Good Path Generation Methods in Quasi-Monte Carlo for Pricing Financial Derivatives

2014 ◽  
Vol 36 (2) ◽  
pp. B171-B197 ◽  
Author(s):  
Zhijian He ◽  
Xiaoqun Wang
Keyword(s):  
Monte Carlo ◽  
Financial Derivatives ◽  
Path Generation ◽  
Quasi Monte Carlo ◽  
Good Path

scholarly journals A Comparative Analysis of Monte Carlo and Quasi-Monte Carlo Methods in Financial Derivative Pricing

2021 ◽  
Vol 69 (1) ◽  
pp. 1-6
Author(s):  
SM Arif Hossen ◽  
ABM Shahadat Hossain
Keyword(s):  
Monte Carlo ◽  
Comparative Analysis ◽  
Monte Carlo Methods ◽  
American Options ◽  
Financial Derivatives ◽  
Numerical Results ◽  
Derivative Pricing ◽  
Quasi Monte Carlo ◽  
Financial Derivative ◽  
Path Dependent

The main purpose of this dissertation is to study Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods for pricing financial derivatives. We estimate the Price of European as well as various path dependent options like Asian, Barrier and American options by using these methods. We also compute the numerical results by the above mentioned methods and compare them graphically as well with the help of the MATLAB Coding. Dhaka Univ. J. Sci. 69(1): 1-6, 2021 (January)

scholarly journals Identification of Efficient Sampling Techniques for Probabilistic Voltage Stability Analysis of Renewable-Rich Power Systems

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2328
Author(s):  
Mohammed Alzubaidi ◽  
Kazi N. Hasan ◽  
Lasantha Meegahapola ◽  
Mir Toufikur Rahman
Keyword(s):  
Monte Carlo ◽  
Stability Analysis ◽  
Power Systems ◽  
Large Scale ◽  
Voltage Stability ◽  
Sampling Technique ◽  
Coefficient Of Determination ◽  
Sampling Techniques ◽  
Quasi Monte Carlo ◽  
Efficient Sampling

This paper presents a comparative analysis of six sampling techniques to identify an efficient and accurate sampling technique to be applied to probabilistic voltage stability assessment in large-scale power systems. In this study, six different sampling techniques are investigated and compared to each other in terms of their accuracy and efficiency, including Monte Carlo (MC), three versions of Quasi-Monte Carlo (QMC), i.e., Sobol, Halton, and Latin Hypercube, Markov Chain MC (MCMC), and importance sampling (IS) technique, to evaluate their suitability for application with probabilistic voltage stability analysis in large-scale uncertain power systems. The coefficient of determination (R2) and root mean square error (RMSE) are calculated to measure the accuracy and the efficiency of the sampling techniques compared to each other. All the six sampling techniques provide more than 99% accuracy by producing a large number of wind speed random samples (8760 samples). In terms of efficiency, on the other hand, the three versions of QMC are the most efficient sampling techniques, providing more than 96% accuracy with only a small number of generated samples (150 samples) compared to other techniques.

QMC integration errors and quasi-asymptotics

2020 ◽  
Vol 26 (3) ◽  
pp. 171-176
Author(s):  
Ilya M. Sobol ◽  
Boris V. Shukhman
Keyword(s):  
Monte Carlo ◽  
Error Estimate ◽  
Numerical Experiments ◽  
Probable Error ◽  
Quasi Monte Carlo ◽  
Integration Error ◽  
Asymptotic Error ◽  
Dimensional Cube ◽  
Integration Errors ◽  
Mc Method

AbstractA crude Monte Carlo (MC) method allows to calculate integrals over a d-dimensional cube. As the number N of integration nodes becomes large, the rate of probable error of the MC method decreases as {O(1/\sqrt{N})}. The use of quasi-random points instead of random points in the MC algorithm converts it to the quasi-Monte Carlo (QMC) method. The asymptotic error estimate of QMC integration of d-dimensional functions contains a multiplier {1/N}. However, the multiplier {(\ln N)^{d}} is also a part of the error estimate, which makes it virtually useless. We have proved that, in the general case, the QMC error estimate is not limited to the factor {1/N}. However, our numerical experiments show that using quasi-random points of Sobol sequences with {N=2^{m}} with natural m makes the integration error approximately proportional to {1/N}. In our numerical experiments, {d\leq 15}, and we used {N\leq 2^{40}} points generated by the SOBOLSEQ16384 code published in 2011. In this code, {d\leq 2^{14}} and {N\leq 2^{63}}.

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