[PDF] Option Pricing With Maximum Entropy Densities eBook

Author : Omid M. Ardakani
Publisher :
Page : 0 pages
File Size : 40,19 MB
Release : 2022
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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.

Author : Weiyu Guo
Publisher :
Page : 258 pages
File Size : 39,10 MB
Release : 1999
Category : Options (Finance)
ISBN :

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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.

Author : Cassio Neri
Publisher :
Page : 27 pages
File Size : 33,53 MB
Release : 2014
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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.

Author : Peter W. Buchen
Publisher :
Page : pages
File Size : 43,47 MB
Release : 2000
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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.

Author : Yoshio Miyahara
Publisher : World Scientific
Page : 200 pages
File Size : 35,60 MB
Release : 2012
Category : Electronic books
ISBN : 1848163487

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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 L(r)vy 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 problem

Author : Carsten Wehn
Publisher : Academic Press
Page : 657 pages
File Size : 49,69 MB
Release : 2012-12-17
Category : Business & Economics
ISBN : 0124158889

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It is widely acknowledged that many financial modelling techniques failed during the financial crisis, and in our post-crisis environment many techniques are being reconsidered. This single volume provides a guide to lessons learned for practitioners and a reference for academics. Including reviews of traditional approaches, real examples, and case studies, contributors consider portfolio theory; methods for valuing equities and equity derivatives, interest rate derivatives, and hybrid products; and techniques for calculating risks and implementing investment strategies. Describing new approaches without losing sight of their classical antecedents, this collection of original articles presents a timely perspective on our post-crisis paradigm. Highlights pre-crisis best classical practices, identifies post-crisis key issues, and examines emerging approaches to solving those issues Singles out key factors one must consider when valuing or calculating risks in the post-crisis environment Presents material in a homogenous, practical, clear, and not overly technical manner

Author : Cassio Neri
Publisher :
Page : 23 pages
File Size : 22,25 MB
Release : 2014
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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.