13.6 Flat volatility term structure


13.6 Flat volatility term structure

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.




Interest Rate Modelling
Interest Rate Modelling (Finance and Capital Markets Series)
ISBN: 1403934703
EAN: 2147483647
Year: 2004
Pages: 132

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