EFFICIENT RANDOM NUMBER GENERATION FROM PROBABILITY DISTRIBUTIONS FOR FINANCIAL MODELLING
Abstract
In this paper we pursue to analyze different aspects of frequently used
random number generators. Although random number generation is frequently considered
a trivial task that can be accomplished by using out-of-box solution, the quality of random
number source can significantly influence the accuracy of end results. We consider how a
random generator can be examined, qualified and tested for effectiveness. A test of
frequently used Mersenne twister pseudo random generator algorithm is also conducted to
demonstrate if its fit for use in a financial simulation.
References
http://www.boost.org/doc/libs/1_54_0/doc/html/boost_random.html
Box, G., & Muller, M. E. (1958). A Note on the Generation of Random Normal
Deviates. The Annals of Mathematical Statistics, 29(2), 610–611.
Clyde, M. F., & Stamp, M. (1998, February). Classification and realization of
pseudo-random number generators. Systems & Control Letters, 14(2), 169–175.
Ekeland, I. (1996). The Broken Dice, and Other Mathematical Tales of Chance.
Chicago: University of Chicago Press.
Group, N. W. (2005, June). Randomness Requirements for Security. Retrieved from
IETF: http://tools.ietf.org/html/rfc4086
Ingali, L., & Kwak, Y. H. (2007, 9). Exploring Monte Carlo Simulation Applications in
Project Management. Risk Management, pp. 44-57.
Kloeden, P. E., & Platen, E. (1992). Numerical Solution of Stochastic Differential
Equations (Stochastic Modelling and Applied Probability). Springer.
Knuth, D. (1981). The Art of Computer Programming. Mass.: Addison-Wesley.
Marsaglia, G., & Tsang, W. W. (1984). A fast, easily implemented method for
sampling from. SIAM Journal on Scientific and Statistical, 349–359.
Marsaglia, G., & Tsang, W. W. (2000). The Ziggurat Method for Generating
Random Variables. Journal of Statistical Software, 1-7.
Matsumoto, M., & Nishimura, T. (1998). Mersenne twister: a 623-dimensionally
equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling
and Computer Simulation, 3-30.
Neumann, J. v. (1949/1951). Various techniques used in connection with random
digits. In G. F. A.S. Householder, Monte Carlo Method (pp. 36-38). Washington D.C.:
National Bureau of Standards Applied Mathematics Series.
Normal Distribution. (2013, 10 06). Retrieved from Boost Random:
http://www.boost.org/doc/libs/1_52_0/boost/random/normal_distribution.hpp
Singla, N., & M. Hall, B. S. (2008). Financial Monte Carlo simulation on
architecturally diverse systems. Workshop on High Performance Computational Finance
(WHPCF), 1-7.
std::mersenne_twister_engine. (n.d.). Retrieved from CPPREFERENCE.COM:
http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine
Stephens, M. A. (1986). Tests Based on EDF Statistics. In R. a. D'Agostino,
Goodness-of-Fit Techniques. New York: Marcel Dekker.
The Marsaglia Random Number CDROM including the Diehard Battery of Tests of
Randomness. (n.d.). Retrieved from The Marsaglia Random Number CDROM:
http://www.stat.fsu.edu/pub/diehard/
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