Explain the framework of a binomial tree for interest rates
The idea
A binomial interest rate tree shows the possible one-period rates at each future date, with up and down moves equally likely. In the standard lognormal model, neighbouring rates at the same date differ by the factor e raised to 2σ, where σ is the annual volatility of rates, so the lower rate equals the upper rate × e raised to −2σ. This keeps rates positive and makes absolute volatility rise with the level of rates. At date n there are n + 1 nodes, and the middle node rates reflect the centre of the distribution. Each node's value is the average of the two values it leads to, plus any cash flow, discounted at that node's rate. Using e raised to σ rather than e raised to 2σ is a classic slip.
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