scholarly journals Exact Monte Carlo simulation of killed diffusions

2008 ◽  
Vol 40 (01) ◽  
pp. 273-291 ◽  
Author(s):  
Bruno Casella ◽  
Gareth O. Roberts
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Barrier Option ◽  
Double Barrier ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Theoretical Predictions ◽  
Efficient Alternative ◽  
Barrier Option Pricing

We describe and implement a novel methodology for Monte Carlo simulation of one-dimensional killed diffusions. The proposed estimators represent an unbiased and efficient alternative to current Monte Carlo estimators based on discretization methods for the cases when the finite-dimensional distributions of the process are unknown. For barrier option pricing in finance, we design a suitable Monte Carlo algorithm both for the single barrier case and the double barrier case. Results from numerical investigations are in excellent agreement with the theoretical predictions.

scholarly journals Exact Monte Carlo simulation of killed diffusions

2008 ◽  
Vol 40 (1) ◽  
pp. 273-291 ◽  
Author(s):  
Bruno Casella ◽  
Gareth O. Roberts
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
Barrier Option ◽  
Double Barrier ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Theoretical Predictions ◽  
Efficient Alternative ◽  
Barrier Option Pricing

We describe and implement a novel methodology for Monte Carlo simulation of one-dimensional killed diffusions. The proposed estimators represent an unbiased and efficient alternative to current Monte Carlo estimators based on discretization methods for the cases when the finite-dimensional distributions of the process are unknown. For barrier option pricing in finance, we design a suitable Monte Carlo algorithm both for the single barrier case and the double barrier case. Results from numerical investigations are in excellent agreement with the theoretical predictions.

scholarly journals Enhancing finite difference approximations for double barrier options: mesh optimization and repeated Richardson extrapolation

2021 ◽  
Author(s):  
Luca Vincenzo Ballestra
Keyword(s):  
Finite Difference ◽  
Optimization Procedure ◽  
Richardson Extrapolation ◽  
Mesh Optimization ◽  
Option Prices ◽  
Barrier Option ◽  
Double Barrier ◽  
Finite Difference Approximations ◽  
Barrier Option Pricing ◽  
Richardson Extrapolation Technique

AbstractWe show that the performances of the finite difference method for double barrier option pricing can be strongly enhanced by applying both a repeated Richardson extrapolation technique and a mesh optimization procedure. In particular, first we construct a space mesh that is uniform and aligned with the discontinuity points of the solution being sought. This is accomplished by means of a suitable transformation of coordinates, which involves some parameters that are implicitly defined and whose existence and uniqueness is theoretically established. Then, a finite difference scheme employing repeated Richardson extrapolation in both space and time is developed. The overall approach exhibits high efficacy: barrier option prices can be computed with accuracy close to the machine precision in less than one second. The numerical simulations also reveal that the improvement over existing methods is due to the combination of the mesh optimization and the repeated Richardson extrapolation.

scholarly journals Asteroseismology of 36 Kepler subgiants – I. Oscillation frequencies, linewidths, and amplitudes

2020 ◽  
Vol 495 (2) ◽  
pp. 2363-2386 ◽  
Author(s):  
Yaguang Li ◽  
Timothy R Bedding ◽  
Tanda Li ◽  
Shaolan Bi ◽  
Dennis Stello ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Oscillation Mode ◽  
Monte Carlo Algorithm ◽  
Scaling Relations ◽  
Mass Dependence ◽  
Seismic Parameters ◽  
Theoretical Predictions ◽  
Mixed Modes ◽  
Oscillation Frequencies ◽  
Spectrum Model

ABSTRACT The presence of mixed modes makes subgiants excellent targets for asteroseismology, providing a probe for the internal structure of stars. Here we study 36 Kepler subgiants with solar-like oscillations and report their oscillation mode parameters. We performed a so-called peakbagging exercise, i.e. estimating oscillation mode frequencies, linewidths, and amplitudes with a power spectrum model, fitted in the Bayesian framework and sampled with a Markov chain Monte Carlo algorithm. The uncertainties of the mode frequencies have a median value of 0.180 μHz. We obtained seismic parameters from the peakbagging, analysed their correlation with stellar parameters, and examined against scaling relations. The behaviour of seismic parameters (e.g. Δν, νmax, ϵp) is in general consistent with theoretical predictions. We presented the observational p–g diagrams, namely γ1–Δν for early subgiants and ΔΠ1–Δν for late subgiants, and demonstrate their capability to estimate stellar mass. We also found a log g dependence on the linewidths and a mass dependence on the oscillation amplitudes and the widths of oscillation excess. This sample will be valuable constraints for modelling stars and studying mode physics such as excitation and damping.

Assessing Curriculum Efficiency Through Monte Carlo Simulation

2018 ◽  
Vol 22 (4) ◽  
pp. 597-610
Author(s):  
David Torres ◽  
Jorge Crichigno ◽  
Carmella Sanchez
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Frequency Distribution ◽  
Relative Frequency ◽  
Monte Carlo Algorithm ◽  
Pass Rate ◽  
Random Numbers ◽  
Pass Rates ◽  
Low Pass ◽  
Relative Frequency Distribution

A Monte Carlo algorithm is designed to predict the average time to graduate by enrolling virtual students in a degree plan. The algorithm can be used to improve graduation rates by identifying bottlenecks in a degree plan (e.g., low pass rate courses and prerequisites). Random numbers are used to determine whether students pass or fail classes by comparing them to institutional pass rates. Courses cannot be taken unless prerequisites and corequisites are satisfied. The output of the algorithm generates a relative frequency distribution which plots the number of students who graduate by semester. Pass rates of courses can be changed to determine the courses that have the greatest impact on the time to graduate. Prerequisites can also be removed to determine whether certain prerequisites significantly affect the time to graduate.

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