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Author : Bhupinder Bahra
Publisher :
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.:/5 (246 download)
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:
Author : Chen Wang
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (129 download)
Download or read book Inversion of Option Prices for Implied Risk Neutral Probability Density Functions written by Chen Wang and published by . This book was released on 2014 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper applies classic linear inverse theory to the estimation of the implied risk neutral probability density function (PDF) from option prices. To overcome non-uniqueness and instability inherent in the option inverse problem, smoothness requirement for the shape of a PDF and an initial model are introduced by a penalty function. Positivity constraints are included as a hard bond on the PDF values. Then the option inverse problem becomes a non-negative least-squares problem which can be solved by the classic methods such as the non-negative least squares program of Lawson and Hanson (1974). The best solution is not the solution that gives best fit, but the solution that gives the optimal trade-off between the goodness of fit and smoothness of the estimated risk natural PDF. The proposed inversion technique is compared to the models of Black-Scholes (BS), a mixture of two lognormals (MLN), Jarrow and Rudd's Edgeworth expansion (JR), and jump diffusion (JD) for the estimation of the PDF from the option prices associated with the September 2007 NYMEX natural gas futures. It is found that the inversion technique not only gives best goodness of fit, but also the significantly better model resolution. BS, JD and MLN models basically cannot resolve the densities far away from the strikes where option prices are observed and can resolve long wavelength features of the densities inside the strikes where option prices are observed. On the other hand, the inversion model can resolve not only the significant details of the densities inside the strikes where option prices are observed, but also the long wavelength features of the densities away from the strikes where option prices are observed. The empirical study for the last three months of the September 2007 futures contract shows that the shapes of the estimated PDFs become more symmetric as the futures contract is closer to the expiration date. The dispersion of the estimated PDFs decreases with decreasing the time to expire, indicating the resolution of uncertainty with time.
Author : Martin Mandler
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (129 download)
Download or read book Comparing Risk-Neutral Probability Density Functions Implied by Option Prices - Market Uncertainty and Ecb-Council Meetings written by Martin Mandler and published by . This book was released on 2002 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years different techniques to uncover the information on market expectations implicit in option prices have been developed. This paper proposes an approach to highlight statistically significant changes in risk-neutral probability density functions by comparing the distributional characteristics of statistics derived from risk-neutral densities to those of a benchmark sample. In an application we extract risk-neutral probability density functions from LIFFE-Euribor futures options and look for characteristic differences in market expectations related to meetings of the Governing Council of the ECB.
Author : Mr.Kevin C. Cheng
Publisher : International Monetary Fund
ISBN 13 : 1455202150
Total Pages : 33 pages
Book Rating : 4.4/5 (552 download)
Download or read book A New Framework to Estimate the Risk-Neutral Probability Density Functions Embedded in Options Prices written by Mr.Kevin C. Cheng and published by International Monetary Fund. This book was released on 2010-08-01 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the widely-used double-lognormal approach by Bahra (1997), this paper presents a multi-lognormal approach with restrictions to extract risk-neutral probability density functions (RNPs) for various asset classes. The contributions are twofold: first, on the technical side, the paper proposes useful transformation/restrictions to Bahra’s original formulation for achieving economically sensible outcomes. In addition, the paper compares the statistical properties of the estimated RNPs among major asset classes, including commodities, the S&P 500, the dollar/euro exchange rate, and the US 10-year Treasury Note. Finally, a Monte Carlo study suggests that the multi-lognormal approach outperforms the double-lognormal approach.
Author : Bhupinder Bahra
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (535 download)
Download or read book Implied Risk-neutral Probability Functions from Option Prices written by Bhupinder Bahra and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rupert De Vincent-Humphreys
Publisher :
ISBN 13 :
Total Pages : 39 pages
Book Rating : 4.:/5 (89 download)
Download or read book Estimating Probability Distributions of Future Asset Prices written by Rupert De Vincent-Humphreys and published by . This book was released on 2012 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The prices of derivatives contracts can be used to estimate 'risk-neutral' probability density functions that give an indication of the weight investors place on different future prices of their underlying assets, were they risk-neutral. In the likely case that investors are risk-averse, this leads to differences between the risk-neutral probability density and the actual distribution of prices. But if this difference displays a systematic pattern over time, it may be exploited to transform the risk-neutral density into a 'real-world' density that better reflect agents' actual expectations. This work offers a methodology for performing this transformation. The resulting real-world densities may better represent market participants' views of future prices, and so offer an enhanced means of quantifying the uncertainty around financial variables. Comparison with their risk-neutral equivalents may also reveal new and useful information as to how attitudes towards risk are affecting pricing."--Abstract.
Author : Bhupinder Bahra
Publisher :
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.:/5 (848 download)
Download or read book Implied Risk-neutral Probality 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:
Author : James Huang
Publisher :
ISBN 13 :
Total Pages : 58 pages
Book Rating : 4.:/5 (129 download)
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.
Author : Martin Mandler
Publisher : Springer Science & Business Media
ISBN 13 : 3642574289
Total Pages : 227 pages
Book Rating : 4.6/5 (425 download)
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 . . . . . . .
Author : Jens Carsten Jackwerth
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (95 download)
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:
Author : Piotr Banbula
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (129 download)
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.
Author : Robert R. Bliss
Publisher :
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.3/5 ( download)
Download or read book Testing the Stability of Implied Probability Density Functions written by Robert R. Bliss and published by . This book was released on 2000 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James Huang
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (129 download)
Download or read book Are We Extracting the True Risk Neutral Density from Option Prices? A Question with No Easy Answer written by James Huang and published by . This book was released on 2009 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we raise a question on the theoretical foundation of option implied risk neutral density. We prove that given any number of options, there exist numerous risk neutral densities which are piecewise constant, have only two values, either an lower bound or an upper bound on the true risk neutral density, and price all these options correctly. We also prove that given any number of options, there exist numerous risk neutral densities consistent with the prices of all these options whose first derivatives are piecewise constant and have only two values, either an lower bound or an upper bound on the true risk neutral density's first derivative. Similar results are proved with respect to the true risk neutral density's higher order derivatives. These results show how large errors we can make when extracting RNDs from option prices.
Author : Áron Gereben
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.X/5 (4 download)
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:
Author : Allan M. Malz
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (382 download)
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 1997 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lawrence Edward Kochard
Publisher :
ISBN 13 :
Total Pages : 364 pages
Book Rating : 4.:/5 (441 download)
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:
Author : Jens Carsten Jackwerth
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (129 download)
Download or read book Option Implied Risk-Neutral Distributions and Implied Binomial Trees written by Jens Carsten Jackwerth and published by . This book was released on 2008 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this partial and selective literature review of option implied risk-neutral distributions and of implied binomial trees, we start by observing that in efficient markets, there is information contained in option prices, which might help us to design option pricing models. To this end, we review the numerous methods of recovering risk-neutral probability distributions from option prices at one particular time-to-expiration and their applications. Next, we extend our attention beyond one time-to-expiration to the construction of implied binomial trees, which model the stochastic process of the underlying asset. Finally, we describe extensions of implied binomial trees, which incorporate stochastic volatility, as well as other non-parametric methods.
