Spectral expansions for Asian (average price) options

Vadim Linetsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

125 Scopus citations

Abstract

Arithmetic Asian or average price options deliver payoffs based on the average underlying price over a prespecified time period. Asian options are an important family of derivative contracts with a wide variety of applications in currency, equity, interest rate, commodity, energy, and insurance markets. We derive two analytical formulas for the value of the continuously sampled arithmetic Asian option when the underlying asset price follows geometric Brownian motion. We use an identity in law between the integral of geometric Brownian motion over a finite time interval [0, t] and the state at time t of a one-dimensional diffusion process with affine drift and linear diffusion and express Asian option values in terms of spectral expansions associated with the diffusion infinitesimal generator. The first formula is an infinite series of terms involving Whittaker functions M and W. The second formula is a single real integral of an expression involving Whittaker function W plus (for some parameter values) a finite number of additional terms involving incomplete gamma functions and Laguerre polynomials. The two formulas allow accurate computation of continuously sampled arithmetic Asian option prices.

Original languageEnglish (US)
Pages (from-to)856-867
Number of pages12
JournalOperations Research
Volume52
Issue number6
DOIs
StatePublished - Nov 2004

Keywords

  • Finance, asset pricing: option pricing
  • Finance, securities: Asian (average price) options
  • Probability, diffusion: average of geometric Brownian motion, spectral theory

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research

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