Computing the Lower and Upper Bound Prices for Multi-asset Bermudan Options via Parallel Monte Carlo Simulations

Chapter

Abstract

We present our work on computing the lower and upper bound prices for multi-asset Bermudan options. For the lower bound price we follow the Longstaff-Schwartz least-square Monte Carlo method. For the upper bound price we follow the Andersen-Broadie duality-based nested simulation procedure. For case studies we computed the prices of Bermudan max-call options and Bermudan interest rate swaptions. The pricing procedures are parallelized through POSIX multi-threading. Times required by the procedures on ×86 multi-core processors are much shortened than those reported in previous work.

Keywords

Interest rate Bermudan swaption LIBOR market model Multi-asset Bermudan options Monte Carlo simulation Multi-threaded programming Parallel computing 

Notes

Acknowledgments

Research is partially funded by ESFA (VP1-3.2-ŠMM-01-K-02-002).

References

  1. 1.
    L. Andersen, J. Andreasen, Volatility skews and extensions of the Libor market model. Appl. Math. Finance 7, 1–32 (2000)CrossRefMATHGoogle Scholar
  2. 2.
    L. Andersen, M. Broadie, Primal-dual simulation algorithm for pricing multidimensional American options. Manage. Sci. 50(9), 1222–1234 (2004)CrossRefGoogle Scholar
  3. 3.
    F. Black, M. Scholes, The pricing of options and corporate liabilities. J. Polit. Econ. 81(3), 637–659 (1973)CrossRefGoogle Scholar
  4. 4.
    A. Brace, D. Gatarek, M. Musiela, The market model of interest rate dynamics. Math. Finance 7(2), 127–155 (1997)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    M. Broadie, M. Cao, Improved lower and upper bound algorithms for pricing American options by simulation. Quant. Finance 8(8), 845–861 (2008)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    J.F. Carriere, Valuation of the early-exercise price for options using simulations and nonparametric regression. Insur.: Math. Econ. 19(1), 19–30 (1996)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    J.C. Cox, S.A. Ross, M. Rubinstein, Option pricing: a simplified approach. J. Finance Econ. 7(3), 229–263 (1979)CrossRefMATHGoogle Scholar
  8. 8.
    J. Crank, The Mathematics of Diffusion, 2nd edn. (Oxford University Press, Oxford, 1980)Google Scholar
  9. 9.
    Intel Corporation. Intel Math Kernel Library for Linux OS: User’s Guide, (2011). Document Number: 314774-018USGoogle Scholar
  10. 10.
    Intel Corporation. Intel Math Kernel Library Reference Manual, (2011). Document Number: 630813-044USGoogle Scholar
  11. 11.
    F. Jamshidian, LIBOR and swap market models and measures. Finance Stochast. 1(4), 293–330 (1997)CrossRefMATHGoogle Scholar
  12. 12.
    D. Leisen, M. Reimer, Binomial models for option valuation-examining and improving convergence. Appl. Math. Finance 3, 319–346 (1996)CrossRefGoogle Scholar
  13. 13.
    F.A. Longstaff, E.S. Schwartz, Valuing American options by simulation: a simple least-squares approach. Rev. Financ. Stud. 14(1), 113–147 (2001)CrossRefGoogle Scholar
  14. 14.
    K.R. Miltersen, K. Sandmann, D. Sondermann, Closed form solutions for term structure derivatives with log-normal interest rates. J. Finance 52, 409–430 (1997)CrossRefGoogle Scholar
  15. 15.
    K.W. Morton, D.F. Mayers, Numerical Solution of Partial Differential Equations: An Introduction, 2nd edn. (Cambridge University Press, Cambridge, 2005)CrossRefGoogle Scholar
  16. 16.
    J.N. Tsitsiklis, B. Van Roy, Optimal stopping of Markov processes: Hilbert space theory, approximation algorithms, and an application to pricing high-dimensional financial derivatives. IEEE Trans. Autom. Control 44(10), 1840–1851 (1999)CrossRefMATHGoogle Scholar
  17. 17.
    N. Zhang, K.L. Man, Accelerating financial code through parallelisation and source-level optimisation, in Proceedings of the International MultiConference of Engineers and Computer Scientists 2014, IMECS 2014, Hong Kong, 12–14 Mar 2014. Lecture Notes in Engineering and Computer Science, pp. 805–806Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Computer Science and Software EngineeringXi’an Jiaotong-Liverpool UniversitySuzhouChina
  2. 2.Informatics FacultyVytautas Magnus UniversityKaunasLithuania
  3. 3.Baltic Institute of Advanced TechnologyVilniusLithuania

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