Pricing and Hedging with Discontinuous Functions: Quasi–Monte Carlo Methods and Dimension Reduction

Published Online:https://doi.org/10.1287/mnsc.1120.1568

References

  • Acworth P, Broadie M, Glasserman P, Niederreiter H, Hellekalek P, Larcher G, Zinterhof P. A comparison of some Monte Carlo and quasi–Monte Carlo techniques for option pricing. Monte Carlo and Quasi-Monte Carlo Methods 1996 (1998) (Springer-Verlag, New York) 1–18CrossrefGoogle Scholar
  • Avramidis AN, L'Ecuyer P. Efficient Monte Carlo and quasi–Monte Carlo option pricing under the variance gamma model. Management Sci. (2006) 52:1930–1944LinkGoogle Scholar
  • Berblinger M, Schlier Ch, Weiss T. Monte Carlo integration with quasi-random numbers: Experience with discontinuos integrands. Comput. Phys. Comm. (1997) 99:151–162CrossrefGoogle Scholar
  • Boyle P, Broadie M, Glasserman P. Monte Carlo methods for security pricing. J. Econom. Dynam. Control (1997) 21:1267–1321CrossrefGoogle Scholar
  • Broadie M, Glasserman P. Estimating security price derivatives using simulation. Management Sci. (1996) 42:269–285LinkGoogle Scholar
  • Caflisch RE, Morokoff W, Owen A. Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension. J. Comput. Finance (1997) 1:27–46CrossrefGoogle Scholar
  • Glasserman P. Monte Carlo Methods in Financial Engineering (2004) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Glasserman P, Heidelberger P, Shahabuddin P. Asymptotically optimal importance sampling and stratification for pricing path-dependent options. Math. Finance (1999) 9:117–152CrossrefGoogle Scholar
  • Imai J, Tan KS. A general dimension reduction method for derivative pricing. J. Comput. Finance (2006) 10:129–155Google Scholar
  • Imai J, Tan KS. An accelerating quasi-Monte Carlo method for option pricing under the generalized hyperbolic Lévy process. SIAM J. Sci. Comput. (2009) 31:2282–2302CrossrefGoogle Scholar
  • Jin X, Zhang AX. Reclaiming quasi-Monte Carlo efficiency in portfolio value-at-risk simulation through Fourier transform. Management Sci. (2006) 52:925–938LinkGoogle Scholar
  • Joy C, Boyle PP, Tan KS. Quasi-Monte Carlo methods in numerical finance. Management Sci. (1996) 42:926–938LinkGoogle Scholar
  • L'Ecuyer P. Quasi-Monte Carlo methods with applications in finance. Finance Stochastics (2009) 13:307–349CrossrefGoogle Scholar
  • L'Ecuyer P, Lemieux C. Variance reduction via lattice rules. Management Sci. (2000) 46:1214–1235LinkGoogle Scholar
  • L'Ecuyer P, Lemieux C, Dror M, L'Ecuyer P, Szidarovszki F. Recent advances in randomized quasi-Monte Carlo methods. Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications (2002) (Kluwer Academic, Norwell, MA) 419–474CrossrefGoogle Scholar
  • L'Ecuyer P, Perron G. On the convergence rates of IPA and FDC derivative estimators. Oper. Res. (1994) 42:643–656LinkGoogle Scholar
  • Lemieux C. Monte Carlo and Quasi-Monte Carlo Sampling (2009) (Springer-Verlag, New York) Google Scholar
  • Liu R, Owen AB. Estimating mean dimensionality of analysis of variance decomposition. J. Am. Stat. Assoc. (2006) 101:712–721CrossrefGoogle Scholar
  • Morokoff WJ, Caflisch RE. Quasi-random sequences and their discrepancies. SIAM J. Sci. Comput. (1994) 15:1251–1279CrossrefGoogle Scholar
  • Morokoff WJ, Caflisch RE. Quasi-Monte Carlo integration. J. Comput. Phys. (1995) 122:218–230CrossrefGoogle Scholar
  • Moskowitz B, Caflisch RE. Smoothness and dimension reduction in quasi–Monte Carlo methods. Math. Comput. Modelling (1996) 23:37–54CrossrefGoogle Scholar
  • Niederreiter H. Random Number Generation and Quasi-Monte Carlo Methods (1992) (SIAM, Philadelphia) CrossrefGoogle Scholar
  • Ninomiya S, Tezuka S. Toward real-time pricing of complex financial derivatives. Appl. Math. Finance (1996) 3:1–20CrossrefGoogle Scholar
  • Owen AB. The dimension distribution and quadrature test functions. Statist. Sinica (2003) 13:1–17Google Scholar
  • Papageorgiou A. The Brownian bridge does not offer a consistent advantage in quasi-Monte Carlo integration. J. Complexity (2002) 18:171–186CrossrefGoogle Scholar
  • Paskov SH, Traub JF. Faster valuation of financial derivatives. J. Portfolio Management (1995) 22:113–120CrossrefGoogle Scholar
  • Sloan IH, Woźniakowski H. When are quasi-Monte Carlo algorithms efficient for high dimensional integrals? J. Complexity (1998) 14:1–33CrossrefGoogle Scholar
  • Sobol' IM. On the distribution of points in a cube and the approximate evaluation of integrals. Zh. Vychisli. Mat. i Mat. Fiz. (1967) 7:784–802Google Scholar
  • Staum J, L'Ecuyer P, Owen AB. Monte Carlo computation in finance. Monte Carlo and Quasi-Monte Carlo 2008 (2009) (Springer-Verlag, New York) 19–42CrossrefGoogle Scholar
  • Wang X. On the effects of dimension reduction techniques on high-dimensional problems in finance. Oper. Res. (2006) 54:1063–1078LinkGoogle Scholar
  • Wang X. Constructing robust good lattice rules for computational finance. SIAM J. Sci. Comput. (2007) 29:598–621CrossrefGoogle Scholar
  • Wang X, Fang K-T. The effective dimensions and quasi-Monte Carlo integration. J. Complexity (2003) 19:101–124CrossrefGoogle Scholar
  • Wang X, Sloan IH. Projections of low discrepancy sequences: How well are they distributed? J. Comput. Appl. Math. (2008) 213:366–386CrossrefGoogle Scholar
  • Wang X, Sloan IH. Quasi-Monte Carlo methods in financial engineering: An equivalent principle and dimension reduction. Oper. Res. (2011) 59:80–95LinkGoogle Scholar
  • Wang X, Tan KS. How do path generation methods affect the accuracy of quasi-Monte Carlo methods for problems in finance? J. Complexity (2012) 28:250–277CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.