Pricing Of Asian Option On Riemannian Manifold

In the Classical Black-Scholes model,it is assumed that the underlying asset price process follows the geometric Euclidean Brownian motion.Under this assumption,there are more mature theories and methods of derivatives pricing.In the real world,however,the price of the underlying asset is affected not only by time,but also by other potential factors such as exchange rate,inflation,policy implementation and so on.That is to say,the change of the underlying asset price is no longer just a process of time.Based on this consideration,YongChao Zhang [3] studied the European option pricing problem under the geometric Riemannian Brownian motion on Riemannian manifold(7)g M,(8).As far as we know,the study of option pricing on manifolds is still in its infancy,with only a few research results,and the main contents of the study are mostly focused on European option pricing.Considering the realistic meaning of Asian option,this paper explores the pricing problem of Asian option on Riemannian manifold in order to give the pricing formula of Asian option.Firstly,by referring to the relation between the Riemannian Brownian motion on the Riemannian manifold and the European Brownian motion,the geometric average Asian option pricing model on Riemannian manifold is derived,and a semi-explicit solution of this kind of models is given by using the fundamental solution technique;Secondly,the pricing problem of Asian option on Riemannian manifold under incomplete hedging is discussed initially,and a semi-explicit solution to a kind of Asian option pricing model based on incomplete hedging is given;Finally,an example of Asian option pricing on Riemannian manifold is given.