Integral Option

In the context of diffusion model of the $(B,S)$-market consisting of two assets: riskless bank account B = (Bₜ )t 0 and risky stock S = (Sₜ )t 0 described by (1.1) and (1.2) we consider the option of American type with payment function of “integral type” f = (fₜ )t 0: \[ f_t = e- λ t [ {∫_0^t {S^u du + sψ _0 } } ], \] The paper solves the problem of definition of the fair price of the integral option under consideration. The structure of the expiration time is also described.