1996-b and 1997-b), log-normal Gram-Charlier series expansion (Jarrow and Rudd, 1982) and Edgeworth series expansion (Rubinstein, 1998). The purpose of this paper is to compare these different multi-moment approximate option pricing models. We first recall the link between risk-neutral densities and moments in a general statistical series expansion framework. We then derive analytical formulae for these different four-moment approximate option pricing models, namely, the Jarrow and Rudd (1982), Corrado and Su (1996-b and 1997-b) and Rubinstein (1998) models. We investigate in particular the conditions that ensure the respect of the martingale restriction (see Longstaff, 1995) and compare with option pricing models such as Black and Scholes (1973) and Hermite polynomial models (see Madan and Milne, 1994, Abken et al.,1996). We also get for these approximate option pricing models analytical expressions of implied probability distribution, implied volatility smile functions and several hedging parameters of interest, such as the Psi and the Chi that measure respectively the changes in the option price with respect to the changes in kurtosis and skewness.
Book Synopsis Risk-Adjusted Option-Implied Moments by : Felix Brinkmann
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.
