Credit analysis model - binomial tree confusion (eoc 8)

The Credit Analysis Model reading’s EOC 8 requires a binomial tree. could anyone please explain to me how they came up with the interest rates for node1,node2 and so on? Ive tried the E^(2*Volatility) formula but thats not how they did it. Im only confused about how they calculated the interest rates on the tree and would really appreciate if anyone could share the calculation/formula?

I checked only one: at time t = 1.

\ln\left(\frac{2.1180\%}{1.4197\%}\right) = 0.4 = 2 × 20\%

Seems right to me.

Thank you for replying. could you please explain to me how they got the 2.1180% and 1.4197% figures in the first place? thats what im confused about.

My pleasure.

By calibrating the tree. They know the par rate for a 2-year bond, so they guess at the lower rate, then move it up or down until the price of a 2-year bond whose coupon is the (known) par rate comes out to par (say, $1,000). It’s generally done using something like Solver in Excel.

You won’t have to calibrate a tree for the exam. At most, you’ll have to figure out the discount rate at one node given the rate at another node at the same time, along with the assumed interest rate volatility.