Answer: 23 bps

The volatility component of the change in interest rate from the upper node of month 1 to the upper node of month 2 is calculated by considering the volatility at month 2 only, as the impact of volatility on the rate change between any two dates is the same at any node on the subsequent date. The formula for the volatility component of the rate change is \( \sigma(t) \cdot \sqrt{dt} \), where \( \sigma(t) \) is the volatility at time \( t \) and \( dt \) is the time interval. Given the annualized volatility for month 2 is 0.0080, and the time interval \( dt \) is one month (which is \( \frac{1}{12} \) of a year), the volatility component is calculated as follows: \[ \text{Volatility component} = 0.0080 \cdot \sqrt{\frac{1}{12}} = 0.0080 \cdot \frac{1}{\sqrt{12}} \approx 0.0023 \] This value represents the volatility component in decimal form. To convert this to basis points (bps), we multiply by 10,000 (since 1 bp = 0.01%): \[ 0.0023 \times 10,000 = 23 \text{ bps} \] Therefore, the correct answer is A. 23 bps, which is the volatility component of the change in interest rate from the upper node of month 1 to the upper node of month 2.

Author: LeetQuiz Editorial Team