In this paper we analytically study the pricing of the arithmetically averaged Asian option in the path integral formalism. By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action  whose potential term is an exponential function , i. e. the Liouville Hamiltonian, which can be explicitly solved .  After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion expression of the value of an Asian option .
In this paper we analytically study the problem of pricing an arithmetically averaged Asian option in the path integral formalism. By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action functional whose potential term is an exponential function . This path integral is evaluated by use of the Feynman-Kac theorem. After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion for the value of Asian options .
R
pricing of the
problem of pricing an
A
functional
D
, i. e. the Liouville Hamiltonian, which can be explicitly solved
A
This path integral is evaluated by use of the Feynman-Kac theorem.
R
expression of
for
R
an Asian option
Asian options