Skip to main content
Erschienen in: The Journal of Supercomputing 9/2015

01.09.2015

Accelerating the least-square Monte Carlo method with parallel computing

verfasst von: Ching-Wen Chen, Kuan-Lin Huang, Yuh-Dauh Lyuu

Erschienen in: The Journal of Supercomputing | Ausgabe 9/2015

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper accelerates the critically important least-squares Monte Carlo method (LSM) in financial derivatives pricing with parallel computing. We parallelize LSM with space decomposition, turning it into an embarrassingly parallel algorithm. The program is implemented with Parallel Virtual Machine and ALGLIB. Our method gives accurate option prices with excellent speedup. Although this paper focuses on the pricing of options, the methodology is applicable to much more complex financial derivatives.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Amdahl GM (1967) Validity of the single processor approach to achieving large-scale computing capabilities. In: Proceedings of the AFIPS ’67, spring joint computer conference. ACM, New York, pp 483–485 Amdahl GM (1967) Validity of the single processor approach to achieving large-scale computing capabilities. In: Proceedings of the AFIPS ’67, spring joint computer conference. ACM, New York, pp 483–485
2.
Zurück zum Zitat Bellman R (1957) Dynamic programming. Princeton University Press, PrincetonMATH Bellman R (1957) Dynamic programming. Princeton University Press, PrincetonMATH
3.
Zurück zum Zitat Benzi J, Damodaran M (2007) Parallel three dimensional direct simulation Monte Carlo for simulating micro flows. In: Proceedings of parallel computational fluid dynamics 2007: implementations and experiences on large scale and grid computing. Springer, Antalya, pp 91–98 Benzi J, Damodaran M (2007) Parallel three dimensional direct simulation Monte Carlo for simulating micro flows. In: Proceedings of parallel computational fluid dynamics 2007: implementations and experiences on large scale and grid computing. Springer, Antalya, pp 91–98
4.
Zurück zum Zitat Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81(3):637–654CrossRefMATH Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81(3):637–654CrossRefMATH
6.
Zurück zum Zitat Bouchard B, Warin X (2010) Monte-Carlo valuation of American options: facts and new algorithms to improve existing methods. In: Carmona RA, Moral PD, Oudjane N (eds) Numerical methods in finance. Springer, Bordeaux Bouchard B, Warin X (2010) Monte-Carlo valuation of American options: facts and new algorithms to improve existing methods. In: Carmona RA, Moral PD, Oudjane N (eds) Numerical methods in finance. Springer, Bordeaux
8.
9.
Zurück zum Zitat Chaudhary SK (2005) American options and the LSM algorithm: quasirandom sequences and Brownian bridges. J Comput Financ 8:101–115 Chaudhary SK (2005) American options and the LSM algorithm: quasirandom sequences and Brownian bridges. J Comput Financ 8:101–115
10.
Zurück zum Zitat Choudhury AR, King A, Kumar S, Sabharwal Y (2008) Optimizations in financial engineering: The least-squares Monte Carlo method of Longstaff and Schwartz. In: Proceedings of the 2008 IEEE international parallel and distributed processing symposium. IEEE Computer Society, Miami, pp 1–11 Choudhury AR, King A, Kumar S, Sabharwal Y (2008) Optimizations in financial engineering: The least-squares Monte Carlo method of Longstaff and Schwartz. In: Proceedings of the 2008 IEEE international parallel and distributed processing symposium. IEEE Computer Society, Miami, pp 1–11
11.
Zurück zum Zitat Clément E, Lamberton D, Protter P (2002) An analysis of a least squares regression method for American option pricing. Financ Stoch 6(3):449–471CrossRefMATH Clément E, Lamberton D, Protter P (2002) An analysis of a least squares regression method for American option pricing. Financ Stoch 6(3):449–471CrossRefMATH
12.
Zurück zum Zitat Cox JC, Ross S, Rubinstein M (1979) Option pricing: a simplified approach. J Financ Econ 7(3):229–263CrossRefMATH Cox JC, Ross S, Rubinstein M (1979) Option pricing: a simplified approach. J Financ Econ 7(3):229–263CrossRefMATH
13.
Zurück zum Zitat Dariusz G, Przemyslaw B, Robert M (2007) Using the LSM approach for derivatives valuation. The LIBOR market model in practice. Wiley, Oxford, pp 229–257 Dariusz G, Przemyslaw B, Robert M (2007) Using the LSM approach for derivatives valuation. The LIBOR market model in practice. Wiley, Oxford, pp 229–257
14.
Zurück zum Zitat Doan VD, Gaikwad A, Bossy M, Baude F, Stokes-Rees I (2010) Parallel pricing algorithms for multi-dimensional Bermudan/American options using Monte Carlo methods. Math Comput Simula 81(3):568–577MathSciNetCrossRefMATH Doan VD, Gaikwad A, Bossy M, Baude F, Stokes-Rees I (2010) Parallel pricing algorithms for multi-dimensional Bermudan/American options using Monte Carlo methods. Math Comput Simula 81(3):568–577MathSciNetCrossRefMATH
16.
Zurück zum Zitat Eager DL, Zahorjan J, Lazowska ED (1989) Speedup versus efficiency in parallel systems. IEEE Trans Comput 38(3):408–423CrossRef Eager DL, Zahorjan J, Lazowska ED (1989) Speedup versus efficiency in parallel systems. IEEE Trans Comput 38(3):408–423CrossRef
17.
Zurück zum Zitat Fox GC, Williams RD, Messina GC (1994) Parallel computing works!. Morgan Kaufmann, Burlington Fox GC, Williams RD, Messina GC (1994) Parallel computing works!. Morgan Kaufmann, Burlington
18.
Zurück zum Zitat Haug EG (2007) The complete guide to option pricing formulas, 2nd edn. McGraw-Hill, New York Haug EG (2007) The complete guide to option pricing formulas, 2nd edn. McGraw-Hill, New York
19.
Zurück zum Zitat Hennessy JL, Patterson DA (2011) Computer architecture: a quantitative approach, 5th edn. Morgan Kaufmann, Burlington Hennessy JL, Patterson DA (2011) Computer architecture: a quantitative approach, 5th edn. Morgan Kaufmann, Burlington
20.
Zurück zum Zitat James L, Dennis G (2009) Multicore computing and scientific discovery. In: Tony H, Stewart T, Kristin T (eds) The fourth paradigm: data-intensive scientific discovery, 1st edn. Microsoft Research, Washington James L, Dennis G (2009) Multicore computing and scientific discovery. In: Tony H, Stewart T, Kristin T (eds) The fourth paradigm: data-intensive scientific discovery, 1st edn. Microsoft Research, Washington
21.
Zurück zum Zitat Létourneau P, Stentoft L (2014) Refining the least squares Monte Carlo method by imposing structure. Quant Financ 14(3):495–508CrossRefMATH Létourneau P, Stentoft L (2014) Refining the least squares Monte Carlo method by imposing structure. Quant Financ 14(3):495–508CrossRefMATH
22.
Zurück zum Zitat Longstaff FA, Schwartz ES (2001) Valuing American options by simulation: a simple least-squares approach. Rev Financ Stud 14(1):113–147CrossRef Longstaff FA, Schwartz ES (2001) Valuing American options by simulation: a simple least-squares approach. Rev Financ Stud 14(1):113–147CrossRef
23.
Zurück zum Zitat Lyuu YD, Wen KW, Wu YC (2014) Performance of GPU for pricing financial derivatives. J Inf Sci Eng 30(1):141–155 Lyuu YD, Wen KW, Wu YC (2014) Performance of GPU for pricing financial derivatives. J Inf Sci Eng 30(1):141–155
24.
Zurück zum Zitat Moreno M, Navas JF (2003) On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives. Rev Deriv Res 6(2):107–128CrossRefMATH Moreno M, Navas JF (2003) On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives. Rev Deriv Res 6(2):107–128CrossRefMATH
25.
Zurück zum Zitat Richard DL, Stephen JT, John MD (2001) Terascale spectral element dynamical core for atmospheric general circulation models. In: Proceedings of the 2001 ACM/IEEE conference on supercomputing. ACM, New York Richard DL, Stephen JT, John MD (2001) Terascale spectral element dynamical core for atmospheric general circulation models. In: Proceedings of the 2001 ACM/IEEE conference on supercomputing. ACM, New York
26.
Zurück zum Zitat Stentoft L (2004) Convergence of the least squares Monte Carlo approach to American option valuation. Manag Sci 50(9):1193–1203CrossRef Stentoft L (2004) Convergence of the least squares Monte Carlo approach to American option valuation. Manag Sci 50(9):1193–1203CrossRef
27.
Zurück zum Zitat Sunderam VS (1990) PVM: a framework for parallel distributed computing. Concurr Pract Exp 2(4):315–339CrossRef Sunderam VS (1990) PVM: a framework for parallel distributed computing. Concurr Pract Exp 2(4):315–339CrossRef
28.
Zurück zum Zitat Wan JWL, Lai K, Kolkiewicz AW, Tan KS (2006) A parallel quasi-Monte Carlo approach to pricing American options on multiple assets. Int J High Perform Comput Network 4(5/6):321–330CrossRef Wan JWL, Lai K, Kolkiewicz AW, Tan KS (2006) A parallel quasi-Monte Carlo approach to pricing American options on multiple assets. Int J High Perform Comput Network 4(5/6):321–330CrossRef
29.
Zurück zum Zitat Wilkinson B, Allen M (1999) Parallel programming: techniques and applications using networked workstations and parallel computers. Prentice Hall, Upper Saddle River Wilkinson B, Allen M (1999) Parallel programming: techniques and applications using networked workstations and parallel computers. Prentice Hall, Upper Saddle River
30.
Zurück zum Zitat Zhang N, Roux A, Zastawniak T (2011) Parallel binomial valuation of American options with proportional transaction costs. In: Temam O, Yew PC, Zang B (eds) Lecture notes in computer science. Advanced parallel processing technologies. Springer, Heidelberg, pp 88–97CrossRef Zhang N, Roux A, Zastawniak T (2011) Parallel binomial valuation of American options with proportional transaction costs. In: Temam O, Yew PC, Zang B (eds) Lecture notes in computer science. Advanced parallel processing technologies. Springer, Heidelberg, pp 88–97CrossRef
Metadaten
Titel
Accelerating the least-square Monte Carlo method with parallel computing
verfasst von
Ching-Wen Chen
Kuan-Lin Huang
Yuh-Dauh Lyuu
Publikationsdatum
01.09.2015
Verlag
Springer US
Erschienen in
The Journal of Supercomputing / Ausgabe 9/2015
Print ISSN: 0920-8542
Elektronische ISSN: 1573-0484
DOI
https://doi.org/10.1007/s11227-015-1451-7

Weitere Artikel der Ausgabe 9/2015

The Journal of Supercomputing 9/2015 Zur Ausgabe