A fixed-income desk quantitative analyst at an investment bank aims to predict future short-term interest rates using the Vasicek model. This model is defined by the following equation:
dr=kโ(eโr)โdt+gโdw
In this context:
- dr represents the change in the short-term interest rate,
- e is the expected long-term average of the short-term interest rate,
- k denotes the speed of mean reversion,
- r is the current short-term interest rate,
- ฯ is the annual volatility of the short-term interest rate, quantified in basis points,
- dt signifies the time period in years, and
- dw is a random variable that follows a normal distribution with zero mean and a standard deviation equal to the square root of dt.
The following data has been gathered for the analysis:
- Current short-term interest rate (r): 3.35%
- Long-term expected short-term interest rate (e): 4.55%
- Mean reversion rate (k): 0.06
- Annual volatility in basis points (ฯ): 120 bps
Using these inputs, the analyst constructs an interest rate tree and projects the anticipated short-term interest rate for the 8th year. Additionally, the analyst calculates the time required for the short-term interest rate to revert halfway to its long-term average. Based on this analysis, what would be an accurate statement for the analyst to make?