TL;DR: In this paper, a financial option of which the payoff depends on the average value of the underlying security over some final time interval is discussed, and an expectation formula for the option value is given.
Abstract: In this paper we shall discuss a financial option of which the payoff depends on the average value of the underlying security over some final time interval After explaining what an option is about we will derive a partial differential equation for the option which is different from the partial differential equation of a simple European call option From this we will get an expectation formula for the option value We will give an economical as well as a mathematical argument for this expectation formula