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Option Pricing With Maximum Entropy Densities
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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 Implementing the Principle of Maximum Entropy in Option Pricing by : Weiyu Guo
Download or read book Implementing the Principle of Maximum Entropy in Option Pricing written by Weiyu Guo and published by . This book was released on 1999 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Black-Scholes option pricing model has been the foundation of option pricing analysis. Yet as well known as the model itself, its empirical deficiencies are also well documented. Option prices generated by the Black-Scholes formula are often found to systematically differ from observed prices. The patterns of mispricing are generally believed to result from violations of one or more assumptions underlying the Black-Scholes option pricing model, such as the natural logarithm of the underlying stock price following a normal distribution with a variance that increases exactly linearly with time. This dissertation concerns an evaluation of the Principle of Maximum Entropy as a method for recovering a probability density function from stock index option prices. Theoretically, the resulting probability density is "the least prejudiced estimate since it is maximally noncommittal with respect to missing or unknown information." Empirically, this dissertation demonstrates that entropy valuation gives much stronger performance than does the Black-Scholes model in pricing stock index options on the S & P 500 and on the Dow Jones Industrial Average.
Book Synopsis Maximum Entropy Option Pricing by : Yuehong Yang
Download or read book Maximum Entropy Option Pricing written by Yuehong Yang and published by . This book was released on 1997 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Family of Maximum Entropy Densities Matching Call Option Prices by : Cassio Neri
Download or read book A Family of Maximum Entropy Densities Matching Call Option Prices written by Cassio Neri and published by . This book was released on 2014 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate the position of the Buchen-Kelly density in the family of entropy maximising densities from Neri & Schneider (2012) which all match European call option prices for a given maturity observed in the market. Using the Legendre transform which links the entropy function and the cumulant generating function, we show that it is both the unique continuous density in this family and the one with the greatest entropy. We present a fast root-finding algorithm that can be used to calculate the Buchen-Kelly density, and give upper boundaries for three different discrepancies that can be used as convergence criteria. Given the call prices, arbitrage-free digital prices at the same strikes can only move within upper and lower boundaries given by left and right call spreads. As the number of call prices increases, these bounds become tighter, and we give two examples where the densities converge to the Buchen-Kelly density in the sense of relative entropy when we use centered call spreads as proxies for digital prices. As pointed out by Breeden and Litzenberger, in the limit a continuous set of call prices completely determines the density.
Book Synopsis The Maximum Entropy Distribution of an Asset Inferred from Option Prices by : Peter W. Buchen
Download or read book The Maximum Entropy Distribution of an Asset Inferred from Option Prices written by Peter W. Buchen and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper describes the application of the Principle of Maximum Entropy to the estimation of the distribution of an underlying asset from a set of option prices. The resulting distribution is least committal with respect to unknown or missing information and is hence the least prejudiced. The maximum entropy distribution is the only information about the asset that can be inferred from the price data alone. An extension to the Principle of Minimum Cross-Entropy allows the inclusion of prior knowledge of the asset distribution. We show that the maximum entropy distribution is able to accurately fit a known density, given simulated option prices at different strikes.
Book Synopsis Maximum Entropy and Its Application to Option Pricing by : Matthew Bryce Hardman
Download or read book Maximum Entropy and Its Application to Option Pricing written by Matthew Bryce Hardman and published by . This book was released on 2000 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing in Incomplete Markets by : Yoshio Miyahara
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 Lvy 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 problems.
Book Synopsis Probability Distributions of Assets Inferred from Option Prices Via the Principle of Maximum Entropy by : Jonathan Borwein
Download or read book Probability Distributions of Assets Inferred from Option Prices Via the Principle of Maximum Entropy written by Jonathan Borwein and published by . This book was released on 2002 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Maximum Entropy Regularization for a Specific Inverse Problem of Option Pricing by : Bernd Hofmann
Download or read book On Maximum Entropy Regularization for a Specific Inverse Problem of Option Pricing written by Bernd Hofmann and published by . This book was released on 2003 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Maximum Entropy Distributions Inferred from Option Portfolios on an Asset by : Cassio Neri
Download or read book Maximum Entropy Distributions Inferred from Option Portfolios on an Asset written by Cassio Neri and published by . This book was released on 2014 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: We obtain the maximum entropy distribution for an asset from call and digital option prices. A rigorous mathematical proof of its existence and exponential form is given, which can also be applied to legitimise a formal derivation by Buchen and Kelly (JFQA 31:143-159, 1996). We give a simple and robust algorithm for our method and compare our results to theirs. We present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options. Finally, we apply our approach to options on the S&P 500 index.
Book Synopsis The Option-Ipod. the Probability of Default Implied by Option Prices Basedon Entropy by : Christian Capuano
Download or read book The Option-Ipod. the Probability of Default Implied by Option Prices Basedon Entropy written by Christian Capuano and published by International Monetary Fund. This book was released on 2008-08-01 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a framework to derive the probability of default implied by the price of equity options. The framework does not require any strong statistical assumption, and provide results that are informative on the expected developments of balance sheet variables, such as assets, equity and leverage, and on the Greek letters (delta, gamma and vega). We show how to extend the framework by using information from the price of a zero-coupon bond and CDS-spreads. In the episode of the collapse of Bear Stearns, option-iPoD was able to early signal market sentiment.
Book Synopsis Estimation of the Asset Price Distribution Using the Maximum Entropy Principle by : Geon Ho Choe
Download or read book Estimation of the Asset Price Distribution Using the Maximum Entropy Principle written by Geon Ho Choe and published by . This book was released on 2008 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Option price contains information on the distribution of the underlying asset. Under insufficient condition we employ the maximum entropy principle to estimate the probability density of the asset price. The problem is equivalent to finding the Lagrange multipliers of a linear functional defined by entropy and payoff functions. Buchen and Kelly proved that the maximum entropy distribution recovered from observed option prices is quite similar with the original asset distribution. In this article we apply a similar method to recover the probability density function of an asset from given option prices for binary options and European options.
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 Using Maximum Entropy to Price Arithmetic Mean Options by : M. Hardman
Download or read book Using Maximum Entropy to Price Arithmetic Mean Options written by M. Hardman and published by . This book was released on 1996 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Hyperbolic Model: Option Pricing Using Approximation and Quasi-Monte Carlo Methods by : Martin Predota
Download or read book The Hyperbolic Model: Option Pricing Using Approximation and Quasi-Monte Carlo Methods written by Martin Predota and published by GRIN Verlag. This book was released on 2009-04 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doctoral Thesis / Dissertation from the year 2002 in the subject Mathematics - Stochastics, grade: 1, Technical University of Graz, language: English, abstract: Aus Sicht der Mathematik spielen Optionen eine wesentliche Rolle seit der bahnbrechenden Arbeit von Black und Scholes im Jahre 1973. Deren Modell basiert jedoch auf der unrealistischen Annahme, das log-returns von Aktienkursen normalverteilt sind. Eberlein und Keller haben 1995 gezeigt, daß solche log-returns hyperbolisch verteilt sind. Die vorliegende Arbeit baut auf dieser Annahme auf und erweitert das Optionsspektrum von Europäischen Optionen auf Asiatische, Amerikanische sowie Multi-Asset-Optionen. Weiters wird das "Standard"-Martingal-Maß, die sogenannte Esscher-Transformation, durch das Entropie-minimierende Maß erweitert. Da jedoch keine exakte Preissetzung solcher Optionen möglich ist, wird auf numerische Simulationen und Approximationen zurückgegriffen. Die verwendeten numerischen Verfahren sind die Monte Carlo-Methode mit verschiedenen Varianzreduktionstechniken und die Quasi-Monte Carlo Methode.
Book Synopsis The Impact of the Prior Density on a Minimum Relative Entropy Density by : Cassio Neri
Download or read book The Impact of the Prior Density on a Minimum Relative Entropy Density written by Cassio Neri and published by . This book was released on 2014 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the problem of finding probability densities that match given European call option prices. To allow prior information about such a density to be taken into account, we generalise the algorithm presented in Neri & Schneider (Applied Mathematical Finance, 2013) to find the maximum entropy density of an asset price to the relative entropy case. This is applied to study the impact the choice of prior density has in two market scenarios. In the first scenario, call option prices are prescribed at only a small number of strikes, and we see that the choice of prior, or indeed its omission, yields notably different densities. The second scenario is given by CBOE option price data for S&P 500 index options at a large number of strikes. Prior information is now considered to be given by calibrated Heston, Schöbel-Zhu or Variance Gamma models. We find that the resulting digital option prices are essentially the same as those given by the (non-relative) Buchen-Kelly density itself. In other words, in a sufficiently liquid market the influence of the prior density seems to vanish almost completely. Finally, we study variance swaps and derive a simple formula relating the fair variance swap rate to entropy. Then we show, again, that the prior loses its influence on the fair variance swap rate as the number of strikes increases.
Book Synopsis Option Prices Under Bayesian Learning by : Massimo Guidolin
Download or read book Option Prices Under Bayesian Learning written by Massimo Guidolin and published by . This book was released on 2001 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:
