Probability distribution of returns in the Heston model with stochastic volatility*

Drăgulescu, Adrian; Yakovenko, Victor M.

doi:10.1088/1469-7688/2/6/303

Cited by 207 publications

(193 citation statements)

References 29 publications

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“…T. L. E. thanks V. Yakovenko for pointing out the similarities of the Heston model to the TWD of vicinals and for several helpful seminal discussions of the FPE derivation in Ref. [21] and H. van Beijeren and N. van Kampen for enlightening discussions about FPE analysis. We also thank M. E. Fisher and E. D. Williams for helpful comments on the manuscript.…”

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confidence: 99%

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Evolution of Terrace-Width Distributions on Vicinal Surfaces: Fokker-Planck Derivation of the Generalized Wigner Surmise

2005

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We use a Fokker-Planck equation to justify the generalization of the Wigner surmise for the energy-level spacing in quantum systems to the simple expression for the equilibrium terrace-width distribution of steps--with arbitrary-strength repulsions--on a vicinal surface, taking advantage of analogies to one-dimensional models of interacting, spinless fermions. This approach leads to an analytic description of the evolution toward equilibrium of steps from several experimentally relevant initial distributions: step bunches, perfect cleaved crystals, and prequench equilibrated distributions at different temperatures.

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confidence: 99%

“…for v in what in quantitative finance is called the Heston model [21]; the equivalent of Eq. (8) describes the evolution of the distribution function for the stochastic variance v in a second stochastic equation for stock returns.…”

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confidence: 99%

Evolution of Terrace-Width Distributions on Vicinal Surfaces: Fokker-Planck Derivation of the Generalized Wigner Surmise

2005

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“…Este modelo extiende el modelo BSM al suponer que la volatilidad del precio del subyacente es conducida por un proceso de difusión, además de incluir una correlación arbitraria entre la volatilidad y los rendimientos del subyacente. A partir de la función de densidad marginal obtenida por Dragulescu y Yakovenko (2002), y con parámetros dados, se analizó dicha densidad. Se concluye que el parámetro de correlación modela el sesgo de la densidad.…”

Section: Conclusionesunclassified

Valuación de opciones europeas sobre AMX-L, WALMEX-V y GMEXICO-B. Calibración de parámetros de volatilidad estocástica con funciones cuadráticas de pérdida

2014

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Esta investigación propone una metodología para estimar los parámetros del modelo de volatilidad estocástica de Heston (1993) por medio de funciones cuadráticas de pérdida, las cuales minimizan el error entre precios de mercado y precios teóricos. Para ello se plantean tres clases de funciones de pérdida, de las cuales dos están asociadas a precios y otra a volatilidades implícitas. La metodología propuesta se aplica a un conjunto de precios de opciones sobre AMX-L, WALMEX-V y GMEXICO-B. Los resultados indican que para opciones de compra sobre AMX-L se generan volatilidades implícitas consistentes con las observadas con base en el criterio de la raíz de la pérdida del error cuadrático medio, mientras que para opciones de compra sobre WALMEX-V y GMEXICO-B se generan volatilidades implícitas consistentes con las observadas con base en el criterio de la raíz de la pérdida relativa del error cuadrático medio

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“…It was reported that probability distributions of the normalized returns can be well described by the so-called double-exponential law (also known as the Laplace distribution), P (r τ ) ∼ exp (−|r τ |/κ), where κ is a constant [22,23]. The double-exponential distribution of return at not-too-long times t is a universal, ubiquitous feature of financial time series, and was observed for different countries, stock-market indices and individual stocks [23].…”

Section: Time Series Of Returnsmentioning

confidence: 99%

Phase distribution and phase correlation of financial time series

Huang

et al. 2006

Phys. Rev. E

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The scaling, phase distribution, and phase correlation of financial time series are investigated based on the Dow Jones Industry Average and NASDAQ 10-min intraday data for a period from 1 Aug. 1997 to 31 Dec. 2003. The returns of the two indices are shown to have nice scaling behaviors and belong to stable distributions according to the criterion of Lévy's alpha stable distribution condition. An approach catching characteristic features of financial time series based on the concept of instantaneous phase is further proposed to study the phase distribution and correlation. Analysis of the phase distribution concludes that return time series fall into a class which is different from other nonstationary time series. The correlation between returns of the two indices probed by the distribution of phase difference indicates that there was a remarkable change of trading activities after the event of the 9/11 attack, and this change persisted in later trading activities.

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Probability distribution of returns in the Heston model with stochastic volatility*

Cited by 207 publications

References 29 publications

Evolution of Terrace-Width Distributions on Vicinal Surfaces: Fokker-Planck Derivation of the Generalized Wigner Surmise

Evolution of Terrace-Width Distributions on Vicinal Surfaces: Fokker-Planck Derivation of the Generalized Wigner Surmise

Valuación de opciones europeas sobre AMX-L, WALMEX-V y GMEXICO-B. Calibración de parámetros de volatilidad estocástica con funciones cuadráticas de pérdida

Phase distribution and phase correlation of financial time series

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