Explain how a binomial interest rate tree is calibrated so that it fits a given term structure
The idea
Calibrating a tree means choosing node rates so that it reproduces the market prices of the benchmark bonds, usually par bonds priced at 100. Start with the one-year rate. For each later date, fix the volatility, which sets the ratio between neighbouring nodes, and search for the lowest rate at that date that makes the next benchmark bond worth exactly 100 when valued backward through the tree. Repeat maturity by maturity. A tree is checked by revaluing each benchmark: if a par bond comes out above 100, the rates are too low. A higher volatility assumption widens the spread between nodes but the tree must still reprice the same benchmarks.
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