LAPLACE BOUNDS APPROXIMATION FOR AMERICAN OPTIONS

Jingtang Ma, Zhenyu Cui, Wenyuan Li

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper, we develop the lower-upper-bound approximation in the space of Laplace transforms for pricing American options. We construct tight lower and upper bounds for the price of a finite-maturity American option when the underlying stock is modeled by a large class of stochastic processes, e.g. a time-homogeneous diffusion process and a jump diffusion process. The novelty of the method is to first take the Laplace transform of the price of the corresponding capped (barrier) option with respect to the time to maturity, and then carry out optimization procedures in the Laplace space. Finally, we numerically invert the Laplace transforms to obtain the lower bound of the price of the American option and further utilize the early exercise premium representation in the Laplace space to obtain the upper bound. Numerical examples are conducted to compare the method with a variety of existing methods in the literature as benchmark to demonstrate the accuracy and efficiency.

Original languageEnglish
Pages (from-to)514-547
Number of pages34
JournalProbability in the Engineering and Informational Sciences
Volume36
Issue number2
DOIs
StatePublished - 1 Apr 2022

Keywords

  • American option pricing
  • Laplace transform
  • early exercise boundary
  • jump diffusions
  • option bounds

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