FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution
In the Ho-Lee model, the short rate follows dr = λ(t)dt + σ dw with σ = 0.90% and a time step of 1 year. In a binomial tree with equal probabilities, the rate at each step moves up by λ·dt + σ√dt or down by λ·dt − σ√dt. The current rate is 3.00%, and λ for the first year is 0.40%. What are the two possible rates after one year?
The two possible rates are 4.30% and 2.50%. Starting from 3.00%, add the drift of 0.40% to get 3.40%, then add or subtract the volatility shock of 0.90% for the up and down moves respectively.
- A4.30% and 2.50%Correct
- B3.40% and 3.00%
- C4.30% and 3.10%
- D3.90% and 2.50%
Explanation
Expected change is 0.40%. Up: 3.00 + 0.40 + 0.90 = 4.30%. Down: 3.00 + 0.40 − 0.90 = 2.50%. Option 4.30%/3.10% errs by not subtracting the shock correctly on the down move.
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