Modeling the volatity of cryptocurrency markets

2021 ◽  
Vol 1 (2 (6)) ◽  
Author(s):  
Volodymyr Moroz ◽  
Ivanna Yalymova
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Diffusion Coefficients ◽  
Geometric Brownian Motion ◽  
Price Movement ◽  
Linear Drift ◽  
Modeling And Forecasting ◽  
And Diffusion

The application of the model of geometric Brownian motion (GBM) for the problem of modeling and forecasting prices for cryptocurrencies is analyzed. For prediction the solution of the stochastic differential equation of the GBM model is used, which has a linear drift and diffusion coefficients. Different scenarios of price movement are considered. Keywords: geometric Brownian motion (GBM), modeling, forecasting, cryptocurrency.

scholarly journals Second Order Itô Processes

1969 ◽  
Vol 36 ◽  
pp. 27-63 ◽  
Author(s):  
Jerome A. Goldstein
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Diffusion Coefficients ◽  
Second Order ◽  
Brownian Motion Process ◽  
First Order ◽  
Motion Process ◽  
And Diffusion

A first order stochastic differential equation is any equation which can be expressed symbolically in the form (1. 1)m and σ are called the drift and diffusion coefficients and z( · ) is usually a Brownian motion process.

Large deviations and Berry–Esseen inequalities for estimators in nonhomogeneous diffusion driven by fractional Brownian motion

2020 ◽  
Vol 28 (3) ◽  
pp. 183-196
Author(s):  
Kouacou Tanoh ◽  
Modeste N’zi ◽  
Armel Fabrice Yodé
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Maximum Likelihood ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Maximum Likelihood Estimator ◽  
Bayes Estimator ◽  
Likelihood Estimator

AbstractWe are interested in bounds on the large deviations probability and Berry–Esseen type inequalities for maximum likelihood estimator and Bayes estimator of the parameter appearing linearly in the drift of nonhomogeneous stochastic differential equation driven by fractional Brownian motion.

scholarly journals The Geometric Brownian Motion of Indosat Telecommunications Daily Stock Price During the Covid-19 Pandemic in Indonesia

2021 ◽  
Vol 2084 (1) ◽  
pp. 012012
Author(s):  
Tiara Shofi Edriani ◽  
Udjianna Sekteria Pasaribu ◽  
Yuli Sri Afrianti ◽  
Ni Nyoman Wahyu Astute
Keyword(s):  
Brownian Motion ◽  
Stock Price ◽  
Service Providers ◽  
Main Idea ◽  
Geometric Brownian Motion ◽  
Government Policies ◽  
Percentage Error ◽  
Price Movement ◽  
Data Movement ◽  
Total Data

Abstract One of the major telecommunication and network service providers in Indonesia is PT Indosat Tbk. During the coronavirus (COVID-19) pandemic, the daily stock price of that company was influenced by government policies. This study addresses stock data movement from February 5, 2020 to February 5, 2021, resulted in 243 data, using the Geometric Brownian motion (GBM). The stochastic process realization of this stock price fluctuates and increases exponentially, especially in the 40 latest data. Because of this situation, the realization is transformed into log 10 and calculated its return. As a result, weak stationary in variance is obtained. Furthermore, only data from December 7, 2020 to February 5, 2021 fulfill the GBM assumption of stock price return, as R t 1 * , t 1 * = 1 , 2 , 3 , … , 40 . The main idea of this study is adding datum one by one as much as 10% – 15% of the total data R t 1 * , starting from December 4, 2020 backwards. Following this procedure, and based on the 3% < p-value < 10%, the study shows that its datum can be included in R t 1 * , so t 1 * = − 4. − 3 , − 2 , … , 40 and form five other data groups, R t 2 * , … , R t 6 * . Considering Mean Absolute Percentage Error (MAPE) and amount of data from each group, R t 6 * is selected for modelling. Thus, GBM succeeded in representing the stock price movement of the second most popular Indonesian telecommunication company during COVID-19 pandemic.

Optimal stopping and maximal inequalities for geometric Brownian motion

1998 ◽  
Vol 35 (04) ◽  
pp. 856-872 ◽  
Author(s):  
S. E. Graversen ◽  
G. Peskir
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Optimal Stopping ◽  
Moving Boundary ◽  
Stopping Time ◽  
Practical Interest ◽  
Maximal Inequality ◽  
Geometric Brownian Motion ◽  
Stopping Times ◽  
Image Position

Explicit formulas are found for the payoff and the optimal stopping strategy of the optimal stopping problem supτ E (max0≤t≤τ X t − c τ), where X = (X t ) t≥0 is geometric Brownian motion with drift μ and volatility σ &gt; 0, and the supremum is taken over all stopping times for X. The payoff is shown to be finite, if and only if μ &lt; 0. The optimal stopping time is given by τ* = inf {t &gt; 0 | X t = g * (max0≤t≤s X s )} where s ↦ g *(s) is the maximal solution of the (nonlinear) differential equation under the condition 0 &lt; g(s) &lt; s, where Δ = 1 − 2μ / σ2 and K = Δ σ2 / 2c. The estimate is established g *(s) ∼ ((Δ − 1) / K Δ)1 / Δ s 1−1/Δ as s → ∞. Applying these results we prove the following maximal inequality: where τ may be any stopping time for X. This extends the well-known identity E (sup t&gt;0 X t ) = 1 − (σ 2 / 2 μ) and is shown to be sharp. The method of proof relies upon a smooth pasting guess (for the Stephan problem with moving boundary) and the Itô–Tanaka formula (being applied two-dimensionally). The key point and main novelty in our approach is the maximality principle for the moving boundary (the optimal stopping boundary is the maximal solution of the differential equation obtained by a smooth pasting guess). We think that this principle is by itself of theoretical and practical interest.

Sign in / Sign up

Export Citation Format

Share Document