American Bond Options Close to Expiry

Abstract

We address the pricing of American-style options on zero coupon bondsunder the assumption that interest rates obey a mean-reverting random walkas given by the Vasicek model.We use a technique due to Kolodner (1956) and Kim (1990) to derive anexpression involving integrals for the price of such an option close toexpiry. We then evaluate this expression on the optimal exercise boundary to obtaina pair  of integral equations for the location of this exercise boundary,and solve these equations close to expiry.As with American equity options, as we approach expiry, there are threepossible behaviors for  the optimal exercise boundary.