The functional form of B ( t, T ) considered in §13.5 does not allow a = 0. This is the case of zero mean reversion. Assuming a constant, flat volatility structure and consequently a zero mean reversion parameter, the equation of the short-term interest rate process becomes:
Consider the relationship of B (0, T ) to the initial interest rate and volatility term structure as shown in (13.2):
Allowing a constant volatility structure implies:
Hence (13.20) reduces to:
To show that this does in fact imply a zero reversion speed parameter, consider equation (7.17) in Chapter 7:
Making use of (13.1) to determine the functional form of A (0, ·) we have:
However, from (13.3)
Hence A (0, T ) = 1 for all T ˆˆ [0, T *].
The calibration of the model now requires the fitting of a single volatility parameter ƒ such that market prices of traded securities are recovered as closely as possible.