IAI Actuarial Core Principles · Economic Modelling · Binomial option-pricing model
In a two-period recombining binomial tree for a non-dividend-paying share, the up factor is u and the down factor is d, with d < 1+r < u per period. How many distinct share prices are possible at time 2?
Three distinct prices are possible at time 2. Because the tree recombines, an up move followed by a down move equals a down move followed by an up move, leaving only S*u^2, S*u*d and S*d^2.
- A2
- B3Correct
- C4
- D5
- 6
Explanation
Recombination means an up-then-down move gives the same price as down-then-up (S*u*d). So the time-2 prices are S*u^2, S*u*d and S*d^2, giving three distinct values. Four would be the count for a non-recombining tree.
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