Market Implied Volatility Functions

Reproduction Example 1 of Generalized Procedure for Building Trees

In a recent (2014) paper John Hull and Alan White demonstrate a generalized method for the construction of short rate trees. Keen to understand the model we tried to reproduce the results of the first example mentioned in the paper on page 10. The example considers the short rate model:

dr = (\Theta(t)-ar)dt + \sigma r dz

which is transformed using

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