John Hull Interest Quotations

When interest rates are high you want the average direction in which interest rates are moving to be downward; when interest rates are low you want the average direction to be upward.

Our tree is actually a tree of the short-term interest rate. The average direction in which the short-term interest rate moves depends on the level of the rate. When the rate is very high, that direction is downward; when the rate is very low, it is upward.

The real challenge was to model all the interest rates simultaneously, so you could value something that depended not only on the three-month interest rate, but on other interest rates as well.

The problem with interest rates are that you are not modeling a single number, you are modeling a whole term structure, so it is a sort of different type of problem.

In the interest rate area, traders have for a long time used a version of what is known as Black's model for European bond options; another version of the same model for caps and floors; and yet another version of the same model for European swap options.