The traditional deviation of the Black and Scholes formula is widely accepted in spite of the unsatisfactory assumptions. One of the parameters affecting the value of option is the interest rate, which is assumed constant in the traditional Black and Scholes models. The assumption is convenient to find the formula and to use the formula in the business world, but not consistent with the knowledge of term structures of interest rates.
The randomness of interest rates is more acceptable assumption. In this paper we investigated the stochastic interest rates and presented alternative option pricing formulae. To include the randomness of interest rates in the model, we proposed that the excess rate of return has the feature of a stochastic process. Various types of option are studied to get the pricing formulae.
