Apart from classical Black-Scholes model which assumes that forward interest rate is (log) normally distributed, what kind of pricing tools can we use as a buy side? We have good estimation on how interest term structure evolves. Moreover, the underlying interest rate is discrete with minimal changing 5 basis point.
First, it is interest rate options including swaptions, cap and floor. I want to price the options given my opinions on interest trend. As a major market player we have clear views on how the interest will evolve. Last, the underlying interest rate is set by central bank with 5 basis point minimum change. For example, it could be 4.25% or 4.20% but never 4.21%. I have finished learning most risk neutral pricing methods and want to know how to combine our points of view on how the interest rate evolve into those models.