We derive a unified model which gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero-coupon bonds. The crucial assumption is that forward rates with a compounding period that matches the contract, which we want to price, is...

Starting with observable annually compounded forward rates we derive a term structure model of interest rates. The model relies upon the assumption that a specific set of annually compounded forward rates is log-normally distributed. We derive solutions for interest rate caps and floors as well...

This paper constructs a model for the evolution of a risky security that is consistent with a set of observed call option prices. It explicitly treats the fact that only a discrete data set can be observed in practice. The framework is general and allows for state dependent volatility and jumps....

The problem of term structure of interest rates modelling is considered in a continuous-time framework. The emphasis is on the bond prices, forward bond prices or LIBOR rates, rather than on the instantaneous rates as in the traditional models. Forward and spot probability measures are...

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...