Option Pricing in Fractional Brownian Markets
Option Pricing in Fractional Brownian Markets

Author: Stefan Rostek

Publisher: Springer Science & Business Media

Published: 2009-04-28

Total Pages: 146

ISBN-13: 3642003311

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Mandelbrot and van Ness (1968) suggested fractional Brownian motion as a parsimonious model for the dynamics of ?nancial price data, which allows for dependence between returns over time. Starting with Rogers(1997) there is an ongoing dispute on the proper usage of fractional Brownian motion in option pricing theory. Problems arise because fractional Brownian motion is not a semimartingale and therefore “no arbitrage pricing” cannot be applied. While this is consensus, the consequences are not as clear. The orthodox interpretation is simply that fractional Brownian motion is an inadequate candidate for a price process. However, as shown by Cheridito (2003) any theoretical arbitrage opportunities disappear by assuming that market p- ticipants cannot react instantaneously. This is the point of departure of Rostek’s dissertation. He contributes to this research in several respects: (i) He delivers a thorough introduction to fr- tional integration calculus and uses the binomial approximation of fractional Brownianmotion to give the reader a ?rst idea of this special market setting.

Option Pricing in a Fractional Brownian Motion Environment
Option Pricing in a Fractional Brownian Motion Environment

Author: Ciprian Necula

Publisher:

Published: 2008

Total Pages: 19

ISBN-13:

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In this paper it is developed a framework for evaluating derivatives if the underlying of the derivative contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. For this purpose we first prove some results regarding the quasi-conditional expectation, especially the behavior to a Girsanov transform. We obtain the risk-neutral valuation formula, the fundamental evaluation equation of a contingent claim, and the formula for the price of a European call option in the case of the fractional Black-Scholes market.

Option Pricing in Fractional Brownian Markets
Option Pricing in Fractional Brownian Markets

Author: Stefan Rostek

Publisher: Springer

Published: 2009-05-04

Total Pages: 137

ISBN-13: 9783642003301

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Mandelbrot and van Ness (1968) suggested fractional Brownian motion as a parsimonious model for the dynamics of ?nancial price data, which allows for dependence between returns over time. Starting with Rogers(1997) there is an ongoing dispute on the proper usage of fractional Brownian motion in option pricing theory. Problems arise because fractional Brownian motion is not a semimartingale and therefore “no arbitrage pricing” cannot be applied. While this is consensus, the consequences are not as clear. The orthodox interpretation is simply that fractional Brownian motion is an inadequate candidate for a price process. However, as shown by Cheridito (2003) any theoretical arbitrage opportunities disappear by assuming that market p- ticipants cannot react instantaneously. This is the point of departure of Rostek’s dissertation. He contributes to this research in several respects: (i) He delivers a thorough introduction to fr- tional integration calculus and uses the binomial approximation of fractional Brownianmotion to give the reader a ?rst idea of this special market setting.

Stochastic Dominance Option Pricing
Stochastic Dominance Option Pricing

Author: Stylianos Perrakis

Publisher: Springer

Published: 2019-05-03

Total Pages: 277

ISBN-13: 3030115909

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This book illustrates the application of the economic concept of stochastic dominance to option markets and presents an alternative option pricing paradigm to the prevailing no arbitrage simultaneous equilibrium in the frictionless underlying and option markets. This new methodology was developed primarily by the author, working independently or jointly with other co-authors, over the course of more than thirty years. Among others, it yields the fundamental Black-Scholes-Merton option value when markets are complete, presents a new approach to the pricing of rare event risk, and uncovers option mispricing that leads to tradeable strategies in the presence of transaction costs. In the latter case it shows how a utility-maximizing investor trading in the market and a riskless bond, subject to proportional transaction costs, can increase his/her expected utility by overlaying a zero-net-cost portfolio of options bought at their ask price and written at their bid price, irrespective of the specific form of the utility function. The book contains a unified presentation of these methods and results, making it a highly readable supplement for educators and sophisticated professionals working in the popular field of option pricing. It also features a foreword by George Constantinides, the Leo Melamed Professor of Finance at the Booth School of Business, University of Chicago, USA, who was a co-author in several parts of the book.

Option Pricing Bounds with Standard Risk Aversion Preferences
Option Pricing Bounds with Standard Risk Aversion Preferences

Author: A. Basso

Publisher:

Published: 2018

Total Pages: 17

ISBN-13:

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For a theoretical valuation of a financial option, various models have been proposed that require specific hypotheses regarding both the stochastic process driving the price behaviour of the underlying security and market efficiency. When some of these assumptions are removed, we obtain an uncertainty interval for the option price. Up to now, the most restrictive intervals for option prices have been obtained using the DARA rule in a state preference approach.Precautionary saving entails the concept of prudence; in particular, decreasing absolute prudence is a necessary and sufficient condition that guarantees that the saving of wealthier people is less sensitive to the risk associated to future incomes. If this condition is coupled with the decreasing absolute risk aversion assumption we obtain standard risk aversion, which guarantees on the one hand that introducing a zero-mean background risk to wealth makes people less willing to accept another independent risk and on the other hand that an increase in the risk of the returns distribution of an asset reduces the demand for this asset.The main idea of this contribution is to apply decreasing absolute prudence and standard risk aversion rules in a state preference context in order to obtain efficient bounds for the value of European-style options portfolio strategies.Lower and upper bounds for the options portfolio value are obtained by solving non linear optimization problems. The numerical experiments carried out show the efficiency of the technique proposed.