The math is a little beyond introductory algebra,but what is clear is that some of our most important pricing models are not designed to accommodate negative interest rates. What’s a regulator to do?
Now that interest rates have become very low or even negative it is no longer reasonable or even possible to use Black’s model since it does not allow negative rates. Of the four models only the Bachelier model allows rates to become negative. In the other three cases when rates may become negative it is necessary to modify the model by adding a shift, , to the forward rate. For example, the shifted or displaced version of Black’s model obeys