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Chapter 10 shows the basic idea of quasi-Monte Carlo methods. These methods differ from ordinary Monte Carlo method in that they make no attempt to mimic randomness. They are based on the idea that random Monte Carlo techniques can often be improved by replacing the underlying source of random numbers with a more uniformly distributed deterministic sequence. Low-discrepancy methods have the potential to accelerate convergence under appropriate conditions. In an example using randomized quasi-Monte Carlo methods it was possible to achieve faster convergence of the option price. (fragment of text)
Rocznik
Strony
169--181
Opis fizyczny
Twórcy
autor
- Wrocław University of Economics, Poland
Bibliografia
- Carr P., Ellis K. (1998), "Static Hedging of Exotic Options", Journal of Finance, 53(3), 1998.
- Faure H. (1992), "Discrèpance de suites associees à un système de numération (en dimension s)", Acta Arithmetica, 41, 337-351.
- Glasserman P. (2002), Monte Carlo Methods in Financial Engineering, New York: Wiley & Sons.
- Halton J. H. (1960), "On the Efficiency of Certain Quasi-Random Sequences of Points in Evaluating Multi-dimensional Integrals", Numerische Mathematik, 2, 84-90.
- Haug E. G. (1997), The Complete Guide to Option Pricing Formulas, New York: McGraw-Hill.
- Hull J. C. (1999), Options, Futures and Other Derivatives, Englewood: Prentice-Hall.
- Jackel P. (2003), Monte Carlo Methods in Finance, Hoboken: Springer-Verlag.
- Niederreiter H. (1992), Random Number Generation and Quasi-Monte Carlo Methods, Philadelphia: SI AM.
- Owen A. B. (1997), "Scrambled Net Variance for Integrals of Smooth Functions", Annals of Statistics, 25, 1541-1562.
- Sobol I. M. (1967), "The Distribution of Points in a Cube and Approximate Evaluation of Integrals", Computational Mathematics and Mathematical Physics, 7, 784-802.
- Sobol I. M. (1994), A Primer for the Monte Carlo Method, Boca Raton: CRC Press.
- Tan K. S., Boyle P. P. (1997), "Applications of Scrambled Low Discrepancy Sequences to Exotic Options", ww-w.actuaries.org/AFIR/colloquia/Cairns/Tan_Boyle.pdf
- Zhang P. G. (2001), Exotic Options. A Guide to second Generation Options, Singapore: World Scientific Publishing.
- Zieliński R. (1970), Metody Monte Carlo (Monte Carlo Methods), Warszawa: WNT.
- Zieliński R. (1997), Komputerowe generowanie liczb pseudolosowych, (Computer Methods for Random Numbers Generation), Warszawa: WNT.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171275475