Continuous-Time Limits in the Generalized Ho-Lee Framework under the Forward Measure

The forward measure in the discrete time Ho/Lee model is derived and passages to the continuous time limit are carried out under this measure. In particular the continuous time valuation formula for call options on zero coupon bonds is obtained as a limit of its discrete time equivalent as well as the continuous time distribution of the continuously compounded short rate. Finally it is shown that the trinomial and quattronomial generalizations of the Ho/Lee model by Bühler and Schulze are essentially equivalent to the Ho/Lee model as concernes their discrete time properties and their continuous time limits.