Mixed Fractional Brownian Motion

Cheridito, Patrick

doi:10.2307/3318626

Cited by 306 publications

(253 citation statements)

References 12 publications

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“…For example, to modelize the discounted stock price, the fractional version of the Samuelson model [23] was studied by Cutland et al [6]. But, since it had also some deficiencies, Cheridito [5] introduced some mixed fractional Gaussian processes. The FMFBMFBS could be used to modelize the diffusion of atmospheric pollutants, either accidental (nuclear, chemical) or not (air pollution).…”

Section: )mentioning

confidence: 99%

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The fractional mixed fractional brownian motion and fractional brownian sheet

El-Nouty

2007

ESAIM: PS

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Abstract.We introduce the fractional mixed fractional Brownian motion and fractional Brownian sheet, and investigate the small ball behavior of its sup-norm statistic. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test. Finally, when we consider the sup-norm statistic, the necessity part is given by a second integral test.Mathematics Subject Classification. 60F15, 60G15.

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Section: )mentioning

confidence: 99%

“…Let λ 1 and λ 2 be two real numbers such that λ 1 λ 2 = 0. In the spirit of Cheridito [5] and El-Nouty [9], we introduce the fractional mixed fractional Brownian motion and fractional Brownian sheet (FMFBMFBS) defined as follows where φ is named the small ball function and γ := H 1 + H 2 + H 3 the scaling factor.…”

Section: )mentioning

confidence: 99%

The fractional mixed fractional brownian motion and fractional brownian sheet

El-Nouty

2007

ESAIM: PS

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“…It is not semi martingale for 12 H  . To overcome this shortcoming, [5] was proposed a mixed fractional Brownian (MFBM) model with…”

Section: Introductionmentioning

confidence: 99%

Time-changed generalized mixed fractional Brownian motion and application to arithmetic average Asian option pricing

Önalan

2017

IJAMR

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In this paper we present a novel model to analyze the behavior of random asset price process under the assumption that the stock price process is governed by time-changed generalized mixed fractional Brownian motion with an inverse gamma subordinator. This model is constructed by introducing random time changes into generalized mixed fractional Brownian motion process. In practice it has been observed that many different time series have long-range dependence property and constant time periods. Fractional Brownian motion provides a very general model for long-term dependent and anomalous diffusion regimes. Motivated by this facts in this paper we investigated the long-range dependence structure and trapping events (periods of prices stay motionless) of CSCO stock price return series. The constant time periods phenomena are modeled using an inverse gamma process as a subordinator. Proposed model include the jump behavior of price process because the gamma process is a pure jump Levy process and hence the subordinated process also has jumps so our model can be capture the random variations in volatility. To show the effectiveness of proposed model, we applied the model to calculate the price of an average arithmetic Asian call option that is written on Cisco stock. In this empirical study first the statistical properties of real financial time series is investigated and then the estimated model parameters from an observed data. The results of empirical study which is performed based on the real data indicated that the results of our model are more accuracy than the results based on traditional models.

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Section: Introductionmentioning

confidence: 99%

“…The mfBm models have been extensively studied in the literature [1][2][3][4][5][6][7][8][9]. Cheridito [2] derived an European call pricing option on an asset driven by a linear combination of a Brownian motion and an independent fractional Brownian motion. Based on this theory, Sun and Yan [9] proposed a mixed fractional Brownian motion version of a credit risk pricing Merton model and assumed that the value of the firm obeys a geometric mixed fractional Brownian motion; the result shows that the mixed fractional model to simulate credit risk pricing is a reasonable one.…”

Section: Introductionmentioning

confidence: 99%

Optimal Exercise Boundary of American Fractional Lookback Option in a Mixed Jump-Diffusion Fractional Brownian Motion Environment

Yang

2017

Mathematical Problems in Engineering

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A new framework for pricing the American fractional lookback option is developed in the case where the stock price follows a mixed jump-diffusion fraction Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.

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Mixed Fractional Brownian Motion

Cited by 306 publications

References 12 publications

The fractional mixed fractional brownian motion and fractional brownian sheet

The fractional mixed fractional brownian motion and fractional brownian sheet

Time-changed generalized mixed fractional Brownian motion and application to arithmetic average Asian option pricing

Optimal Exercise Boundary of American Fractional Lookback Option in a Mixed Jump-Diffusion Fractional Brownian Motion Environment

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