393
Views
5
CrossRef citations to date
0
Altmetric
Research Papers

High-performance financial simulation using randomized quasi-Monte Carlo methods

&
Pages 1425-1436 | Received 31 Mar 2013, Accepted 18 Mar 2014, Published online: 11 May 2015

References

  • Antonov, I.A. and Saleev, V.M., An economic method of computing LPt–-Sequences. English translation. U.S.S.R. Comput. Maths. Math. Phys., 1979, 19, 252–256.
  • Black, F., The pricing of commodity contracts. J. Financ. Econ., 1976, 3, 167–179.
  • Brace, A., Gatarek, D. and Musiela, M., The market model of interest rate dynamics. Math. Finance, 1997, 7, 127–155.
  • Bromley, B.C., Quasirandom number generators for parallel Monte Carlo algorithms. J. Parallel Distrib. Comput., 1996, 38, 101–104.
  • Caflisch, R.E., Morokoff, W. and Owen, A.B., Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension. J. Comput. Finance, 1997, 1, 27–46.
  • Chen, G., Thulasiraman, P. and Thulasiram, R.K., Distributed quasi-Monte Carlo algorithm for option pricing on HNOWs using mpC. In Proceedings of the 39th Annual Simulation Symposium, Huntsville, AL, 2--6 April, 2006, pp. 90–97, 2006.
  • deDoncker, E., Zanny, R., Ciobanu, M. and Guan, Y., Distributed quasi Monte-Carlo methods in a heterogeneous environment. In Proceedings of the 9th Heterogeneous Computing Workshop, Cancun, Mexico, May, 2000, pp. 200–206, 2000.
  • Glasserman, P., Monte Carlo Methods in Financial Engineering, 2003 (Springer: New York).
  • Heath, D., Jarrow, R. and Morton, A., Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 1992, 60, 77–105.
  • Hofbauer, H., Uhl, A. and Zinterhof, P., Parameterization of Zinterhof sequences for GRID-based QMC integration. In Proceedings of the 2nd Austrian Grid Symposium, volume 221 of [email protected], edited by J. Volkert, T. Fahringer, D. Kranzlmüller and W. Schreiner, pp. 91–105, 2007 (Austrian Computer Society: Innsbruck).
  • Jamshidian, F., Libor and swap market models and measures. Finance Stoch., 1997, 1, 43–67.
  • Joe, S. and Kuo, F.Y., Constructing Sobol’ sequences with better two-dimensional projections. SIAM J. Sci. Comput., 2008, 30, 2635–2654.
  • Li, J.X. and Mullen, G.L., Parallel computing of a quasi-Monte Carlo algorithm for valuing derivatives. Parallel Comput., 2000, 26, 641–653.
  • Marsaglia, G., Xorshift RNGs. J. Stat. Softw., 2003, 8(14), 1–6.
  • Matoušek, J., On the L2-discrepancy for anchored boxes. J. Complexity, 1998, 14, 527–556.
  • Matsumoto, M. and Nishimura, T., Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Trans. Model. Comput. Simul., 1998, 8(1), 3–30.
  • Matsumoto, M. and Nishimura, T., Dynamic creation of pseudorandom number generators. In Monte Carlo and Quasi-Monte Carlo Methods 1998, edited by H. Niederreiter and J. Spanier, pp. 56–69, 2000 (Springer: Berlin).
  • Miltersen, K.R., Sandmann, K. and Sondermann, D., Closed-form solutions for term structure derivatives with lognormal interest rates. J. Finance, 1997, 52, 409–430.
  • Musiela, M. and Rutkowski, M., Continuous-time term structure models: Forward measure approach. Finance Stoch., 1997, 1, 261–292.
  • Niederreiter, H., Random Number Generation and Quasi-Monte Carlo Methods, 1992, 8(14) (SIAM: Philadelphia, PA).
  • Ökten, G., Generalized von Neumann--Kakutani transformation and random-start scrambled Halton sequences. J. Complexity, 2009, 25(4), 318–331.
  • Ökten, G. and Eastman, W., Randomized quasi-Monte Carlo methods in pricing securities. J. Econ. Dyn. Control, 2004, 28, 2399–2426.
  • Ökten, G., Shah, M. and Goncharov, Y., Random and deterministic digit permutations of the Halton sequence. In Monte Carlo and Quasi-Monte Carlo Methods 2010, edited by L. Plaskota and H. Woźniakowski, pp. 609–622, 2012 (Springer: Berlin).
  • Ökten, G. and Srinivasan, A., Parallel quasi-Monte Carlo applications on a heterogeneous cluster. In Monte Carlo and Quasi-Monte Carlo Methods 2000, edited by K.T. Fang, F.J. Hickernell and H. Niederreiter, pp. 406–421, 2002 (Springer-Verlag: Berlin).
  • Ökten, G. and Willyard, M., Parameterization based on randomized quasi-Monte Carlo methods. Parallel Comput., 2010, 36, 415–422.
  • Saito, M. and Matsumoto, M., A deviation of CURAND: Standard pseudorandom number generator in CUDA for GPGPU. In 10th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Sydney, Australia, 13--17 February, 2012.
  • Salmon, J.K., Moraes, M.A., Dror, R.O. and Shaw, D.E., Parallel random numbers: As easy as 1, 2, 3. In SC’11 Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, New York, 2011.
  • Schmid, W. and Uhl, A., Parallel Quasi-Monte Carlo integration using (t, s)-sequences. Vol. 1557, Lecture Notes in Computer Science, 2010 (Springer), pp. 96–106.
  • Schmid, W. and Uhl, A., Techniques of parallel quasi-Monte Carlo integration with digital sequences and associated problems. Math. Comput. Simul., 2001, 55, 249–257.
  • Struckmeier, J., Fast generation of low-discrepancy sequences. J. Comput. Appl. Math., 1993, 61, 29–41.
  • Vandewoestyne, B. and Cools, R., Good permutations for deterministic scrambled Halton sequences in terms of L2-discrepancy. J. Comput. Appl. Math., 2006, 189, 341–361.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.