Bounds on prices for Asian options via Fourier methods

Scott Alexander, Alexander Novikov, Nino Kordzakhia

Abstract


The problem of pricing arithmetic Asian options is nontrivial, and has attracted much interest over the last two decades. This paper provides a method for calculating bounds on option prices and approximations to option deltas in a market where the underlying asset follows a geometric Lévy process. The core idea is to find a highly correlated, yet more tractable proxy to the event that the option finishes in-the-money. The paper provides a means for calculating the joint characteristic function of the underlying asset and proxy processes, and relies on Fourier methods to compute prices and deltas. Numerical studies show that the lower bound provides accurate approximations to prices and deltas, while the upper bound provides good though less accurate results.

doi:10.1017/S1446181115000231

Keywords


Asian option; lower bound; characteristic function; Fourier transform; inverse Fourier transform; exponential damping



DOI: http://dx.doi.org/10.21914/anziamj.v57i0.9004



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.