Monte-Carlo Simulation with Boundary Conditions (with Applications to Stress Testing, CEV and Variance-Gamma Simulation)

2010 ◽  
Author(s):  
Christian P. Fries ◽  
Joerg Kienitz
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Boundary Conditions ◽  
Stress Testing ◽  
Variance Gamma

Boundary conditions for Monte Carlo simulation of charged systems

1981 ◽  
Vol 43 (2) ◽  
pp. 275-286 ◽  
Author(s):  
E.R. Smith ◽  
C.C. Wright ◽  
C.S. Hoskins
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Boundary Conditions

VARIANCE GAMMA PROCESS WITH MONTE CARLO SIMULATION AND CLOSED FORM APPROACH FOR EUROPEAN CALL OPTION PRICE DETERMINATION

2021 ◽  
Vol 14 (2) ◽  
pp. 183-193
Author(s):  
Abdul Hoyyi ◽  
Abdurakhman Abdurakhman ◽  
Dedi Rosadi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Closed Form ◽  
Stock Price ◽  
Option Price ◽  
Secondary Data ◽  
Exponential Model ◽  
Variance Gamma ◽  
Variance Gamma Process ◽  
Normally Distributed

The Option is widely applied in the financial sector.  The Black-Scholes-Merton model is often used in calculating option prices on a stock price movement. The model uses geometric Brownian motion which assumes that the data is normally distributed. However, in reality, stock price movements can cause sharp spikes in data, resulting in nonnormal data distribution. So we need a stock price model that is not normally distributed. One of the fastest growing stock price models today is the  process exponential model. The  process has the ability to model data that has excess kurtosis and a longer tail (heavy tail) compared to the normal distribution. One of the members of the  process is the Variance Gamma (VG) process. The VG process has three parameters which each of them, to control volatility, kurtosis and skewness. In this research, the secondary data samples of options and stocks of two companies were used, namely zoom video communications, Inc. (ZM) and Nokia Corporation (NOK).  The price of call options is determined by using closed form equations and Monte Carlo simulation. The Simulation was carried out for various  values until convergent result was obtained.

Investigation Into the Effect of Uncertainty in Thermal Properties on Turbomachinery Disc Heat Transfer Using Both a Monte Carlo Simulation Technique and a Taylor Series Uncertainty Propagation Method

2007 ◽  
Author(s):  
Adam Cooke ◽  
Peter Childs ◽  
Christopher Long
Keyword(s):  
Heat Transfer ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Thermal Properties ◽  
Boundary Conditions ◽  
Taylor Series ◽  
Uncertainty Propagation ◽  
Outer Radius ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients

The effect of uncertainties in the thermal properties of components and surrounding fluids is often ignored in the field of experimental turbomachinery heat transfer. The work reported here uses two different methods of uncertainty analysis to help quantify these effects: 1) a stochastic Monte Carlo simulation and 2) a Taylor series uncertainty propagation. These two methods were used on a steady state free disc test case having a turbulent flow regime. The disc modelled was made from IMI 318 titanium and had an inner and outer radius of 0.115 m and 0.22 m respectively, representative of engine and test rig geometry. The disc thickness was 0.016 m. Convective boundary conditions were derived from the relevant equation for local Nusselt number. The applied boundary conditions resulted in local heat transfer coefficients in the range of approximately 120 W/m2 K to 170 W/m2 K. Uncertainties for these heat transfer coefficients were a near identical match between the two different uncertainty methods and were found to be ± 0.66%. Calculated heat flux values fell within the range of approximately 1500 W/m2 and 5200 W/m2. The Monte Carlo uncertainty method returned uncertainty values varying from ± 1.17% to ± 0.47% from the inner and outer radii respectively. An extended Taylor series of uncertainty propagation returned uncertainties varying from ± 1.82% to ± 0.96%, from the inner and outer radius respectively and increased and decreased a number of times in between. These differences are due to assumptions and simplifications which need to be made when using the Taylor series method and shows that a Monte Carlo simulation analysis offers a better way of quantifying the uncertainties associated with disc to air heat transfer as it is more realistic. Studying the magnitudes of uncertainty allows the analyst to understand the impact that uncertainties in thermal properties can have on calculated values of disc to air heat fluxes and heat transfer coefficients.

Unphysical Frozen States in Monte Carlo Simulation of 2D Ising Model

1998 ◽  
Vol 09 (06) ◽  
pp. 881-886 ◽  
Author(s):  
Andres R. R. Papa
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Ising Model ◽  
Boundary Conditions ◽  
Monte Carlo Simulations ◽  
Periodic Boundary ◽  
Random Access ◽  
Periodic Boundary Conditions ◽  
Two Dimensional ◽  
Ising Systems

We show that for two-dimensional square Ising systems unphysical frozen states are obtained by just changing the instant of application of periodic boundary conditions during Monte Carlo simulations. The strange behavior is observed up to sample sizes currently used in literature. The anomalous results appear to be associated to the simultaneous use of type writer updating algorithms; they disappear when random access routines are implemented.

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