Option pricing under deformed Gaussian distributions

Moretto, Enrico; Pasquali, Sara; Trivellato, Barbara

doi:10.1016/j.physa.2015.11.026

Cited by 13 publications

(9 citation statements)

References 20 publications

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“…Of special interest are papers fitting several distributions to the same data, with an eye on relative performance. From comparative studies such as [17], who considered the distribution of household income in Italy for the years 1989 to 2006, it emerges that model (31) typically outperforms its three-parameter competitors such as the Singh-Maddala [73] and Dagum type I [74] distributions, apart from the GB2 which has an extra parameter. 7 The model was also fitted by [18] to data from other household budget surveys, namely Germany 1984-2007, Great Britain 1991-2004, and the United States 1980-2005 In a remarkable number of cases, the distribution of household income follows the κ-generalized more closely than the Singh-Maddala and Dagum type I.…”

Section: Applications Of κ-Generalized Models To Income and Wealth Datamentioning

confidence: 99%

“…Clearly this distribution function had to be motivated by solid and indisputable first principles. In the early 2000s a new proposal was advanced which immediately attracted the attention of many researchers [22][23][24][25][26][27][28][29][30][31]. The new proposed distribution is given by…”

Section: The κ-Exponential Function and Its Relativistic Originmentioning

confidence: 99%

“…It has a fast left tail convergence to zero, and therefore it has finite moments of all orders. The other continuous distribution, specified as the κ-generalized model (31), accounts for the positive values of net wealth and presents a heavy right tail, thus having a small number of finite moments of positive order. This different behavior at the two tails of the distribution stems form the fact that, unlike the right tail of income and (gross or net) wealth distributions-which tend slowly to zero when income and wealth tend to infinity-the distribution of the negative values (left tail) of net wealth tends very fast to zero when the variable tends to minus infinity, since economic units face a short-term challenge of either moving out of the negative range of net wealth or bankruptcy.…”

Section: The κ-Generalized Mixture Model For the Size Distribution Of...mentioning

confidence: 99%

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κ-generalized models of income and wealth distributions: A survey

Clementi

Gallegati

Kaniadakis

et al. 2016

Eur. Phys. J. Spec. Top.

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The paper provides a survey of results related to the "κ-generalized distribution", a statistical model for the size distribution of income and wealth. Topics include, among others, discussion of basic analytical properties, interrelations with other statistical distributions as well as aspects that are of special interest in the income distribution field, such as the Gini index and the Lorenz curve. An extension of the basic model that is most able to accommodate the special features of wealth data is also reviewed. The survey of empirical applications given in this paper shows the κ-generalized models of income and wealth to be in excellent agreement with the observed data in many cases.

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Section: Applications Of κ-Generalized Models To Income and Wealth Datamentioning

confidence: 99%

Section: The κ-Exponential Function and Its Relativistic Originmentioning

confidence: 99%

Section: The κ-Generalized Mixture Model For the Size Distribution Of...mentioning

confidence: 99%

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κ-generalized models of income and wealth distributions: A survey

Clementi

Gallegati

Kaniadakis

et al. 2016

Eur. Phys. J. Spec. Top.

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“…In the last five years, there are still many researchers contributing to the theory of option pricing. Moretto et al [9] study option pricing under deformed Gaussian distributions. Leippold and Scharer [10] develop a stochastic liquidity model, and they investigate discrete-time option pricing with stochastic liquidity.…”

Section: Introductionmentioning

confidence: 99%

European Option Pricing Formula in Risk-Aversive Markets

Wu¹,

Wang²

2021

Mathematical Problems in Engineering

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In this study, using the method of discounting the terminal expectation value into its initial value, the pricing formulas for European options are obtained under the assumptions that the financial market is risk-aversive, the risk measure is standard deviation, and the price process of underlying asset follows a geometric Brownian motion. In particular, assuming the option writer does not need the risk compensation in a risk-neutral market, then the obtained results are degenerated into the famous Black–Scholes model (1973); furthermore, the obtained results need much weaker conditions than those of the Black–Scholes model. As a by-product, the obtained results show that the value of European option depends on the drift coefficient μ of its underlying asset, which does not display in the Black–Scholes model only because μ = r in a risk-neutral market according to the no-arbitrage opportunity principle. At last, empirical analyses on Shanghai 50 ETF options and S&P 500 options show that the fitting effect of obtained pricing formulas is superior to that of the Black–Scholes model.

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“…The analytic and geometric features of deformed exponentials suggest that they are well suited to model non-normally distributed returns of contingent claims. In this direction, for instance, a non-Gaussian option pricing theory has been successfully proposed in terms of diffusion processes associated to q -Gaussian distributions [ 4 , 7 , 16 , 17 , 18 ]. Other related developments are summarized in [ 6 , 19 ].…”

Section: Introductionmentioning

confidence: 99%

Principal Curves for Statistical Divergences and an Application to Finance

Rodrigues

Cavalcante

2018

Entropy

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This paper proposes a method for the beta pricing model under the consideration of non-Gaussian returns by means of a generalization of the mean-variance model and the use of principal curves to define a divergence model for the optimization of the pricing model. We rely on the q-exponential model so consider the properties of the divergences which are used to describe the statistical model and fully characterize the behavior of the assets. We derive the minimum divergence portfolio, which generalizes the Markowitz's (mean-divergence) approach and relying on the information geometrical aspects of the distributions the Capital Asset Pricing Model (CAPM) is then derived under the geometrical characterization of the distributions which model the data, all by the consideration of principal curves approach. We discuss the possibility of integration of our model into an adaptive procedure that can be used for the search of optimum points on finance applications.

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Option pricing under deformed Gaussian distributions

Cited by 13 publications

References 20 publications

κ-generalized models of income and wealth distributions: A survey

κ-generalized models of income and wealth distributions: A survey

European Option Pricing Formula in Risk-Aversive Markets

Principal Curves for Statistical Divergences and an Application to Finance

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