Abstract
Is this chapter we will learn the basics of pricing derivatives using simulation methods. We will consider both Monte-Carlo and quasi-Monte Carlo but – of course – with a special emphasis on the latter. The aim of our exposition is not to provide a large toolbox for the quantitative analyst, but to help getting started with the topic. QMC-pricing is an active area of research by its own and the reader is encouraged to consult the specialized literature. We will, however, take a look at some popular examples that frequently serve as benchmarks for refined simulation techniques.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Albrecher, H., Binder, A., Lautscham, V., Mayer, P.: Introduction to Quantitative Methods for Financial Markets. Birkhäuser, Basel (2013)
Caflisch, R.E., Morokoff, W., Owen, A.: Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension. J. Comput. Finance 1, 27–46 (1997)
Dick, J., Zhu, H.: A discrepancy bound for a deterministic acceptance-rejection sampler. Electron. J. Statist. 8, 678–707 (2014)
Eichler A., Leobacher G., Zellinger, H.: Calibration of financial models using quasi-Monte Carlo. Monte-Carlo Methods Appl. 17, 99–131 (2011)
Fournier, E., Lasry, J., Lebouchoux, J., Lions, P., Touzi, N.: Applications of Malliavin calculus to Monte Carlo methods in finance. Finance Stoch. 3, 391–412 (1999)
Giles, M.B.: Multilevel Monte Carlo path simulation. Oper. Res. 56, 607–617 (2008)
Glasserman, P.: Monte Carlo Methods in Financial Engineering. Springer, New York (2004)
Heinrich, S.: Multilevel Monte Carlo methods. Lect. Notes Comput. Sci. 2179, 58–67 (2001)
Hörmann, W., Leydold, J., Derflinger, G.: Automatic Nonuniform Random Variate Generation. Springer, Berlin (2004)
Imai, J., Tan, K.S.: A general dimension reduction technique for derivative pricing. J. Comput. Finance 10, 129–155 (2007)
Imai, J., Tan, K.S.: An accelerating quasi-Monte Carlo method for option pricing under the generalized hyperbolic Lévy process. SIAM J. Sci. Comput. 31, 2282–2302 (2009)
Irrgeher, C., Leobacher, G.: Fast orthogonal transforms for pricing derivatives with quasi-Monte Carlo. In: Laroque, C., Himmelspach, J., Pasupathy, R., Rose, O., Uhrmacher, A.M. (eds.) Proceedings of the 2012 Winter Simulation Conference, pp 385–398. Brussels (2012)
Irrgeher, C., Leobacher, G.: Fast orthogonal transforms for multilevel quasi-Monte Carlo simulation in computational finance. In: Vanmaele, W., et al. (eds.) Proceedings of Actuarial and Financial Mathematics Conference 2013, Interplay between Finance and Insurance, pp. 45–49. Berlin (2013)
Keiner, J., Waterhouse, B.J.: Fast principal components analysis method for finance problems with unequal time steps. In: L’Ecuyer, P., Owen, A.B. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2008, pp. 455–465. Springer, Berlin (2009)
Leobacher, G.: Stratified sampling and quasi-Monte Carlo simulation of Lévy processes. Monte-Carlo Methods Appl. 12, 231–238 (2006)
Leobacher, G.: Fast orthogonal transforms and generation of Brownian paths. J. Complex. 28, 278–302 (2012)
Novak, E., Woźniakowski, H.: Tractability of Multivariate Problems, Volume I: Linear Information. EMS, Zurich (2008)
Papageorgiou, A.: The Brownian bridge does not offer a consistent advantage in quasi-Monte Carlo integration. J. Complex. 18, 171–186 (2002)
Scheicher, K.: Complexity and effective dimension of discrete Lévy areas. J. Complex. 23, 152–168 (2007)
Wang, X., Sloan, I.H.: Quasi-Monte Carlo methods in financial engineering: an equivalence principle and dimension reduction. Oper. Res. 59, 80–95 (2011)
Wichura, M.J.: Algorithm AS 241: the percentage points of the normal distribution. J. R. Stat. Soc. Ser. C (Appl. Stat.) 37, 477–484 (1988)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Leobacher, G., Pillichshammer, F. (2014). Monte Carlo and Quasi-Monte Carlo Simulation. In: Introduction to Quasi-Monte Carlo Integration and Applications. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-03425-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-03425-6_8
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-03424-9
Online ISBN: 978-3-319-03425-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)