The valuation of currency options by fractional Brownian motion

Shokrollahi, Foad; Kılıçman, Adem

doi:10.1186/s40064-016-2784-2

Cited by 9 publications

(6 citation statements)

References 22 publications

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“…It was validated by a rigorous statistical test with added white Gaussian noise based on the autocovariance function [59] and has been applied in studies both for stock indexes [60] and for the price of financial securities [61], in the case of cryptocurrencies [62], in the case of modeling epidemic diseases, such as coronavirus [63], and for the price of goods [50]. Furthermore, the GFBM has been utilized in a great deal of literature research to evaluate derivative titles (options) [64][65][66][67].…”

Section: Introductionmentioning

confidence: 99%

Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion

et al. 2021

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In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major goal is to show how to appropriately model return distributions for financial market indexes, specifically which geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM) dynamic equations best define the evolution of the S&P 500 and Stoxx Europe 600 stock indexes. Daily stock index data were acquired from the Thomson Reuters Eikon database during a ten-year period, from January 2011 to December 2020. The main contribution of this work is determining whether these markets are efficient (as defined by the EMH), in which case the appropriate stock indexes dynamic equation is the GBM, or fractal (as described by the FMH), in which case the appropriate stock indexes dynamic equation is the GFBM. In this paper, we consider two methods for calculating the Hurst exponent: the rescaled range method (RS) and the periodogram method (PE). To determine which of the dynamics (GBM, GFBM) is more appropriate, we employed the mean absolute percentage error (MAPE) method. The simulation results demonstrate that the GFBM is better suited for forecasting stock market indexes than the GBM when the analyzed markets display fractality. However, while these findings cannot be generalized, they are verisimilar.

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Section: Introductionmentioning

confidence: 99%

Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion

et al. 2021

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“…Various methods were used to determine the pK a values including spectrophotometry, 1-9 spectro-uorimetry, 10 potentiometry, 1,10-13 conductometry, 14,15 cyclic voltammetry, 16 chromatography, 1,17-20 electrophoresis, 21,22 NMR, 23,24 mass spectrometry, 25 and Raman spectroscopy; 26 however the majority of these methods require expensive and sophisticated instruments. Therefore, solution scanometric methods were used, [27][28][29][30] but the lack of uniformity of the captured images greatly affected the precision of the analysis posing a serious disadvantage of these methods. [27][28][29][30] Recently, digital image-based analysis (DIBA) methods have been widely used for colorimetric analysis.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, solution scanometric methods were used, [27][28][29][30] but the lack of uniformity of the captured images greatly affected the precision of the analysis posing a serious disadvantage of these methods. [27][28][29][30] Recently, digital image-based analysis (DIBA) methods have been widely used for colorimetric analysis. These methods use digital cameras, [31][32][33] smartphone cameras, [32][33][34][35][36] or scanners, 32,33,37 as colorimetric sensors, where various colour spaces parameters were used as analytical signalling tools.…”

Section: Introductionmentioning

confidence: 99%

Determination of acid dissociation constants of Alizarin Red S, Methyl Orange, Bromothymol Blue and Bromophenol Blue using a digital camera

Shalaby

Mohamed

2020

RSC Adv.

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Acid dissociation constants (pK a ) are important parameters for the characterization of organic and inorganic compounds. They play a crucial role in different physical, chemical, and biological studies. Herein, we introduce a new approach for the determination of acid dissociation constant based on digital image analysis using a low-cost, precise, accurate, sensitive, and portable home-made, camera-based platform. Digital images of Alizarin Red S, Bromophenol Blue, Bromothymol Blue, and Methyl Orange solutions were captured at various pH values. The captured images were analysed to obtain the RGB (Red, Green, and Blue) colour intensities that are used to calculate the RGB colour absorbances. The pK a values were calculated from the RGB colour absorbance-pH relationship using graphical and mathematical methods, and with the aid of DATAN software. For the four studied dyes, the results obtained from digital image analysis were in excellent agreement with the data of sophisticated spectrophotometers and the previously reported literature data.

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“…In the literature, e.g., [12,13], the stock price S can be modeled by the so-called geometric fractional Brownian motion, i.e., S t = S 0 exp µt + σB H (t) − 1 2…”

Section: Introductionmentioning

confidence: 99%

Drawdown and Drawup for Fractional Brownian Motion with Trend

Bai

Liu

2018

J Theor Probab

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We consider the drawdown and drawup of a fractional Brownian motion with trend, which corresponds to the logarithm of geometric fractional Brownian motion representing the stock price in financial market. We derive the asymptotics of tail probabilities of the maximum drawdown and maximum drawup as the threshold goes to infinity, respectively. It turns out that the extremes of drawdown leads to new scenarios of asymptotics depending on Hurst index of fractional Brownian motion.

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The valuation of currency options by fractional Brownian motion

Cited by 9 publications

References 22 publications

Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion

Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion

Determination of acid dissociation constants of Alizarin Red S, Methyl Orange, Bromothymol Blue and Bromophenol Blue using a digital camera

Drawdown and Drawup for Fractional Brownian Motion with Trend

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