Path Dependent Options on Yields in the Affine Term Structure Model

We give analytical pricing formulae for path dependent options on yields in the framework of the affine term structure model. More precisely, European call options such as the arithmetic average call, the call on maximum and the lookback call are examined. For the two last options approximate formulae using the law of hitting times of an Ornstein-Uhlenbeck process are proposed. Numerical implementation is also briefly discussed and results are given in the case of the arithmetic average option