A Monte Carlo Simulation of Brownian Motion in the Freshman Laboratory

1970 ◽  
Vol 38 (6) ◽  
pp. 716-719 ◽  
Author(s):  
C. D. Anger ◽  
J. R. Prescott
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Brownian Motion

Monte Carlo simulation of Brownian motion with viscous drag

1978 ◽  
Vol 46 (5) ◽  
pp. 543-545 ◽  
Author(s):  
L. Gunther ◽  
D. L. Weaver
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Viscous Drag

scholarly journals Confidence bands for Brownian motion and applications to Monte Carlo simulation

2007 ◽  
Vol 17 (1) ◽  
pp. 1-10 ◽  
Author(s):  
W. S. Kendall ◽  
J.-M. Marin ◽  
C. P. Robert
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Confidence Bands

Some Observations on the Random Response of an Elasto-Plastic System

1988 ◽  
Vol 55 (4) ◽  
pp. 911-917 ◽  
Author(s):  
L. G. Paparizos ◽  
W. D. Iwan
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Markov Process ◽  
Practical Interest ◽  
Random Excitation ◽  
Process Models ◽  
Mean Square ◽  
Random Response ◽  
Monte Carlo Simulation Study

The nature of the response of strongly yielding systems subjected to random excitation, is examined. Special attention is given to the drift response, defined as the sum of yield increments associated with inelastic response. Based on the properties of discrete Markov process models of the yield increment process, it is suggested that for many cases of practical interest, the drift can be considered as a Brownian motion. The approximate Gaussian distribution and the linearly divergent mean square value of the process, as well as an expression for the probability distribution of the peak drift response, are obtained. The validation of these properties is accomplished by means of a Monte Carlo simulation study.

scholarly journals Monte Carlo simulation of coagulation in discrete particle-size distributions. Part 1. Brownian motion and fluid shearing

1984 ◽  
Vol 143 ◽  
pp. 367-385 ◽  
Author(s):  
H. J. Pearson ◽  
I. A. Valioulis ◽  
E. J. List
Keyword(s):  
Monte Carlo Simulation ◽  
Particle Size ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Size Distributions ◽  
Unit Size ◽  
Particle Size Distributions ◽  
Maximum Volume ◽  
Discrete Particle ◽  
Constant Rate

A method for the Monte Carlo simulation, by digital computer, of the evolution of a colliding and coagulating population of suspended particles is described. Collision mechanisms studied both separately and in combination are: Brownian motion of the particles, and laminar and isotropic turbulent shearing motions of the suspending fluid. Steady-state distributions are obtained by adding unit-size particles at a constant rate and removing all particles once they reach a preset maximum volume. The resulting size distributions are found to agree with those obtained by dimensional analysis (Hunt 1982).

scholarly journals Simulation hedge investment portfolios through options portfolio

2019 ◽  
Vol 16 (2) ◽  
pp. 843
Author(s):  
Miguel Jiménez-Gómez ◽  
Natalia Acevedo-Prins ◽  
Miguel David Rojas-López
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Lower Cost ◽  
Market Risk ◽  
Stock Index ◽  
Call Option ◽  
Hedging Strategies ◽  
Financial Options ◽  
Investment Portfolios

<p>This paper presents two hedging strategies with financial options to mitigate the market risk associated with the future purchase of investment portfolios that exhibit the same behavior as Colombia's COLCAP stock index. The first strategy consists in the purchase of a Call plain vanilla option and the second strategy in the purchase of a Call option and the sale of a Call option. The second strategy corresponds to a portfolio of options called Bull Call Spread. To determine the benefits of hedging and the best strategy, the Geometric Brownian Motion and Monte Carlo simulation is used. The results show that the two hedging strategies manage to mitigate market risk and the best strategy is the first one despite the fact that the Bull Call Spread strategy is lower cost.</p>

Distribution of Discrete Time Delta-Hedging Error via a Recursive Relation

2016 ◽  
Vol 6 (3) ◽  
pp. 314-336 ◽  
Author(s):  
Minseok Park ◽  
Kyungsub Lee ◽  
Geon Ho Choe
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Jump Diffusion ◽  
Recursive Relation ◽  
Strike Price ◽  
Delta Hedging ◽  
Approximate Distribution ◽  
Jump Diffusion Model ◽  
Path Dependent

AbstractWe introduce a new method to compute the approximate distribution of the Delta-hedging error for a path-dependent option, and calculate its value over various strike prices via a recursive relation and numerical integration. Including geometric Brownian motion and Merton's jump diffusion model, we obtain the approximate distribution of the Delta-hedging error by differentiating its price with respect to the strike price. The distribution from Monte Carlo simulation is compared with that obtained by our method.

scholarly journals Volatility Modelling and VaR: The Case of Bitcoin, Ether and Ripple

2020 ◽  
Vol 11 (3) ◽  
pp. 253-269
Author(s):  
Jakub Ječmínek ◽  
Gabriela Kukalová ◽  
Lukáš Moravec
Keyword(s):  
Stochastic Process ◽  
Monte Carlo Simulation ◽  
Risk Management ◽  
Monte Carlo ◽  
Brownian Motion ◽  
Value At Risk ◽  
Risk Estimation ◽  
Geometric Brownian Motion ◽  
Empirical Literature ◽  
Digital Assets

Abstract Since Bitcoin introduction in 2008, the cryptocurrency market has grown into hundreds-of-billion-dollar market. The cryptocurrency market is well known as very volatile, mainly for the fact that the cryptocurrencies have not the price to fall back upon and that anybody can join the trading (no license or approval is required). Since empirical literature suggests that GARCH-type models dominate as VaR estimators the overall objective of this paper is to perform comprehensive volatility and VaR estimation for three major digital assets and conclude which method gives the best results in terms of risk management. The methods we used are parametric (GARCH and EWMA model), non-parametric (historical VaR) and Monte Carlo simulation (given by Geometric Brownian Motion). We conclude that the best method for value-at-risk estimation for cryptocurrencies is the Monte Carlo simulation due to the heavy diffusion (stochastic) process and robustness of the results.

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