Asian Option Pricing Under Stochastic Interest Rate Model

Asian option is a typical representative of strongly path dependent option.Its value depends on the the average price of the underlying asset at a certain period of time.It first,appeared in Japan,so we call it Asian option.Because of strong path dependernce,the price of Asian option is cheaper than the corresponding European Option.Asian option plays an important role in limiting the subject of manipulation of underlying asset price behavior.For these reasons,people pay much attention on Asian option.Because of its strong path dependence,its pricing problem is also very complicate but a hot and very meaningful topic.This paper presents a theory of continuous sampled Asian option pricing when the interest rate is modeled by Vasicek model.For geometric average Asian option,we get a PDE which the price of the geometric average Asian option satisfied.We take the method of changing of numeraire as a reference,then we struct a fully new numeraire method,so that we can get a one-dimensional PDE which the price of the geometric average Asian option satisfied.Finally,we give a explicit solution to the PDE.For arithmetic average Asian option,we make a adopt infinite scheme to calculate the solution numerically.And we give an example of how to calculate the price of arithmetic average Asian option.