In "The Art of Term Structure Models : Drift" Tuckman mentions regarding term structure of volatility that:
"The term structure of volatility in Model 1 is constant at 113 basis points."
He also mentions that the Model 2 and the Ho-Lee, both do not change the term structure of volatility.
Coming to the Vasicek model, The standard deviation of the terminal distribution of the short rate after T years is derived as sqrt(σ2(1-e^(-2kT))/2k), and with a volatility (σ) of 126 basis points, "the short rate in 10 years is normally distributed with a standard deviation of 353 basis points. "
Q. Figure 9.7 shows the par rate volatility decreasing with increase in maturity and is around 113 bps for 10 years. How is Figure 9.7 derived (par rate volatility) and how is it different from the 353 bps number for the volatility of the short rate in 10 years?
"The term structure of volatility in Model 1 is constant at 113 basis points."
He also mentions that the Model 2 and the Ho-Lee, both do not change the term structure of volatility.
Coming to the Vasicek model, The standard deviation of the terminal distribution of the short rate after T years is derived as sqrt(σ2(1-e^(-2kT))/2k), and with a volatility (σ) of 126 basis points, "the short rate in 10 years is normally distributed with a standard deviation of 353 basis points. "
Q. Figure 9.7 shows the par rate volatility decreasing with increase in maturity and is around 113 bps for 10 years. How is Figure 9.7 derived (par rate volatility) and how is it different from the 353 bps number for the volatility of the short rate in 10 years?
