LO 13.4: Construct a short-term rate tree under the Ho-Lee M odel with time-

LO 13.4: Construct a short-term rate tree under the Ho-Lee M odel with time- dependent drift.
The Ho-Lee model further generalizes the drift to incorporate time-dependency. That is, the drift in time 1 may be different than the drift in time 2; additionally, each drift does not have to increase and can even be negative. Thus, the model is more flexible than the constant drift model. Once again, the drift is a combination of the risk premium over the period and the expected rate change. The tree in Figure 4 illustrates the interest rate structure and effect of time-dependent drift.
Figure 4: Interest Rate Tree with Time-Dependent Drift
It is clear that if X1 = X2 then the Ho-Lee model reduces to Model 2. Also, it should not be surprising that X j and X2 are estimated from observed market prices. In other words, the observed one-period spot rate. Xj could then be estimated so that the model rate equals the observed two-period market rate. X2 could be calibrated from using observed market rate for a three-period security, and so on.
and X1 and the
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A r b i t r a g e -F r e e M o d e l s

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