Answer: equal.

## Explanation Under the assumption of a **lognormal distribution** in binomial interest rate trees, the probabilities for the rate going up or down are typically set to be **equal** (50% each). **Key points about lognormal distribution in binomial trees:** 1. **Equal probabilities**: The up and down movements are assigned equal probabilities of 0.5 each 2. **Lognormal property**: This ensures that interest rates remain positive (they cannot go below zero), which is a realistic assumption for interest rates 3. **Mathematical foundation**: The lognormal distribution implies that the logarithm of interest rates follows a normal distribution, which leads to symmetric probabilities in the binomial tree 4. **Common implementation**: In models like Black-Derman-Toy, the assumption of equal probabilities simplifies the tree construction while maintaining the lognormal property **Alternative**: Some models may use unequal probabilities, but under the specific assumption of lognormal distribution, equal probabilities are the standard approach.

Author: LeetQuiz Editorial Team