Least Square Regression Methods for Bermudan Derivatives and Systems of Functions

Part of the Advances in Mathematical Economics book series (MATHECON, volume 19)


Least square regression methods are Monte Carlo methods to solve non-linear problems related to Markov processes and are widely used in practice. In these methods, first we choose a system of functions to approximate value functions. So one of questions on these methods is what kinds of systems of functions one has to take to get a good approximation. In the present paper, we will discuss on this problem.


Computational finance Option pricing Malliavin calculus Least square regression methods 


  1. 1.
    Bally V, Pagés G (2003) A quantization algorithm for solving multi-dimensional discrete-time optimal stopping problems. Bernoulli 9:1003–1049MathSciNetCrossRefGoogle Scholar
  2. 2.
    Belomestny D (2011) Pricing Bermudan options by nonparametric regression: optimal rates of convergence for lower estimates. Financ Stoch 15:655–683MathSciNetCrossRefGoogle Scholar
  3. 3.
    Castaing C, Valadier M (1977) Convex analysis and measurable multifunctions. Lecture notes in mathematics, vol 580. Springer, Berlin/New YorkGoogle Scholar
  4. 4.
    Clement E, Lamberton D, Protter P (2002) An analysis of a least squares regression algorithm for American option pricing. Financ Stoch 6:449–471MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gobet E, Lemor J-P, Warin X (2005) A regression-based Monte Carlo method to solve backward stochastic differential equations. Ann Appl Probab 15:2172–2202MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Kusuoka S, Morimoto Y (2014) Stochastic mesh methods for Hörmander type diffusion processes. In: Kusuoka S, Maruyama T (eds) Advances in mathematical economics, vol 18. Springer, Tokyo Heidelberg New York Dordrecht London, pp 61–99Google Scholar
  7. 7.
    Kusuoka S, Stroock DW (1985) Applications of Malliavin calculus II. J Fac Sci Univ Tokyo Sect IA Math 32:1–76MathSciNetGoogle Scholar
  8. 8.
    Longstaff F, Schwartz E (2001) Valuing American options by simulation: a simple least-squares approach. Rev Financ Stud 14:113–147CrossRefGoogle Scholar
  9. 9.
    Tsitsiklis J, Van Roy B (1999) Regression methods for pricing complex American style options. IEEE Trans Neural Netw 12:694–703CrossRefGoogle Scholar

Copyright information

© Springer Japan 2015

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan
  2. 2.Bank of Tokyo Mitsubishi UFJTokyoJapan

Personalised recommendations