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Vasicek model recombining tree

Thread starter #1
Hi,

Can anyone demonstrate an example of how the rates in the Vasicek model tree is calculated? I am looking at Tuckman's chapter 9 study notes on page 57 (see attached). For example, how is the rate at (1,1) of 5.5060% calculated?

Thank you
 

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Thread starter #2
also im not sure if its a typo? in the picture the formula says (k*theta-r) but at the top of chapter it says k*(theta-r). Which one is correct?
 

David Harper CFA FRM

David Harper CFA FRM
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#3
HI @SalinaMiao The formula featured in the study note text is correct: dr = k (θ -r)dt + σdw. The displayed blue formula (that is part of the XLS screen) is incorrect (although the calculations are fine), apologies, and should match the text and consequently should appear as follows:


In regard to the calculations, they are in the XLS and explained by Tuckman in Chapter 7 (see below). However, the problem is that the node does not recombine naturally, see difference in values at node[2,1] inside red box:



Which he resolves as follows, I hope this explains(!):

 
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