Computing short term rate using volatility

I want to know how to compute the short term rate given the volatility. Specific problem would be practice question 2 on page 297 of the alternative assets and fixed income book (vol 5). Can it be done or is it just given?

it can be done, and it is explained somewhere is the CFA curriculum although not very well… it is not very hard to understand, but it would be a waste of your time to try to learn it now, and a waste of mine to try to explain it… it is not required for the exam…if you want we talk about it on June 5th all you want…


just so that you dont go empty handed assume you wana do this for the first year one way is i up=i low *e^(2 sigma) you makes a guess a i low, then you compute i up according to this formula then you try to price a 1 year option free gov bond with your tiny tree if you get the market value, good your tree works if not, you make another guess based on whether you got a value too high or too low you compute i up again, you repeat untill you get it… a computer will do it for you obviously… and the formula above is not fact, it depends on the model you decide to use

* correction, i ment 2 year option free bond, obviously your one year would be valued using the first rate in the tree, r0