A Term Structure Model and the Pricing of Interest Rate Derivative

The paper developes a general arbitrage free model for the term structure of interest rates. The principal model is formulated in a discrete time structure. It differs substantially from the Ho--Lee-- Model (1986) and does not generate negative spot and forward rates. The results for the continuous time limit support this. The probability distribution with finite support is derived for the spot rate return. The model permits the arbitrage free valuation of bond options and interest rate options and produces dynamic portfolio strategies to duplicate these contracts.