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A Family Of Maximum Entropy Densities Matching Call Option Prices
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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 American-Type Options by : Dmitrii S. Silvestrov
Download or read book American-Type Options written by Dmitrii S. Silvestrov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-12-17 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematical presentation of stochastic approximation methods for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The volume presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
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 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 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 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 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 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 Calculation of Maximum Entropy Densities with Application to Income Distribtuions by : Ximing Wu
Download or read book Calculation of Maximum Entropy Densities with Application to Income Distribtuions written by Ximing Wu and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper shows that there exits a unique maximum entropy density for any finite sample when arithmetic sample moments are used as side conditions. A sequential updating method to calculate the maxent entropy density subject to known moment constraints is proposed. Instead of imposing the moment constraints simultaneously, the sequential updating method incorporates the moment constraints into the calculation from lower to higher moments and updates the density estimates sequentially. The proposed method is employed to approximate the size distribution of U.S. family income. Numerical experiments and empirical evidence demonstrate the efficiency of this method.
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 An Efficient Algorithm to Compute Maximum Entropy Densities by : Dirk Ormoneit
Download or read book An Efficient Algorithm to Compute Maximum Entropy Densities written by Dirk Ormoneit and published by . This book was released on 1997 with total page 4 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 The Unimodal Maximum Entropy Density by : Patrick Brockett
Download or read book The Unimodal Maximum Entropy Density written by Patrick Brockett and published by . This book was released on 1982 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Entropy Densities by : Michael Rockinger
Download or read book Entropy Densities written by Michael Rockinger and published by . This book was released on 2000 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
