In 1986 Ho/Lee presented a discrete-time binomial model of the stochastic movements of the term-structure of interest-rates. It has since been established that there is a fairly simple equivalent time framework using stochastic calculus it is straightforward to derive closed formulae for a number of interest-rate contingent claims.
In contrast to this approach the present paper follows the line of Cox, Ross and Rubinstein who derived the Black/Scholes formula as the continuous time limit of a discrete time option pricing formula. Similarly we show by considering the example of a European call option on a zero coupon bond how to derive discrete time pricing formulae for interest-rate contingent claims along with their continuous time limits in the Ho/Lee framework. This approach also makes transparent the relationship between Arrow/Debreu prices and the forward measure introduced by El Karoui/Rochet.
Using the results from the option pricing exercise we show how the continuous time distribution of the short-term interest rate under the forward measure can be obtained as a limit form dicrete time.
Finally, we consider multi-nomial generalizations of the Ho/Lee model that have been suggested in the literature and show that the continuous time limit of the distribution of sort-term interest-rates does not differ from the well known result for the Ho/Lee model.
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