Quasi-Monte Carlo methods for derivatives on realised variance of an index under the benchmark approach


  • Jan Baldeaux
  • Leung Lung Chan
  • Eckhard Platen




Quasi-Monte Carlo Methods, Mathematical Finance, Benchmark Approach


We apply quasi-Monte Carlo methods to the pricing of derivatives on realised variance of an index under the benchmark approach. The resulting integration problem is shown to depend on the joint density of the realised variance of the index and the terminal value of the index. Employing a transformation mapping for this joint density to the unit square reduces the difficulty of the resulting integration problem. The quasi-Monte Carlo methods compare favourably to Monte Carlo methods when applied to the given problem. References
  • J. Abate and W. Whitt, Numerical inversion of Laplace transforms of probability distributions, ORSA J. Comput., 7(1), 36--43, 1995. http://www.columbia.edu/ ww2040/Fall03/LaplaceInversionJoC95.pdf
  • J. Baldeaux, L. Chan, and E. Platen, Derivatives on realised variance and volatility of an index under the benchmark approach, University of Technology, Sydney, (working paper).
  • M. Craddock and K. Lennox, The calculation of expectations for classes of diffusion processes by Lie symmetry methods, Ann. Appl. Prob., 19(1), 127--157, 2009. http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.4806v1.pdf
  • H. Hong and F. Hickernell, Algorithm 823: Implementing scrambled digital sequences, ACM Transactions on Mathematical Software, 29(2), 95--109, 2003.
  • F. Y. Kuo, W. T. M. Dunsmuir, I. H. Sloan, M. P. Wand, and R. Womersley, Quasi-Monte Carlo for highly structured generalised response models, Methodology and Comp. Appl. Prob., 10(2), 239--275, 2008. http://www.uow.edu.au/ mwand/publicns/Kuo08.pdf
  • A. B. Owen, Randomly permuted $(t,m,s)$-nets and $(t,s)$-sequences, In H. Niederreiter and J. S. Shiue (Eds.), Monte Carlo and quasi-Monte Carlo methods in scientific computing, 299--317, Springer, 1995.
  • E. Platen and D. Heath, A Benchmark Approach to Quantitative Finance, Springer Finance, Springer, 2006.





Proceedings Computational Techniques and Applications Conference