Financial Simulation Modeling in Excel

HULL-WHITE INTEREST RATE MODEL

In the previous chapters we introduced many concepts related to stochastic analysis and in the previous sections we introduced how tree processes can be used to model financial derivatives. In the remainder of this chapter we will use those concepts to understand and implement the Hull-White interest rate model that is used to price bonds and derivatives. A number of methods can be used to perform this analysis. For example, the rating agency Moody's prefers a purely stochastic method by which the forward rate is explicitly determined by fitting the zero coupon yield curve with Nelson-Siegel parameters. For our purposes, however, we will expand on our previous discussion of the binomial tree method by using the trinomial tree strategy that was first proposed by John Hull and Alan White.

At first glance, you might be thinking, “Hey, sequentially constructing branches of a tree is not a simulation! Where is the randomness?” All this talk about random processes might have led you to believe that simulation is relevant only in a stochastic world. It is perfectly reasonable to associate simulation only with a method of getting information about an event that happens by chance. After all, if you can directly calculate an event, why would you need to simulate it? The answer to that question is rooted in the complexity of the problem. Sometimes a problem, even though it is solvable, is far too complex to actually solve! Let's take gravity as a physical example ...