QUASI-MONTE CARLO METHODS IN COMPUTATIONAL FINANCE

COSMOS ◽  
2005 ◽  
Vol 01 (01) ◽  
pp. 113-125
Author(s):  
HARALD NIEDERREITER
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Scientific Computing ◽  
Computational Finance ◽  
Quasi Monte Carlo ◽  
Random Samples ◽  
Mortgage Backed Securities

Quasi-Monte Carlo methods are deterministic versions of Monte Carlo methods, in the sense that the random samples used in the implementation of a Monte Carlo method are replaced by judiciously chosen deterministic points with good distribution properties. They outperform classical Monte Carlo methods in many problems of scientific computing. This paper discusses applications of quasi-Monte Carlo methods to computational finance, with a special emphasis on the problems of pricing mortgage-backed securities and options. The necessary background on Monte Carlo and quasi-Monte Carlo methods is also provided.

QUASI MONTE–CARLO EVALUATION OF SENSITIVITIES OF OPTIONS IN COMMODITY AND ENERGY MARKETS

2003 ◽  
Vol 06 (08) ◽  
pp. 865-884 ◽  
Author(s):  
FRED E. BENTH ◽  
LARS O. DAHL ◽  
KENNETH H. KARLSEN
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Random Variable ◽  
Numerical Differentiation ◽  
Energy Markets ◽  
Forward Contracts ◽  
Quasi Monte Carlo ◽  
Adaptive Techniques ◽  
Monte Carlo Evaluation

In this paper we consider the evaluation of sensitivities of options on spots and forward contracts in commodity and energy markets. We derive different expressions for these sensitivities, based on techniques from the recently introduced Malliavin approach [8, 9]. The Malliavin approach provides representations of the sensitivities in terms of expectations of the payoff and a random variable only depending on the underlying dynamics. We apply Monte–Carlo methods to evaluate such expectations, and to compare with numerical differentiation. We propose to use a refined quasi Monte–Carlo method based on adaptive techniques to reduce variance. Our approach gives a significant improvement of convergence.

Pseudo-Random Monte-Carlo Methods

1982 ◽  
Vol 5 (3-4) ◽  
pp. 301-312
Author(s):  
Ivan Kramosil
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Random Sampling ◽  
Algorithmic Complexity ◽  
Binary Sequences ◽  
Random Event ◽  
Unknown Probability ◽  
The Monte Carlo Method ◽  
Random Samples

In this paper we investigate the Monte-Carlo method for estimation of the unknown probability of a random event on the ground of relative frequencies and under the condition that random sampling is replaced by a deterministic side input producing binary sequences of high algorithmic complexity. It is proved that if this complexity exceeds a treshold value, the sequences may be used in the Monte-Carlo methods instead of random samples as the obtained estimates converge to the estimated probability when the length of these binary sequences increases.

scholarly journals Comparison of Monte Carlo Methods Efficiency to Solve Radiative Energy Transfer in High Fidelity Unsteady 3D Simulations

2017 ◽  
Author(s):  
Lorella Palluotto ◽  
Nicolas Dumont ◽  
Pedro Rodrigues ◽  
Chai Koren ◽  
Ronan Vicquelin ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Computational Cost ◽  
Statistical Error ◽  
Radiative Energy ◽  
Maximum Temperature ◽  
Quasi Monte Carlo ◽  
High Scalability ◽  
Transfer Problems

The present work assesses different Monte Carlo methods in radiative heat transfer problems, in terms of accuracy and computational cost. Achieving a high scalability on numerous CPUs with the conventional forward Monte Carlo method is not straightforward. The Emission-based Reciprocity Monte Carlo Method (ERM) allows to treat each mesh point independently from the others with a local monitoring of the statistical error, becoming a perfect candidate for high-scalability. ERM is however penalized by a slow statistical convergence in cold absorbing regions. This limitation has been overcome by an Optimized ERM (OERM) using a frequency distribution function based on the emission distribution at the maximum temperature of the system. Another approach to enhance the convergence is the use of low-discrepancy sampling. The obtained Quasi-Monte Carlo method is combined with OERM. The efficiency of the considered Monte-Carlo methods are compared.

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