The optimal method for pricing Bermudan options by simulation Articles uri icon

publication date

  • October 2018

start page

  • 1

end page

  • 38

issue

  • 4

volume

  • 28

International Standard Serial Number (ISSN)

  • 0960-1627

Electronic International Standard Serial Number (EISSN)

  • 1467-9965

abstract

  • Least-squares methods enable us to price Bermudan-style options by Monte Carlo simulation. They are based on estimating the option continuation value by least-squares. We show that the Bermudan price is maximized when this continuation value is estimated near the exercise boundary, which is equivalent to implicitly estimating the optimal exercise boundary by using the value-matching condition. Localization is the key difference with respect to global regression methods, but is fundamental for optimal exercise decisions and requires estimation of the continuation value by iterating local least-squares (because we estimate and localize the exercise boundary at the same time). In the numerical example, in agreement with this optimality, the new prices or lower bounds (i) improve upon the prices reported by other methods and (ii) are very close to the associated dual upper bounds. We also study the method's convergence.

subjects

  • Economics

keywords

  • american and bermudan options; local least-squares; optimal stopping-times; optimization; simulation