Trinomial approach

The first stage in the approach ignores the observed market rates and centres the evolution of rates around zero and identifies the point at which the mean-reversion process takes effect. The second stage introduces the observed market rates into the framework established in stage one. The trinomial approach gives the tree a great deal more flexibility over its binomial counterpart, not least in relaxing the assumption that rates can either rise or fall with probability 0.5. 

One popular way of turning theory into practice is to use a tree approach to modelling. The tree can be either binomial or trinomial in its construction. To illustrate the idea consider first the binomial approach. The tree could be set up to reflect observed or estimated market short rates and the data provided in Exhibit 18.2 will help to demonstrate this idea. 

As an alternative to this binomial approach, Hull and White have suggested a two-stage methodology that uses a mean-reverting process with the short rate as the source of uncertainty and calculated in a trinomial tree framework. 

It is seen that lines 1, 2 and lines 3, 4 diverge as they approach the cloud boundary (P/Pq 1), but they converge with increasing distance from the epicenter (P/Pq c>o). The accuracy of the above correlations is about of 15%. The advantage of these dependencies over the pioneering correlations presented by the trinomial equations in [2, 3] is that there is no need to take into account the part of the blast transition energy leaving with the pressure wave. 

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