Suppose you are modeling the price evolution of a stock on a tree using a general version of the CRR model.The stock price is stochastic (lognormal),but the rate of interest each time step may not be the same,and the time step itself may be different across periods.The following is sufficient for a binomial tree representation of the stock price process to be recombining:
A)The volatility of the stock is constant each period,and the time step and interest rate are different each period.
B)The volatility of the stock is constant each period,the time step on the tree is the same each period,and the interest rate may be different each period.
C)The volatility of the stock is constant,the time step on the tree is the different each period,and the up and down probabilities are equal.
D)The volatility of the stock is different each period,the time step on the tree is the same each period,and the interest rate is the same each period.

Question

Quizplus · Accepted Answer

The tree does not recombine if the time step is varied or if volatility is not the same each period,except for very special cases.But if volatility is constant across the tree with a constant time step,then if the interest rate if different each period,the tree will still recombine.However,the risk-neutral probabilities will no longer be the same across the tree,but the tree will still recombine.

Suppose You Are Modeling the Price Evolution of a Stock